├── Manifest.toml ├── Project.toml ├── README.md ├── benders ├── acceleration │ ├── benders_acceleration.ipynb │ └── benders_acceleration.pdf └── intro │ ├── benders_intro.ipynb │ └── ufl.jl └── callbacks ├── Manifest.toml ├── Project.toml ├── TSP.ipynb ├── TSP.slides.html ├── callbacks_intro.ipynb ├── callbacks_intro.slides.html ├── tsp_iterative_35.gif └── tsp_lazy_35.gif /Manifest.toml: -------------------------------------------------------------------------------- 1 | # This file is machine-generated - editing it directly is not advised 2 | 3 | julia_version = "1.8.1" 4 | manifest_format = "2.0" 5 | project_hash = "fbdd4e61855b05b97f65891521cefab5f2dc6cf5" 6 | 7 | [[deps.ArgCheck]] 8 | git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4" 9 | uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197" 10 | version = "2.3.0" 11 | 12 | [[deps.ArgTools]] 13 | uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" 14 | version = "1.1.1" 15 | 16 | [[deps.Artifacts]] 17 | uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" 18 | 19 | [[deps.Base64]] 20 | uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" 21 | 22 | [[deps.BenchmarkTools]] 23 | deps = ["JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"] 24 | git-tree-sha1 = "d9a9701b899b30332bbcb3e1679c41cce81fb0e8" 25 | uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" 26 | version = "1.3.2" 27 | 28 | [[deps.BitFlags]] 29 | git-tree-sha1 = "43b1a4a8f797c1cddadf60499a8a077d4af2cd2d" 30 | uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35" 31 | version = "0.1.7" 32 | 33 | [[deps.Bzip2_jll]] 34 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 35 | git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2" 36 | uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" 37 | version = "1.0.8+0" 38 | 39 | [[deps.Cairo_jll]] 40 | deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] 41 | git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2" 42 | uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" 43 | version = "1.16.1+1" 44 | 45 | [[deps.ChainRulesCore]] 46 | deps = ["Compat", "LinearAlgebra", "SparseArrays"] 47 | git-tree-sha1 = "e30f2f4e20f7f186dc36529910beaedc60cfa644" 48 | uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" 49 | version = "1.16.0" 50 | 51 | [[deps.ChangesOfVariables]] 52 | deps = ["LinearAlgebra", "Test"] 53 | git-tree-sha1 = "f84967c4497e0e1955f9a582c232b02847c5f589" 54 | uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0" 55 | version = "0.1.7" 56 | 57 | [[deps.CodecBzip2]] 58 | deps = ["Bzip2_jll", "Libdl", "TranscodingStreams"] 59 | git-tree-sha1 = "2e62a725210ce3c3c2e1a3080190e7ca491f18d7" 60 | uuid = "523fee87-0ab8-5b00-afb7-3ecf72e48cfd" 61 | version = "0.7.2" 62 | 63 | [[deps.CodecZlib]] 64 | deps = ["TranscodingStreams", "Zlib_jll"] 65 | git-tree-sha1 = "9c209fb7536406834aa938fb149964b985de6c83" 66 | uuid = "944b1d66-785c-5afd-91f1-9de20f533193" 67 | version = "0.7.1" 68 | 69 | [[deps.ColorSchemes]] 70 | deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"] 71 | git-tree-sha1 = "be6ab11021cd29f0344d5c4357b163af05a48cba" 72 | uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4" 73 | version = "3.21.0" 74 | 75 | [[deps.ColorTypes]] 76 | deps = ["FixedPointNumbers", "Random"] 77 | git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4" 78 | uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" 79 | version = "0.11.4" 80 | 81 | [[deps.ColorVectorSpace]] 82 | deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"] 83 | git-tree-sha1 = "600cc5508d66b78aae350f7accdb58763ac18589" 84 | uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4" 85 | version = "0.9.10" 86 | 87 | [[deps.Colors]] 88 | deps = ["ColorTypes", "FixedPointNumbers", "Reexport"] 89 | git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a" 90 | uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" 91 | version = "0.12.10" 92 | 93 | [[deps.CommonSubexpressions]] 94 | deps = ["MacroTools", "Test"] 95 | git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7" 96 | uuid = "bbf7d656-a473-5ed7-a52c-81e309532950" 97 | version = "0.3.0" 98 | 99 | [[deps.Compat]] 100 | deps = ["Dates", "LinearAlgebra", "UUIDs"] 101 | git-tree-sha1 = "7a60c856b9fa189eb34f5f8a6f6b5529b7942957" 102 | uuid = "34da2185-b29b-5c13-b0c7-acf172513d20" 103 | version = "4.6.1" 104 | 105 | [[deps.CompilerSupportLibraries_jll]] 106 | deps = ["Artifacts", "Libdl"] 107 | uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" 108 | version = "0.5.2+0" 109 | 110 | [[deps.ConcurrentUtilities]] 111 | deps = ["Serialization", "Sockets"] 112 | git-tree-sha1 = "96d823b94ba8d187a6d8f0826e731195a74b90e9" 113 | uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb" 114 | version = "2.2.0" 115 | 116 | [[deps.Contour]] 117 | git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781" 118 | uuid = "d38c429a-6771-53c6-b99e-75d170b6e991" 119 | version = "0.6.2" 120 | 121 | [[deps.Crayons]] 122 | git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15" 123 | uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f" 124 | version = "4.1.1" 125 | 126 | [[deps.DataAPI]] 127 | git-tree-sha1 = "8da84edb865b0b5b0100c0666a9bc9a0b71c553c" 128 | uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" 129 | version = "1.15.0" 130 | 131 | [[deps.DataStructures]] 132 | deps = ["Compat", "InteractiveUtils", "OrderedCollections"] 133 | git-tree-sha1 = "d1fff3a548102f48987a52a2e0d114fa97d730f0" 134 | uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8" 135 | version = "0.18.13" 136 | 137 | [[deps.DataValueInterfaces]] 138 | git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6" 139 | uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464" 140 | version = "1.0.0" 141 | 142 | [[deps.Dates]] 143 | deps = ["Printf"] 144 | uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" 145 | 146 | [[deps.DefaultApplication]] 147 | deps = ["InteractiveUtils"] 148 | git-tree-sha1 = "c0dfa5a35710a193d83f03124356eef3386688fc" 149 | uuid = "3f0dd361-4fe0-5fc6-8523-80b14ec94d85" 150 | version = "1.1.0" 151 | 152 | [[deps.DelimitedFiles]] 153 | deps = ["Mmap"] 154 | uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" 155 | 156 | [[deps.DiffResults]] 157 | deps = ["StaticArraysCore"] 158 | git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621" 159 | uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5" 160 | version = "1.1.0" 161 | 162 | [[deps.DiffRules]] 163 | deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"] 164 | git-tree-sha1 = "a4ad7ef19d2cdc2eff57abbbe68032b1cd0bd8f8" 165 | uuid = "b552c78f-8df3-52c6-915a-8e097449b14b" 166 | version = "1.13.0" 167 | 168 | [[deps.DocStringExtensions]] 169 | deps = ["LibGit2"] 170 | git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d" 171 | uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" 172 | version = "0.9.3" 173 | 174 | [[deps.Downloads]] 175 | deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] 176 | uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" 177 | version = "1.6.0" 178 | 179 | [[deps.Expat_jll]] 180 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 181 | git-tree-sha1 = "bad72f730e9e91c08d9427d5e8db95478a3c323d" 182 | uuid = "2e619515-83b5-522b-bb60-26c02a35a201" 183 | version = "2.4.8+0" 184 | 185 | [[deps.FFMPEG]] 186 | deps = ["FFMPEG_jll"] 187 | git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8" 188 | uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a" 189 | version = "0.4.1" 190 | 191 | [[deps.FFMPEG_jll]] 192 | deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Pkg", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"] 193 | git-tree-sha1 = "74faea50c1d007c85837327f6775bea60b5492dd" 194 | uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5" 195 | version = "4.4.2+2" 196 | 197 | [[deps.FileWatching]] 198 | uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" 199 | 200 | [[deps.FixedPointNumbers]] 201 | deps = ["Statistics"] 202 | git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc" 203 | uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93" 204 | version = "0.8.4" 205 | 206 | [[deps.Fontconfig_jll]] 207 | deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"] 208 | git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03" 209 | uuid = "a3f928ae-7b40-5064-980b-68af3947d34b" 210 | version = "2.13.93+0" 211 | 212 | [[deps.Formatting]] 213 | deps = ["Printf"] 214 | git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8" 215 | uuid = "59287772-0a20-5a39-b81b-1366585eb4c0" 216 | version = "0.4.2" 217 | 218 | [[deps.ForwardDiff]] 219 | deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"] 220 | git-tree-sha1 = "00e252f4d706b3d55a8863432e742bf5717b498d" 221 | uuid = "f6369f11-7733-5829-9624-2563aa707210" 222 | version = "0.10.35" 223 | 224 | [[deps.FreeType2_jll]] 225 | deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 226 | git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9" 227 | uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7" 228 | version = "2.10.4+0" 229 | 230 | [[deps.FriBidi_jll]] 231 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 232 | git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91" 233 | uuid = "559328eb-81f9-559d-9380-de523a88c83c" 234 | version = "1.0.10+0" 235 | 236 | [[deps.GLFW_jll]] 237 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"] 238 | git-tree-sha1 = "d972031d28c8c8d9d7b41a536ad7bb0c2579caca" 239 | uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89" 240 | version = "3.3.8+0" 241 | 242 | [[deps.GR]] 243 | deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"] 244 | git-tree-sha1 = "d014972cd6f5afb1f8cd7adf000b7a966d62c304" 245 | uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71" 246 | version = "0.72.5" 247 | 248 | [[deps.GR_jll]] 249 | deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt5Base_jll", "Zlib_jll", "libpng_jll"] 250 | git-tree-sha1 = "f670f269909a9114df1380cc0fcaa316fff655fb" 251 | uuid = "d2c73de3-f751-5644-a686-071e5b155ba9" 252 | version = "0.72.5+0" 253 | 254 | [[deps.Gettext_jll]] 255 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"] 256 | git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046" 257 | uuid = "78b55507-aeef-58d4-861c-77aaff3498b1" 258 | version = "0.21.0+0" 259 | 260 | [[deps.Glib_jll]] 261 | deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Pkg", "Zlib_jll"] 262 | git-tree-sha1 = "d3b3624125c1474292d0d8ed0f65554ac37ddb23" 263 | uuid = "7746bdde-850d-59dc-9ae8-88ece973131d" 264 | version = "2.74.0+2" 265 | 266 | [[deps.Graphite2_jll]] 267 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 268 | git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011" 269 | uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472" 270 | version = "1.3.14+0" 271 | 272 | [[deps.Grisu]] 273 | git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2" 274 | uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe" 275 | version = "1.0.2" 276 | 277 | [[deps.Gurobi]] 278 | deps = ["LazyArtifacts", "Libdl", "MathOptInterface"] 279 | git-tree-sha1 = "22439b1c2bacb7d50ed0df7dbd10211e0b4cd379" 280 | uuid = "2e9cd046-0924-5485-92f1-d5272153d98b" 281 | version = "1.0.1" 282 | 283 | [[deps.HTTP]] 284 | deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"] 285 | git-tree-sha1 = "ba9eca9f8bdb787c6f3cf52cb4a404c0e349a0d1" 286 | uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3" 287 | version = "1.9.5" 288 | 289 | [[deps.HarfBuzz_jll]] 290 | deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"] 291 | git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3" 292 | uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566" 293 | version = "2.8.1+1" 294 | 295 | [[deps.HiGHS]] 296 | deps = ["HiGHS_jll", "MathOptInterface", "SnoopPrecompile", "SparseArrays"] 297 | git-tree-sha1 = "08535862ef6d42a01ffcaaf6507cfb8a0fe329a6" 298 | uuid = "87dc4568-4c63-4d18-b0c0-bb2238e4078b" 299 | version = "1.5.1" 300 | 301 | [[deps.HiGHS_jll]] 302 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"] 303 | git-tree-sha1 = "53aadc2a53ef3ecc4704549b4791dea67657a4bb" 304 | uuid = "8fd58aa0-07eb-5a78-9b36-339c94fd15ea" 305 | version = "1.5.1+0" 306 | 307 | [[deps.InteractiveUtils]] 308 | deps = ["Markdown"] 309 | uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" 310 | 311 | [[deps.InverseFunctions]] 312 | deps = ["Test"] 313 | git-tree-sha1 = "6667aadd1cdee2c6cd068128b3d226ebc4fb0c67" 314 | uuid = "3587e190-3f89-42d0-90ee-14403ec27112" 315 | version = "0.1.9" 316 | 317 | [[deps.IrrationalConstants]] 318 | git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2" 319 | uuid = "92d709cd-6900-40b7-9082-c6be49f344b6" 320 | version = "0.2.2" 321 | 322 | [[deps.IteratorInterfaceExtensions]] 323 | git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856" 324 | uuid = "82899510-4779-5014-852e-03e436cf321d" 325 | version = "1.0.0" 326 | 327 | [[deps.JLFzf]] 328 | deps = ["Pipe", "REPL", "Random", "fzf_jll"] 329 | git-tree-sha1 = "f377670cda23b6b7c1c0b3893e37451c5c1a2185" 330 | uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c" 331 | version = "0.1.5" 332 | 333 | [[deps.JLLWrappers]] 334 | deps = ["Preferences"] 335 | git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1" 336 | uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" 337 | version = "1.4.1" 338 | 339 | [[deps.JSON]] 340 | deps = ["Dates", "Mmap", "Parsers", "Unicode"] 341 | git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a" 342 | uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" 343 | version = "0.21.4" 344 | 345 | [[deps.JpegTurbo_jll]] 346 | deps = ["Artifacts", "JLLWrappers", "Libdl"] 347 | git-tree-sha1 = "6f2675ef130a300a112286de91973805fcc5ffbc" 348 | uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8" 349 | version = "2.1.91+0" 350 | 351 | [[deps.JuMP]] 352 | deps = ["LinearAlgebra", "MathOptInterface", "MutableArithmetics", "OrderedCollections", "Printf", "SnoopPrecompile", "SparseArrays"] 353 | git-tree-sha1 = "3e4a73edf2ca1bfe97f1fc86eb4364f95ef0fccd" 354 | uuid = "4076af6c-e467-56ae-b986-b466b2749572" 355 | version = "1.11.1" 356 | 357 | [[deps.LAME_jll]] 358 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 359 | git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c" 360 | uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d" 361 | version = "3.100.1+0" 362 | 363 | [[deps.LERC_jll]] 364 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 365 | git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434" 366 | uuid = "88015f11-f218-50d7-93a8-a6af411a945d" 367 | version = "3.0.0+1" 368 | 369 | [[deps.LZO_jll]] 370 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 371 | git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6" 372 | uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac" 373 | version = "2.10.1+0" 374 | 375 | [[deps.LaTeXStrings]] 376 | git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996" 377 | uuid = 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430 | [[deps.Libgpg_error_jll]] 431 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 432 | git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9" 433 | uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8" 434 | version = "1.42.0+0" 435 | 436 | [[deps.Libiconv_jll]] 437 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 438 | git-tree-sha1 = "c7cb1f5d892775ba13767a87c7ada0b980ea0a71" 439 | uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531" 440 | version = "1.16.1+2" 441 | 442 | [[deps.Libmount_jll]] 443 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 444 | git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73" 445 | uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9" 446 | version = "2.35.0+0" 447 | 448 | [[deps.Libtiff_jll]] 449 | deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"] 450 | git-tree-sha1 = "3eb79b0ca5764d4799c06699573fd8f533259713" 451 | uuid = "89763e89-9b03-5906-acba-b20f662cd828" 452 | version = "4.4.0+0" 453 | 454 | [[deps.Libuuid_jll]] 455 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 456 | git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066" 457 | uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700" 458 | version = "2.36.0+0" 459 | 460 | [[deps.LinearAlgebra]] 461 | deps = ["Libdl", "libblastrampoline_jll"] 462 | uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 463 | 464 | [[deps.LogExpFunctions]] 465 | deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"] 466 | git-tree-sha1 = "0a1b7c2863e44523180fdb3146534e265a91870b" 467 | uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688" 468 | version = "0.3.23" 469 | 470 | [[deps.Logging]] 471 | uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" 472 | 473 | [[deps.LoggingExtras]] 474 | deps = ["Dates", "Logging"] 475 | git-tree-sha1 = "cedb76b37bc5a6c702ade66be44f831fa23c681e" 476 | uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36" 477 | version = "1.0.0" 478 | 479 | 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1017 | uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" 1018 | version = "1.5.5+0" 1019 | 1020 | [[deps.fzf_jll]] 1021 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1022 | git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56" 1023 | uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09" 1024 | version = "0.29.0+0" 1025 | 1026 | [[deps.libaom_jll]] 1027 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1028 | git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4" 1029 | uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" 1030 | version = "3.4.0+0" 1031 | 1032 | [[deps.libass_jll]] 1033 | deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 1034 | git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" 1035 | uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" 1036 | version = "0.15.1+0" 1037 | 1038 | [[deps.libblastrampoline_jll]] 1039 | deps = ["Artifacts", "Libdl", "OpenBLAS_jll"] 1040 | uuid = 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-------------------------------------------------------------------------------- /Project.toml: -------------------------------------------------------------------------------- 1 | [deps] 2 | BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" 3 | GR = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71" 4 | Gurobi = "2e9cd046-0924-5485-92f1-d5272153d98b" 5 | HiGHS = "87dc4568-4c63-4d18-b0c0-bb2238e4078b" 6 | JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" 7 | JuMP = "4076af6c-e467-56ae-b986-b466b2749572" 8 | LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 9 | PGFPlotsX = "8314cec4-20b6-5062-9cdb-752b83310925" 10 | Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" 11 | Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" 12 | UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228" 13 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # OR tutorials 2 | 3 | A collection of tutorials on some OR techniques. Material includes slides, notebooks and code fragments. 4 | 5 | Author: Mathieu Tanneau 6 | ## License 7 | The contents of this repository are released under the following terms: 8 | * the _code_ is released under the [MIT license](https://mit-license.org/) 9 | * the _text_ and the _slides_ are released under the [CC BY-SA 4.0 license](https://creativecommons.org/licenses/by-sa/4.0/) 10 | 11 | ## Installation 12 | 13 | Most of the code is written in julia. See https://julialang.org/ to download and install julia. 14 | 15 | ## Tutorials 16 | 17 | Navigate the repository to see the various tutorials 18 | 19 | * Benders decomposition 20 | * Introduction to Benders 21 | * Acceleration techniques 22 | * Callbacks 23 | -------------------------------------------------------------------------------- /benders/acceleration/benders_acceleration.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "attachments": {}, 5 | "cell_type": "markdown", 6 | "id": "1eb8dc7e", 7 | "metadata": {}, 8 | "source": [ 9 | "# Accelerating Benders Decomposition\n", 10 | "\n", 11 | "Author: Mathieu Tanneau, \n", 12 | "\n", 13 | "This notebook illustrates various acceleration techniques for Benders decomposition,\n", 14 | " on artificial instances of the uncapacitated facility location problem.\n", 15 | "\n", 16 | "The notebook is released under the following terms:\n", 17 | "* the _code_ is released under the [MIT license](https://mit-license.org/)\n", 18 | "* the _text_ is released under the [CC BY-SA 4.0 license](https://creativecommons.org/licenses/by-sa/4.0/)\n", 19 | "\n", 20 | "### Julia & compilation\n", 21 | "\n", 22 | "Julia code is compiled the first time it is executed.\n", 23 | "Thus, it is recommended to always execute code twice, to ensure the reported time does not include any compilation.\n", 24 | "\n", 25 | "For further details, see the [Julia documentation](https://docs.julialang.org/en/v1/) and its [Performance tips section](https://docs.julialang.org/en/v1/manual/performance-tips/)." 26 | ] 27 | }, 28 | { 29 | "cell_type": "code", 30 | "execution_count": 1, 31 | "id": "2fdc472c", 32 | "metadata": {}, 33 | "outputs": [ 34 | { 35 | "name": "stderr", 36 | "output_type": "stream", 37 | "text": [ 38 | "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m new project at `~/Git/or_tutorials/benders`\n" 39 | ] 40 | }, 41 | { 42 | "name": "stderr", 43 | "output_type": "stream", 44 | "text": [ 45 | "\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Git/or_tutorials/benders/Project.toml`\n", 46 | "\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Git/or_tutorials/benders/Manifest.toml`\n" 47 | ] 48 | } 49 | ], 50 | "source": [ 51 | "# Activate the Julia environment defined in the Project.toml file\n", 52 | "using Pkg\n", 53 | "Pkg.activate(joinpath(@__DIR__, \"..\", \"..\"))\n", 54 | "\n", 55 | "# The following line ensures that all packages are installed\n", 56 | "# You can comment it out if you've already run this notebook at least once.\n", 57 | "Pkg.instantiate() " 58 | ] 59 | }, 60 | { 61 | "cell_type": "code", 62 | "execution_count": 2, 63 | "id": "66c4803f", 64 | "metadata": {}, 65 | "outputs": [ 66 | { 67 | "name": "stdout", 68 | "output_type": "stream", 69 | "text": [ 70 | "Academic license - for non-commercial use only - expires 2022-07-04\n" 71 | ] 72 | } 73 | ], 74 | "source": [ 75 | "# Load standard library packages\n", 76 | "using BenchmarkTools\n", 77 | "using LinearAlgebra\n", 78 | "using Printf\n", 79 | "using Random\n", 80 | "\n", 81 | "using Plots\n", 82 | "\n", 83 | "# JuMP is a modeling language embedded in Julia\n", 84 | "# For more details: https://jump.dev/\n", 85 | "using JuMP\n", 86 | "\n", 87 | "# Gurobi (https://gurobi.com) is a commercial solver; you need to download it manually.\n", 88 | "# Then, follow installation instructions at https://github.com/jump-dev/Gurobi.jl#installation\n", 89 | "using Gurobi\n", 90 | "# To avoid checking out multiple Gurobi licenses, we define a global Gurobi environment,\n", 91 | "# which will be re-used throughout the code.\n", 92 | "if !isdefined(Main, :GRBENV) # Avoid re-defining a const\n", 93 | " const GRBENV = Gurobi.Env()\n", 94 | "end\n", 95 | "\n", 96 | "# HiGHS (https://github.com/ERGO-Code/HiGHS) is an open-source solver.\n", 97 | "# Julia's package manager will automatically download and install HiGHS.\n", 98 | "using HiGHS" 99 | ] 100 | }, 101 | { 102 | "attachments": {}, 103 | "cell_type": "markdown", 104 | "id": "4d182b59", 105 | "metadata": {}, 106 | "source": [ 107 | "# Uncapacitated Facility Location\n", 108 | "\n", 109 | "This problem is a classical example for applying Benders decomposition." 110 | ] 111 | }, 112 | { 113 | "attachments": {}, 114 | "cell_type": "markdown", 115 | "id": "90e32c2e", 116 | "metadata": {}, 117 | "source": [ 118 | "## Problem data\n", 119 | "\n", 120 | "The problem data is composed of\n", 121 | "* $m$ sites where facilities may be built\n", 122 | "* $n$ customers to be served\n", 123 | "* the location of each customer and potential site" 124 | ] 125 | }, 126 | { 127 | "cell_type": "code", 128 | "execution_count": 3, 129 | "id": "a59bfa9e", 130 | "metadata": {}, 131 | "outputs": [], 132 | "source": [ 133 | "m = 8 # Number of sites\n", 134 | "n = 32 # Number of customers\n", 135 | "\n", 136 | "# To ensure reproducibility, always use a seed!\n", 137 | "Random.seed!(1804)\n", 138 | "\n", 139 | "# Generate coordinates for customers and sites\n", 140 | "# To introduce some symmetries, all coordinates lay on a grid\n", 141 | "grid_param = 50\n", 142 | "\n", 143 | "Xc = rand(0:grid_param, n, 2) ./ grid_param # Customer coordinates\n", 144 | "Xf = rand(-1:21, m, 2) ./ 20 # Facility coordinates\n", 145 | ";" 146 | ] 147 | }, 148 | { 149 | "cell_type": "code", 150 | "execution_count": 4, 151 | "id": "01975c0f", 152 | "metadata": {}, 153 | "outputs": [ 154 | { 155 | "data": { 156 | "image/svg+xml": [ 157 | "\n", 158 | "\n", 159 | "\n", 160 | " \n", 161 | " \n", 162 | " \n", 163 | "\n", 164 | "\n", 167 | "\n", 168 | " \n", 169 | " \n", 170 | " \n", 171 | "\n", 172 | "\n", 175 | "\n", 176 | " \n", 177 | " \n", 178 | " \n", 179 | "\n", 180 | "\n", 183 | "\n", 186 | "\n", 189 | "\n", 192 | "\n", 195 | "\n", 198 | "\n", 201 | "\n", 204 | "\n", 207 | "\n", 210 | "\n", 213 | "\n", 216 | "\n", 219 | "\n", 222 | "\n", 225 | "\n", 228 | "\n", 231 | "\n", 234 | "\n", 237 | "\n", 240 | "\n", 243 | "\n", 246 | "\n", 249 | "\n", 252 | "\n", 255 | "\n", 258 | "\n", 261 | "\n", 264 | "\n", 267 | "\n", 270 | "\n", 273 | "\n", 276 | "\n", 277 | "\n", 278 | "\n", 279 | "\n", 280 | "\n", 281 | "\n", 282 | "\n", 283 | "\n", 284 | "\n", 285 | "\n", 286 | "\n", 287 | "\n", 288 | "\n", 289 | "\n", 290 | "\n", 291 | "\n", 292 | "\n", 293 | "\n", 294 | "\n", 295 | "\n", 296 | "\n", 297 | "\n", 298 | "\n", 299 | "\n", 300 | "\n", 301 | "\n", 302 | "\n", 303 | "\n", 304 | "\n", 305 | "\n", 306 | "\n", 307 | "\n", 308 | "\n", 309 | "\n", 310 | "\n", 311 | "\n", 312 | "\n", 313 | "\n", 314 | "\n", 315 | "\n", 316 | "\n", 319 | "\n", 322 | "\n", 323 | "\n", 324 | "\n" 325 | ] 326 | }, 327 | "execution_count": 4, 328 | "metadata": {}, 329 | "output_type": "execute_result" 330 | } 331 | ], 332 | "source": [ 333 | "# Since we have coordinates, we can visualize what the instance looks like\n", 334 | "plt = plot(\n", 335 | " legend=:topleft,\n", 336 | " xlim=(-0.25, 1.25),\n", 337 | " ylim=(-0.25, 1.5),\n", 338 | ")\n", 339 | "\n", 340 | "scatter!(plt, Xf[:, 1], Xf[:, 2], label=\"Locations\", marker=:rect, ms=8, opacity=0.5)\n", 341 | "scatter!(plt, Xc[:, 1], Xc[:, 2], label=\"Customers\", marker=:circ, ms=5)" 342 | ] 343 | }, 344 | { 345 | "attachments": {}, 346 | "cell_type": "markdown", 347 | "id": "7b6b741a", 348 | "metadata": {}, 349 | "source": [ 350 | "## Mathematical formulation" 351 | ] 352 | }, 353 | { 354 | "attachments": {}, 355 | "cell_type": "markdown", 356 | "id": "7a9fd7aa", 357 | "metadata": {}, 358 | "source": [ 359 | "### Decision variables\n", 360 | "\n", 361 | "\\begin{align*}\n", 362 | " y_{i} &= \n", 363 | " \\left\\{\n", 364 | " \\begin{array}{cl}\n", 365 | " 1 & \\quad \\text{if a facility is built at location $i$},\\\\\n", 366 | " 0 & \\quad \\text{otherwise}\n", 367 | " \\end{array}\n", 368 | " \\right.\n", 369 | " && \\forall i \\in \\{1, ..., m \\},\\\\\n", 370 | " \\ \\\\\n", 371 | " x_{i, j} &= \n", 372 | " \\left\\{\n", 373 | " \\begin{array}{cl}\n", 374 | " 1 & \\quad \\text{if customer $j$ is served by facility $i$},\\\\\n", 375 | " 0 & \\quad \\text{otherwise}\n", 376 | " \\end{array}\n", 377 | " \\right.\n", 378 | " &&\\forall (i, j) \\in \\{1, ..., m \\} \\times \\{1, ..., n\\}\n", 379 | "\\end{align*}" 380 | ] 381 | }, 382 | { 383 | "attachments": {}, 384 | "cell_type": "markdown", 385 | "id": "215ef740", 386 | "metadata": {}, 387 | "source": [ 388 | "### Constraints\n", 389 | "\n", 390 | "* Each customer must be served by exactly one facility:\n", 391 | "\\begin{align*}\n", 392 | " \\sum_{i} x_{i, j} & = 1, && \\forall j = \\{1, ..., n\\}.\n", 393 | "\\end{align*}\n", 394 | "* A facility can only serve a customer if it has been built:\n", 395 | "\\begin{align*}\n", 396 | " x_{i, j} & \\leq y_{i}, && \\forall (i,j) \\in \\{1, ..., m\\} \\times \\{1, ..., n\\}.\n", 397 | "\\end{align*}\n", 398 | "* All variables are binary\n", 399 | "\\begin{align*}\n", 400 | " y & \\in \\{0, 1\\}^{m},\\\\\n", 401 | " x & \\in \\{0, 1\\}^{m \\times n}.\n", 402 | "\\end{align*}" 403 | ] 404 | }, 405 | { 406 | "attachments": {}, 407 | "cell_type": "markdown", 408 | "id": "c548661a", 409 | "metadata": {}, 410 | "source": [ 411 | "### Objective \n", 412 | "\n", 413 | "The objective (to be minimized) reads\n", 414 | "\\begin{align*}\n", 415 | " f^{T}y + \\sum_{i, j} D_{i, j} x_{i, j},\n", 416 | "\\end{align*}\n", 417 | "where\n", 418 | "* $f_{i}$ is the cost of building a facility at location $i$,\n", 419 | "* $D_{i, j}$ is the distance between location $i$ and customer $j$." 420 | ] 421 | }, 422 | { 423 | "cell_type": "code", 424 | "execution_count": 5, 425 | "id": "e1c177cd", 426 | "metadata": {}, 427 | "outputs": [], 428 | "source": [ 429 | "# Sample fixed building costs\n", 430 | "f = rand(10:20, m)\n", 431 | "\n", 432 | "# Compute distance matrix\n", 433 | "D = zeros(Float64, m, n)\n", 434 | "for j in 1:n, i in 1:m\n", 435 | " D[i, j] = norm(Xf[i, :] - Xc[j, :], 2)\n", 436 | "end\n", 437 | "# Increase the distances to make the problem a little harder\n", 438 | "D .*= 10\n", 439 | ";" 440 | ] 441 | }, 442 | { 443 | "attachments": {}, 444 | "cell_type": "markdown", 445 | "id": "70f5a0d3", 446 | "metadata": {}, 447 | "source": [ 448 | "# MIP formulation\n", 449 | "\n", 450 | "The overall problem reads\n", 451 | "\n", 452 | "\\begin{align}\n", 453 | " \\min_{x, y} \\quad\n", 454 | " & \\sum_{i} f_{i} y_{i} + \\sum_{i, j} D_{i, j} x_{i, j}\\\\\n", 455 | " \\text{s.t.} \\quad\n", 456 | " & \\sum_{i} x_{i, j} = 1, && \\forall j,\\\\\n", 457 | " & x_{i, j} \\leq y_{i}, && \\forall (i, j),\\\\\n", 458 | " & y \\in \\{0, 1\\}^{m},\\\\\n", 459 | " & x \\in \\{0, 1\\}^{m \\times n}.\n", 460 | "\\end{align}\n", 461 | "\n", 462 | "Small instances can be solved efficiently with off-the-shelf MIP solvers." 463 | ] 464 | }, 465 | { 466 | "cell_type": "code", 467 | "execution_count": null, 468 | "id": "321e0048", 469 | "metadata": {}, 470 | "outputs": [], 471 | "source": [ 472 | "mip = Model() # You can defined a JuMP model without a solver...\n", 473 | "\n", 474 | "# Decision variables\n", 475 | "@variable(mip, y[1:m], Bin)\n", 476 | "@variable(mip, x[1:m, 1:n], Bin)\n", 477 | "\n", 478 | "# Constraints\n", 479 | "@constraint(mip, customer_served[j in 1:n], sum(x[:, j]) == 1)\n", 480 | "@constraint(mip, facility_open[i in 1:m, j in 1:n], x[i, j] <= y[i])\n", 481 | "\n", 482 | "# Objective function\n", 483 | "@objective(mip, Min, dot(f, y) + dot(D, x))\n", 484 | "\n", 485 | "# ... and attach a MIP solver afterwards\n", 486 | "# Un-comment the line you want, to choose the corresponding MIP solver\n", 487 | "set_optimizer(mip, Gurobi.Optimizer) # Gurobi is much faster on large instances\n", 488 | "# set_optimizer(mip, HiGHS.Optimizer)\n", 489 | "\n", 490 | "optimize!(mip)\n", 491 | "\n", 492 | "sname = solver_name(mip)\n", 493 | "stime = solve_time(mip)\n", 494 | "\n", 495 | "println(\"$(sname) solved the problem in $(stime) seconds.\")" 496 | ] 497 | }, 498 | { 499 | "cell_type": "code", 500 | "execution_count": null, 501 | "id": "57509565", 502 | "metadata": {}, 503 | "outputs": [], 504 | "source": [ 505 | "# Get the optimal solution value...\n", 506 | "y_ = Bool.(round.(value.(mip[:y])))\n", 507 | "x_ = Bool.(round.(value.(mip[:x])))\n", 508 | "\n", 509 | "println(\"There are $(sum(y_)) facilities open.\")\n", 510 | "\n", 511 | "# ... and plot it\n", 512 | "plt = plot(\n", 513 | " title=\"$(sname) solution\",\n", 514 | " legend=:bottomleft,\n", 515 | " ylim=(-0.25, 1.25),\n", 516 | ")\n", 517 | "\n", 518 | "# Show which customer is served by which facility\n", 519 | "for i in 1:m\n", 520 | " for j in 1:n\n", 521 | " if x_[i, j]\n", 522 | " # Plot a line between yi and xj\n", 523 | " plot!(plt, [Xc[j, 1], Xf[i, 1]], [Xc[j, 2], Xf[i, 2]], label=nothing, lw=0.5, color=:black)\n", 524 | " end\n", 525 | " end\n", 526 | "end\n", 527 | "\n", 528 | "# Customers\n", 529 | "scatter!(plt, Xc[:, 1], Xc[:, 2], label=\"Customers\", marker=:circ, ms=4, color=:red)\n", 530 | "\n", 531 | "# Facilities (open and closed)\n", 532 | "scatter!(plt, [Xf[.! y_, 1]], [Xf[.!y_, 2]],\n", 533 | " color=:lightblue,\n", 534 | " label=\"Facilities (closed)\",\n", 535 | " marker=:rect,\n", 536 | " ms=6\n", 537 | ")\n", 538 | "scatter!(plt, [Xf[y_, 1]], [Xf[y_, 2]],\n", 539 | " color=:darkblue,\n", 540 | " label=\"Facilities (open)\",\n", 541 | " marker=:rect,\n", 542 | " ms=6\n", 543 | ")\n", 544 | "\n", 545 | "\n", 546 | "plt" 547 | ] 548 | }, 549 | { 550 | "attachments": {}, 551 | "cell_type": "markdown", 552 | "id": "b49fd5a6", 553 | "metadata": {}, 554 | "source": [ 555 | "# Benders Decomposition\n", 556 | "\n", 557 | "The Benders decomposition-based formulation keeps the $y$ variables in the master problem,\n", 558 | "and the $x$ variables in the sub-problem." 559 | ] 560 | }, 561 | { 562 | "attachments": {}, 563 | "cell_type": "markdown", 564 | "id": "abdc440e", 565 | "metadata": {}, 566 | "source": [ 567 | "## Benders sub-problem\n", 568 | "\n", 569 | "For fixed $y$, the sub-problem consists in assigning each customer to an open facility,\n", 570 | "so as to minimize the sum of distances between customers and facilities.\n", 571 | "\n", 572 | "Two important observations are in order:\n", 573 | "1. The sub-problem is separable per customer, i.e., we can consider $n$ sub-problems: one for each customer $j$.\n", 574 | "2. If $y$ is integer, then the integrality condition on $x$ can be dropped.\n", 575 | " Thus, the sub-problem is always a (continuous) linear program.\n", 576 | "\n", 577 | "### Mathematical formulation\n", 578 | "\n", 579 | "The Benders sub-problem for customer $j$ and current master solution $\\bar{y}$ reads\n", 580 | "\n", 581 | "\\begin{align}\n", 582 | " SP_{j}(\\bar{y}) \\quad \\min_{x} \\quad & \\sum_{i} d_{i, j} x_{j}\\\\\n", 583 | " s.t. \\quad\n", 584 | " & \\sum_{i} x_{i, j} = 1 &&[\\mu]\\\\\n", 585 | " & \\forall i, \\ x_{i, j} \\leq \\bar{y}_{i} && [\\lambda_{i}]\\\\\n", 586 | " & \\forall i, \\ 0 \\leq x_{i, j} \\leq 1\n", 587 | "\\end{align}\n", 588 | "\n", 589 | "Given the sub-problem's optimal objective value $\\phi_{j}(\\bar{y})$ and dual solution $\\lambda$,\n", 590 | "the Benders cut has the form\n", 591 | "$$\n", 592 | " \\phi_{j}(y) \\geq \\phi_{j}(\\bar{y}) + \\lambda^{T}(y - \\bar{y})\n", 593 | "$$" 594 | ] 595 | }, 596 | { 597 | "attachments": {}, 598 | "cell_type": "markdown", 599 | "id": "4d7538b5", 600 | "metadata": {}, 601 | "source": [] 602 | }, 603 | { 604 | "cell_type": "code", 605 | "execution_count": null, 606 | "id": "ef83de89", 607 | "metadata": {}, 608 | "outputs": [], 609 | "source": [ 610 | "\"\"\"\n", 611 | " solve_benders_sp(d::AbstractVector, y; kwargs...)\n", 612 | "\n", 613 | "Solve the Benders sub-problem for customer ``j``.\n", 614 | "\n", 615 | "# Arguments\n", 616 | "* `d::AbstractVector`: the vector of distances between the customer and all locations.\n", 617 | "* `y::AbstractVector`: the current master solution. May be integer or fractional.\n", 618 | "\n", 619 | "# Returns\n", 620 | "* `z::Float`: the optimal objective value of the sub-problem\n", 621 | "* `λ::Vector{Float64}`: the sub-problem dual solution, used to form the Benders cut\n", 622 | "* `x::Vector{Float64}`: the sub-problem primal solution, for information\n", 623 | "\"\"\"\n", 624 | "function solve_benders_sp(d::AbstractVector, y; kwargs...)\n", 625 | " m = length(d)\n", 626 | " \n", 627 | " sp = direct_model(Gurobi.Optimizer(GRBENV))\n", 628 | " \n", 629 | " @variable(sp, x[1:m] >= 0) # we don't need the upper bound, because it's implied by sum(x) == 1\n", 630 | " @variable(sp, q[1:m])\n", 631 | " \n", 632 | " @constraint(sp, sum(x) == 1)\n", 633 | " @constraint(sp, benders, q .== y) # Kevin's trick to make your life easier\n", 634 | " @constraint(sp, x .<= q)\n", 635 | " \n", 636 | " @objective(sp, Min, dot(d, x))\n", 637 | " \n", 638 | " set_silent(sp)\n", 639 | " for (k, v) in kwargs\n", 640 | " set_optimizer_attribute(sp, string(k), v)\n", 641 | " end\n", 642 | " \n", 643 | " optimize!(sp)\n", 644 | " z = objective_value(sp)\n", 645 | " λ = dual.(benders)\n", 646 | " x_ = value.(x)\n", 647 | " \n", 648 | " return z, λ, x_\n", 649 | "end" 650 | ] 651 | }, 652 | { 653 | "cell_type": "code", 654 | "execution_count": null, 655 | "id": "cec6c853", 656 | "metadata": {}, 657 | "outputs": [], 658 | "source": [ 659 | "?solve_benders_sp # show the function's documentation" 660 | ] 661 | }, 662 | { 663 | "attachments": {}, 664 | "cell_type": "markdown", 665 | "id": "7c953ef4", 666 | "metadata": {}, 667 | "source": [ 668 | "### Closed-form solution\n", 669 | "\n", 670 | "The sub-problem for customer $j$ has a closed-form solution, which can be computed efficiently.\n", 671 | "\n", 672 | "The mathematical correctness of the code below is left as an exercise." 673 | ] 674 | }, 675 | { 676 | "cell_type": "code", 677 | "execution_count": null, 678 | "id": "772f2af6", 679 | "metadata": {}, 680 | "outputs": [], 681 | "source": [ 682 | "function solve_benders_sp_fast(d::AbstractVector, y; kwargs...)\n", 683 | " m = length(d)\n", 684 | " \n", 685 | " # Find the closest facilities...\n", 686 | " p = sortperm(d)\n", 687 | " # ... then greedily allocate until we hit 1.0\n", 688 | " w = 1.0 # we record w == 1 - sum(x)\n", 689 | " x_ = zeros(Float64, m)\n", 690 | " d_ = Inf # Distance to the furthest facility that serves this customer\n", 691 | " z_ = 0.0 # Objective value\n", 692 | " for i in p\n", 693 | " x_[i] += min(y[i], w)\n", 694 | " z_ += x_[i] * d[i]\n", 695 | " w -= x_[i]\n", 696 | " d_ = y[i] > 0 ? d[i] : d_\n", 697 | " w <= 0 && break\n", 698 | " end\n", 699 | " \n", 700 | " # Now we build the dual solution\n", 701 | " λ = zeros(m)\n", 702 | " for i in 1:m\n", 703 | " λ[i] = (d[i] < d_) * (d[i] - d_)\n", 704 | " end\n", 705 | " \n", 706 | " return z_, λ, x_\n", 707 | "end" 708 | ] 709 | }, 710 | { 711 | "attachments": {}, 712 | "cell_type": "markdown", 713 | "id": "b0b4b8a0", 714 | "metadata": {}, 715 | "source": [ 716 | "\\begin{align}\n", 717 | " SD_{j} \\quad \\max_{\\mu, \\lambda} \\quad & \\mu + \\sum_{i} y_{i} \\lambda_{i}\\\\\n", 718 | " s.t. \\quad\n", 719 | " & \\mu + \\lambda_{i} \\leq d_{i, j}\\\\\n", 720 | " & \\lambda_{i} \\leq 0\n", 721 | "\\end{align}\n", 722 | "\n", 723 | "\\begin{align}\n", 724 | " SD_{j} \\quad \\max_{\\mu, \\lambda} \\quad & \\mu - \\sum_{i} y_{i} \\lambda_{i}\\\\\n", 725 | " s.t. \\quad\n", 726 | " & \\mu \\leq d_{i, j} + \\lambda_{i}\\\\\n", 727 | " & \\lambda_{i} \\geq 0\n", 728 | "\\end{align}" 729 | ] 730 | }, 731 | { 732 | "attachments": {}, 733 | "cell_type": "markdown", 734 | "id": "d28395e6", 735 | "metadata": {}, 736 | "source": [ 737 | "The following set of benchmarks show that the closed-form is about 1000x faster than using Gurobi." 738 | ] 739 | }, 740 | { 741 | "cell_type": "code", 742 | "execution_count": null, 743 | "id": "3efdde2b", 744 | "metadata": {}, 745 | "outputs": [], 746 | "source": [ 747 | "Random.seed!(0)\n", 748 | "y_ = rand(Bool, m)\n", 749 | "@benchmark solve_benders_sp($(D[:, 1]), $(y_))" 750 | ] 751 | }, 752 | { 753 | "cell_type": "code", 754 | "execution_count": null, 755 | "id": "579724ab", 756 | "metadata": {}, 757 | "outputs": [], 758 | "source": [ 759 | "Random.seed!(0)\n", 760 | "y_ = rand(Bool, m)\n", 761 | "@benchmark solve_benders_sp_fast($(D[:, 1]), $(y_))" 762 | ] 763 | }, 764 | { 765 | "attachments": {}, 766 | "cell_type": "markdown", 767 | "id": "f9547f2a", 768 | "metadata": {}, 769 | "source": [ 770 | "## Master problem\n", 771 | "\n", 772 | "The initial master problem reads\n", 773 | "\n", 774 | "\\begin{align}\n", 775 | " \\min_{y, \\theta} \\quad & f^{T}y + \\sum_{j} \\theta_{j}\\\\\n", 776 | " s.t. \\quad\n", 777 | " & \\sum_{i} y_{i} \\geq 1\\\\\n", 778 | " & y \\in \\{0, 1\\}^{n}\\\\\n", 779 | " & \\theta_{j} \\geq 0 & \\forall j\n", 780 | "\\end{align}\n", 781 | "\n", 782 | "Notes:\n", 783 | "* the constraint $\\sum_{i} y_{i} \\geq 1$ is not necessary, but ensures the subproblems are always feasible.\n", 784 | "* Whether we consider a multi-cut, single-cut, or aggregated cut variant, there $\\theta$ variables have at most $n$ coordinates.\n", 785 | " Thus, for simplicity, we always create $n$ of them." 786 | ] 787 | }, 788 | { 789 | "cell_type": "code", 790 | "execution_count": null, 791 | "id": "e9cdbce4", 792 | "metadata": {}, 793 | "outputs": [], 794 | "source": [ 795 | "function generate_mp()\n", 796 | " mp = direct_model(Gurobi.Optimizer(GRBENV))\n", 797 | "\n", 798 | " @variable(mp, y[1:m], Bin)\n", 799 | " @variable(mp, θ[1:n] >= 0)\n", 800 | "\n", 801 | " @constraint(mp, sum(y) >= 1)\n", 802 | "\n", 803 | " @objective(mp, Min, dot(f, y) + sum(θ))\n", 804 | "\n", 805 | " # Set a few additional parameters\n", 806 | " set_optimizer_attribute(mp, \"Threads\", 1) # Only use one thread\n", 807 | "\n", 808 | " return mp\n", 809 | "end" 810 | ] 811 | }, 812 | { 813 | "attachments": {}, 814 | "cell_type": "markdown", 815 | "id": "bcacdd4d", 816 | "metadata": {}, 817 | "source": [ 818 | "## Benders decomposition loop\n", 819 | "\n", 820 | "The function `solve_benders` below solves the uncapacitated facility location problem using Benders decomposition.\n", 821 | "Its sole argument is the master problem `mp`.\n", 822 | "Other key-word arguments are described below.\n", 823 | "\n", 824 | "The algorithm's overall behavior is controlled by\n", 825 | "* `niter_max`: the maximum number of BD iterations\n", 826 | "* `seed`: A random seed, for reproducibility\n", 827 | "* `verbose`: If zero, no log is produced.\n", 828 | " If `>0`, then a log is produced every `verbose` iterations, or whenever the upper bound is improved\n", 829 | "* `ϵ_gap`: the MIP gap tolerance for convergence\n", 830 | "* `time_limit`: the time limit, in seconds. Will be checked at the _end_ of each iteration\n", 831 | "\n", 832 | "### Closed-form solution for the sub-problem\n", 833 | "\n", 834 | "Set the parameter `fast_sp` to `true` to use the fast separation oracle.\n", 835 | "Unless you want to study Pareto-optimal cuts (see below), this parameter should always be set to `true`.\n", 836 | "\n", 837 | "### Pareto-optimal cuts\n", 838 | "\n", 839 | "For the facility location problem, it is very unlikely **not** to get Pareto-optimal cuts (this is because the sub-problem has little degeneracy).\n", 840 | "In particular, the fast separation will almost always produce a Pareto-optimal cut.\n", 841 | "\n", 842 | "To study the benefits of Pareto-optimal cuts, first set `fast_sp` to `false`, then set `pareto_freq` to a value between `0.0` and `1.0`.\n", 843 | "This number is the frequency at which Pareto cuts will be separated: `0.0` means never and `1.0` means always.\n", 844 | "\n", 845 | "To force the separation of non-Pareto cuts, the code will solve the sub-problem with the barrier method and no crossover: this is guaranteed to yield very weak cuts.\n", 846 | "\n", 847 | "### Benders at the root\n", 848 | "\n", 849 | "Setting the parameter `root_benders` to `true` will perform Benders decomposition at the root.\n", 850 | "The stopping criterion for the root is determined by `ϵ_root`: integrality constraints are re-instated when the relative improvement in the lower bound is less than `ϵ_root`.\n", 851 | "\n", 852 | "### Cut aggregation\n", 853 | "\n", 854 | "Sub-problems can be aggregated in arbitrary clusters; the only rule is that clusters should form a partition of the $n$ sub-problems.\n", 855 | "\n", 856 | "An example is provided later in the notebook.\n", 857 | "\n", 858 | "### Partial cutting\n", 859 | "\n", 860 | "When the number of sub-problems/clusters is large, it can be beneficial to generate only a few cuts at each iterations.\n", 861 | "This keeps the size of the master problem under control.\n", 862 | "\n", 863 | "Setting `partial_cut` to a positive integer value `p`, ensures that no more than `p` cuts will be generated at each iteration.\n", 864 | "\n", 865 | "\n", 866 | "### Reading the logs\n", 867 | "\n", 868 | "The logs look something like\n", 869 | "```\n", 870 | "Solving Benders with 32 sub-problems and 32 clusters\n", 871 | "Iter Primal bound Dual bound Gap(%) #cuts T-MP T-SP T-Jump T(s)\n", 872 | " 0* +2.666480e+02 +1.000000e+01 96.25% 32 0.00 0.00 0.00 0.00\n", 873 | " 1* +1.454178e+02 +5.883625e+01 59.54% 64 0.01 0.00 0.00 0.01\n", 874 | " 2* +1.337201e+02 +1.335820e+02 0.10% 65 0.04 0.00 0.00 0.04\n", 875 | " 3* +1.337201e+02 +1.337201e+02 0.00% 65 0.06 0.00 0.00 0.06\n", 876 | "Found optimal solution within tolerances\n", 877 | "```\n", 878 | "The first line indicates the number of sub-problems and clusters.\n", 879 | "\n", 880 | "When `root_benders` is set to `true`, the following line will be printed:\n", 881 | "```\n", 882 | "Relaxing integer variables\n", 883 | "```\n", 884 | "and later\n", 885 | "```\n", 886 | "Re-instating integer variables\n", 887 | "```\n", 888 | "when integer variables are re-instated.\n", 889 | "\n", 890 | "The columns are as follows:\n", 891 | "* `Iter` is the number of BD iterations\n", 892 | "* `Primal bound` is the current best primal (upper) bound\n", 893 | "* `Dual bound` is the current best dual (lower) bound\n", 894 | "* `Gap` is the current optimality gap\n", 895 | "* `#cuts` is the current number of cuts in the master problem\n", 896 | "* Computing time is measured as follows\n", 897 | " * `T-MP` is the total time spent solving the master problem\n", 898 | " * `T-SP` is the total time spent solving the sub-problems\n", 899 | " * `T-JuMP` is the total time spent by JuMP to add constraints to the master problem\n", 900 | " * `T(s)` is the total elapsed time thus far" 901 | ] 902 | }, 903 | { 904 | "cell_type": "code", 905 | "execution_count": null, 906 | "id": "7f103f19", 907 | "metadata": {}, 908 | "outputs": [], 909 | "source": [ 910 | "function solve_benders(mp;\n", 911 | " niter_max::Int=250,\n", 912 | " seed::Int=0,\n", 913 | " verbose::Int=1,\n", 914 | " ϵ_gap::Float64=1e-4,\n", 915 | " time_limit::Real=180,\n", 916 | " fast_sp::Bool=false,\n", 917 | " pareto_freq::Float64=1.0,\n", 918 | " root_benders::Bool=false,\n", 919 | " ϵ_root::Real=1e-3,\n", 920 | " sp_clusters::Vector{Vector{Int}}=[[j] for j in 1:n],\n", 921 | " partial_cut::Int=(length(sp_clusters)+1),\n", 922 | ")\n", 923 | " # Set the random seed\n", 924 | " Random.seed!(seed)\n", 925 | " \n", 926 | " # Count number of clusters\n", 927 | " n_clusters = length(sp_clusters)\n", 928 | " verbose > 0 && println(\"Solving Benders with $(n) sub-problems and $(n_clusters) clusters\")\n", 929 | " \n", 930 | " is_mp_integer = true\n", 931 | " if root_benders\n", 932 | " verbose > 0 && println(\"Relaxing integer variables\")\n", 933 | " undo_relax = relax_integrality(mp)\n", 934 | " is_mp_integer = false\n", 935 | " end\n", 936 | " \n", 937 | " # Extract a few things from master problem\n", 938 | " y::Vector{JuMP.VariableRef} = mp[:y]\n", 939 | " θ::Vector{JuMP.VariableRef} = mp[:θ]\n", 940 | " \n", 941 | " # Benders main loop\n", 942 | " z_lb = -Inf\n", 943 | " z_ub = +Inf\n", 944 | " y_hist = [] # History of master solutions\n", 945 | " Z_lb = Float64[]\n", 946 | " Z_ub = Float64[]\n", 947 | " T = Float64[]\n", 948 | "\n", 949 | " gap = Inf\n", 950 | " niter = 0\n", 951 | " ncuts_tot = 0\n", 952 | "\n", 953 | " y_best = zeros(Float64, m)\n", 954 | " x_best = zeros(Int, n)\n", 955 | " solflag = false\n", 956 | "\n", 957 | " t_mp = 0.0\n", 958 | " t_sp = 0.0\n", 959 | " t_tot = 0.0\n", 960 | " t_jump = 0.0\n", 961 | "\n", 962 | " t0 = time()\n", 963 | "\n", 964 | " verbose > 0 && @printf(\n", 965 | " \"%4s %18s %18s %7s %6s %6s %6s %6s %6s\\n\",\n", 966 | " \"Iter\",\n", 967 | " \"Primal bound\",\n", 968 | " \"Dual bound\",\n", 969 | " \"Gap(%)\",\n", 970 | " \"#cuts\",\n", 971 | " \"T-MP\",\n", 972 | " \"T-SP\",\n", 973 | " \"T-Jump\",\n", 974 | " \"T(s)\"\n", 975 | " )\n", 976 | " \n", 977 | " while niter < niter_max\n", 978 | " set_silent(mp)\n", 979 | " t_mp += @elapsed optimize!(mp)\n", 980 | " st = termination_status(mp)\n", 981 | " st == MOI.OPTIMAL || break\n", 982 | "\n", 983 | " # Get the current lower bound...\n", 984 | " z_mp = objective_value(mp)\n", 985 | "\n", 986 | " # ... and current master solution\n", 987 | " y_ = value.(y)\n", 988 | " θ_ = value.(θ)\n", 989 | " if is_mp_integer\n", 990 | " y_ = round.(y_)\n", 991 | " end\n", 992 | " push!(y_hist, y_)\n", 993 | "\n", 994 | " # TODO: stabilization\n", 995 | "\n", 996 | " # Check lower bound improvement\n", 997 | " if !is_mp_integer && (z_mp < z_lb + ϵ_root)\n", 998 | " # Re-instate integrality\n", 999 | " verbose > 0 && println(\"Re-instating integer variables\")\n", 1000 | " undo_relax()\n", 1001 | " is_mp_integer = true\n", 1002 | " end\n", 1003 | " \n", 1004 | " z_lb = max(z_lb, z_mp)\n", 1005 | " push!(Z_lb, z_lb)\n", 1006 | " \n", 1007 | " # Cut-generation loop\n", 1008 | " ncuts = 0\n", 1009 | " pareto_flag = rand() > pareto_freq\n", 1010 | " Λ = zeros(m, n_clusters)\n", 1011 | " ΔZsp = -θ_\n", 1012 | " P = randperm(n_clusters)\n", 1013 | " for k in P # first iterate over the clusters...\n", 1014 | " S = sp_clusters[k]\n", 1015 | " for j in S # ... then solve all sub-problems for that cluster\n", 1016 | " t_sp += @elapsed if fast_sp\n", 1017 | " zj, λj, xj = solve_benders_sp_fast(D[:, j], y_)\n", 1018 | " else\n", 1019 | " zj, λj, xj = solve_benders_sp(D[:, j], y_;\n", 1020 | " Presolve=0,\n", 1021 | " Method=2,\n", 1022 | " Crossover=!pareto_flag, # De-activate crossover p% of the time\n", 1023 | " )\n", 1024 | " end\n", 1025 | " \n", 1026 | " # Aggregate the cut coefficients\n", 1027 | " ΔZsp[k] += zj\n", 1028 | " Λ[:, k] .+= λj\n", 1029 | " end\n", 1030 | " \n", 1031 | " if ΔZsp[k] > 1e-6\n", 1032 | " # Only add the cut if it violated (up to tolerance)\n", 1033 | " t_jump += @elapsed begin\n", 1034 | " @constraint(mp, θ[k] ≥ (θ_[k] + ΔZsp[k]) + dot(Λ[:, k], y - y_))\n", 1035 | " end\n", 1036 | " ncuts += 1\n", 1037 | " end\n", 1038 | " \n", 1039 | " if !is_mp_integer && (ncuts > partial_cut)\n", 1040 | " # Early stopping --> no valid upper bound\n", 1041 | " ΔZsp .= Inf\n", 1042 | " break\n", 1043 | " end\n", 1044 | " end\n", 1045 | " \n", 1046 | " ncuts_tot += ncuts\n", 1047 | "\n", 1048 | " # If improved upper bound, record the current solution\n", 1049 | " solflag = false\n", 1050 | " if is_mp_integer && (z_ub > z_mp + sum(ΔZsp))\n", 1051 | " # Trigger an improvement in the upper bound\n", 1052 | " z_ub = z_mp + sum(ΔZsp)\n", 1053 | " solflag = true\n", 1054 | " y_best .= y_\n", 1055 | " end\n", 1056 | " push!(Z_ub, z_ub)\n", 1057 | " \n", 1058 | " # Log\n", 1059 | " gap = (z_ub - z_lb) / (1e-10 + abs(z_ub))\n", 1060 | " isnan(gap) && (gap = 1.0)\n", 1061 | " t_tot = time() - t0\n", 1062 | " push!(T, t_tot)\n", 1063 | " if verbose > 0 && (solflag || (niter % verbose == 0))\n", 1064 | " @printf(\n", 1065 | " \"%4d%1s %+18.6e %+18.6e %6.2f%% %6d %6.2f %6.2f %6.2f %6.2f\\n\",\n", 1066 | " niter,\n", 1067 | " ( solflag ? \"*\" : \"\"),\n", 1068 | " z_ub,\n", 1069 | " z_lb,\n", 1070 | " 100*gap,\n", 1071 | " ncuts_tot,\n", 1072 | " t_mp,\n", 1073 | " t_sp,\n", 1074 | " t_jump,\n", 1075 | " t_tot\n", 1076 | " )\n", 1077 | " flush(stdout)\n", 1078 | " end\n", 1079 | " t_tot > time_limit && break\n", 1080 | " gap < ϵ_gap && break\n", 1081 | "\n", 1082 | " niter += 1\n", 1083 | " end\n", 1084 | "\n", 1085 | " # Final log\n", 1086 | " if verbose > 0\n", 1087 | " niter == niter_max && println(\"Maximum number of iterations reached\")\n", 1088 | " gap < ϵ_gap && println(\"Found optimal solution within tolerances\")\n", 1089 | " t_tot > time_limit && println(\"Time limit reached\")\n", 1090 | " end\n", 1091 | " \n", 1092 | " return y_hist, Z_lb, Z_ub, T\n", 1093 | "end" 1094 | ] 1095 | }, 1096 | { 1097 | "attachments": {}, 1098 | "cell_type": "markdown", 1099 | "id": "36a2ca24", 1100 | "metadata": {}, 1101 | "source": [ 1102 | "## Examples\n", 1103 | "\n", 1104 | "The following examples illustrate various of the aforementioned settings.\n", 1105 | "\n", 1106 | "For each run, the progress of the lower and upper bound are plotted against\n", 1107 | "(i) the number of BD iterations, and \n", 1108 | "(ii) the elasped computing time." 1109 | ] 1110 | }, 1111 | { 1112 | "attachments": {}, 1113 | "cell_type": "markdown", 1114 | "id": "fc7d46f3", 1115 | "metadata": {}, 1116 | "source": [ 1117 | "### Example 1: vanilla Benders" 1118 | ] 1119 | }, 1120 | { 1121 | "cell_type": "code", 1122 | "execution_count": null, 1123 | "id": "e1bcf8bc", 1124 | "metadata": {}, 1125 | "outputs": [], 1126 | "source": [ 1127 | "mp = generate_mp()\n", 1128 | "clusters = [[j] for j in 1:n] # Classical multi-cut\n", 1129 | "\n", 1130 | "@time Y, Zlb, Zub, T = solve_benders(mp;\n", 1131 | " niter_max=500,\n", 1132 | " seed=0,\n", 1133 | " verbose=5,\n", 1134 | " ϵ_gap=1e-4,\n", 1135 | " time_limit=180,\n", 1136 | " fast_sp=false\n", 1137 | ");\n", 1138 | "niter = length(Y);" 1139 | ] 1140 | }, 1141 | { 1142 | "cell_type": "code", 1143 | "execution_count": null, 1144 | "id": "86b17b88", 1145 | "metadata": {}, 1146 | "outputs": [], 1147 | "source": [ 1148 | "plt = plot(\n", 1149 | " legend=:bottomright,\n", 1150 | " xlabel=\"# Benders iteration\",\n", 1151 | " ylabel=\"Bound\",\n", 1152 | ")\n", 1153 | "\n", 1154 | "plot!(plt, Zlb, color=:red, label=\"LB\")\n", 1155 | "plot!(plt, Zub, color=:blue, label=\"UB\")\n", 1156 | "display(plt)\n", 1157 | "\n", 1158 | "plt = plot(\n", 1159 | " legend=:bottomright,\n", 1160 | " xlabel=\"Time (s)\",\n", 1161 | " ylabel=\"Bound\",\n", 1162 | ")\n", 1163 | "\n", 1164 | "plot!(plt, T, Zlb, color=:red, label=\"LB\")\n", 1165 | "plot!(plt, T, Zub, color=:blue, label=\"UB\")\n", 1166 | "display(plt)\n", 1167 | ";" 1168 | ] 1169 | }, 1170 | { 1171 | "attachments": {}, 1172 | "cell_type": "markdown", 1173 | "id": "0cbd2c58", 1174 | "metadata": {}, 1175 | "source": [ 1176 | "### Example 2: vanilla Benders with non-Pareto cuts\n", 1177 | "\n", 1178 | "This example is identical as above, except that Pareto cuts are separated only 10% of the time.\n", 1179 | "\n", 1180 | "The effect of the progression of both lower and upper bound is drastic." 1181 | ] 1182 | }, 1183 | { 1184 | "cell_type": "code", 1185 | "execution_count": null, 1186 | "id": "0d0bb224", 1187 | "metadata": {}, 1188 | "outputs": [], 1189 | "source": [ 1190 | "mp = generate_mp()\n", 1191 | "clusters = [[j] for j in 1:n] # Classical multi-cut\n", 1192 | "\n", 1193 | "@time Y, Zlb, Zub, T = solve_benders(mp;\n", 1194 | " niter_max=500,\n", 1195 | " seed=0,\n", 1196 | " verbose=5,\n", 1197 | " ϵ_gap=1e-4,\n", 1198 | " time_limit=180,\n", 1199 | " fast_sp=false,\n", 1200 | " pareto_freq=0.10, # Generate Pareto cuts only 10% of the time\n", 1201 | ");\n", 1202 | "niter = length(Y);" 1203 | ] 1204 | }, 1205 | { 1206 | "cell_type": "code", 1207 | "execution_count": null, 1208 | "id": "12ad2617", 1209 | "metadata": {}, 1210 | "outputs": [], 1211 | "source": [ 1212 | "plt = plot(\n", 1213 | " legend=:bottomright,\n", 1214 | " xlabel=\"# Benders iteration\",\n", 1215 | " ylabel=\"Bound\",\n", 1216 | ")\n", 1217 | "\n", 1218 | "plot!(plt, Zlb, color=:red, label=\"LB\")\n", 1219 | "plot!(plt, Zub, color=:blue, label=\"UB\")\n", 1220 | "display(plt)\n", 1221 | "\n", 1222 | "plt = plot(\n", 1223 | " legend=:bottomright,\n", 1224 | " xlabel=\"Time (s)\",\n", 1225 | " ylabel=\"Bound\",\n", 1226 | ")\n", 1227 | "\n", 1228 | "plot!(plt, T, Zlb, color=:red, label=\"LB\")\n", 1229 | "plot!(plt, T, Zub, color=:blue, label=\"UB\")\n", 1230 | "display(plt)\n", 1231 | ";" 1232 | ] 1233 | }, 1234 | { 1235 | "attachments": {}, 1236 | "cell_type": "markdown", 1237 | "id": "f2e3082f", 1238 | "metadata": {}, 1239 | "source": [ 1240 | "### Example 3: Benders at the root\n", 1241 | "\n", 1242 | "This example is identical to Example 1, except that Benders decomposition is performed at the root first.\n", 1243 | "\n", 1244 | "The benefits are more visible on larger instances." 1245 | ] 1246 | }, 1247 | { 1248 | "cell_type": "code", 1249 | "execution_count": null, 1250 | "id": "562c6fe1", 1251 | "metadata": {}, 1252 | "outputs": [], 1253 | "source": [ 1254 | "mp = generate_mp()\n", 1255 | "clusters = [[j] for j in 1:n] # Classical multi-cut\n", 1256 | "\n", 1257 | "@time Y, Zlb, Zub, T = solve_benders(mp;\n", 1258 | " niter_max=500,\n", 1259 | " seed=0,\n", 1260 | " verbose=5,\n", 1261 | " ϵ_gap=1e-4,\n", 1262 | " time_limit=180,\n", 1263 | " root_benders=true,\n", 1264 | ");\n", 1265 | "niter = length(Y);" 1266 | ] 1267 | }, 1268 | { 1269 | "cell_type": "code", 1270 | "execution_count": null, 1271 | "id": "f3ec37a1", 1272 | "metadata": {}, 1273 | "outputs": [], 1274 | "source": [ 1275 | "plt = plot(\n", 1276 | " legend=:bottomright,\n", 1277 | " xlabel=\"# Benders iteration\",\n", 1278 | " ylabel=\"Bound\",\n", 1279 | ")\n", 1280 | "\n", 1281 | "plot!(plt, Zlb, color=:red, label=\"LB\")\n", 1282 | "plot!(plt, Zub, color=:blue, label=\"UB\")\n", 1283 | "display(plt)\n", 1284 | "\n", 1285 | "plt = plot(\n", 1286 | " legend=:bottomright,\n", 1287 | " xlabel=\"Time (s)\",\n", 1288 | " ylabel=\"Bound\",\n", 1289 | ")\n", 1290 | "\n", 1291 | "plot!(plt, T, Zlb, color=:red, label=\"LB\")\n", 1292 | "plot!(plt, T, Zub, color=:blue, label=\"UB\")\n", 1293 | "display(plt)\n", 1294 | ";" 1295 | ] 1296 | }, 1297 | { 1298 | "attachments": {}, 1299 | "cell_type": "markdown", 1300 | "id": "af83a5c4", 1301 | "metadata": {}, 1302 | "source": [ 1303 | "# Dealing with many sub-problems\n", 1304 | "\n", 1305 | "Note: for this section, it is recommend to increase the number of subproblems to at least a thousand.\n", 1306 | "A reasonable setting is $m=128$ and $n=1024$." 1307 | ] 1308 | }, 1309 | { 1310 | "attachments": {}, 1311 | "cell_type": "markdown", 1312 | "id": "cf2e9436", 1313 | "metadata": {}, 1314 | "source": [ 1315 | "## Clustering the sub-problems\n", 1316 | "\n", 1317 | "A simple way of clustering the sub-problems is to use each customer's coordinates.\n", 1318 | "\n", 1319 | "The following code first partitions the $[0, 1] \\times [0, 1]$ square into a $G \\times G$ grid,\n", 1320 | " then assigns each customer to the cell it belongs to.\n", 1321 | "The number of clusters is thus equal to $G^{2}$.\n", 1322 | "\n", 1323 | "If the `random` argument is set to `true`, then customers are assigned to clusters in a random fashion." 1324 | ] 1325 | }, 1326 | { 1327 | "cell_type": "code", 1328 | "execution_count": null, 1329 | "id": "f2d8a100", 1330 | "metadata": {}, 1331 | "outputs": [], 1332 | "source": [ 1333 | "# Will create G^2 clusters, one for each grid cell\n", 1334 | "function compute_clusters(X;\n", 1335 | " G::Int=1,\n", 1336 | " random::Bool=false\n", 1337 | ")\n", 1338 | " # Cluster the customers\n", 1339 | " n = size(X, 1)\n", 1340 | " clusters_id = zeros(Int, n)\n", 1341 | " for j in 1:n\n", 1342 | " xj = clamp(X[j, 1], 1e-6, 1- 1e-6)\n", 1343 | " yj = clamp(X[j, 2], 1e-6, 1- 1e-6)\n", 1344 | " n1 = 1 + Int(floor(xj * G))\n", 1345 | " n2 = 1 + Int(floor(yj * G))\n", 1346 | " \n", 1347 | " if random\n", 1348 | " n1 = rand(1:G)\n", 1349 | " n2 = rand(1:G)\n", 1350 | " end\n", 1351 | "\n", 1352 | " clusters_id[j] = n1 + G * (n2 - 1)\n", 1353 | " end\n", 1354 | " \n", 1355 | " # Count how many clusters we have\n", 1356 | " n_clusters = length(Set(clusters_id))\n", 1357 | " clusters = [Int[] for _ in 1:n_clusters]\n", 1358 | " for j in 1:n\n", 1359 | " k = clusters_id[j]\n", 1360 | " push!(clusters[k], j)\n", 1361 | " end\n", 1362 | " return clusters\n", 1363 | "end" 1364 | ] 1365 | }, 1366 | { 1367 | "cell_type": "code", 1368 | "execution_count": null, 1369 | "id": "fd86a5b1", 1370 | "metadata": {}, 1371 | "outputs": [], 1372 | "source": [ 1373 | "clusters = compute_clusters(Xc, G=2, random=false);" 1374 | ] 1375 | }, 1376 | { 1377 | "cell_type": "code", 1378 | "execution_count": null, 1379 | "id": "fa5277c5", 1380 | "metadata": {}, 1381 | "outputs": [], 1382 | "source": [ 1383 | "# Plot locations on a grid\n", 1384 | "plt = plot(\n", 1385 | " title=\"Clustered customers\",\n", 1386 | ")\n", 1387 | "\n", 1388 | "for S in clusters\n", 1389 | " scatter!(plt, Xc[S, 1], Xc[S, 2], label=nothing, marker=:circ, ms=5)\n", 1390 | "end\n", 1391 | "\n", 1392 | "plt" 1393 | ] 1394 | }, 1395 | { 1396 | "attachments": {}, 1397 | "cell_type": "markdown", 1398 | "id": "370af9a8", 1399 | "metadata": {}, 1400 | "source": [ 1401 | "## Computational comparison" 1402 | ] 1403 | }, 1404 | { 1405 | "cell_type": "code", 1406 | "execution_count": null, 1407 | "id": "4bff56ec", 1408 | "metadata": {}, 1409 | "outputs": [], 1410 | "source": [ 1411 | "# Multi-cut\n", 1412 | "mp_mc = generate_mp()\n", 1413 | "clusters_mc = [[j] for j in 1:n]\n", 1414 | "@time Y_mc, Zlb_mc, Zub_mc, T_mc = solve_benders(mp_mc;\n", 1415 | " niter_max=500,\n", 1416 | " seed=0,\n", 1417 | " verbose=5,\n", 1418 | " ϵ_gap=1e-4,\n", 1419 | " time_limit=180,\n", 1420 | " fast_sp=true,\n", 1421 | " root_benders=true,\n", 1422 | " sp_clusters=clusters_mc,\n", 1423 | " partial_cut=128, # This controls how many cuts can be generated at each BD iteration\n", 1424 | ");\n", 1425 | "niter_mc = length(Y_mc);" 1426 | ] 1427 | }, 1428 | { 1429 | "cell_type": "code", 1430 | "execution_count": null, 1431 | "id": "4703f3a5", 1432 | "metadata": {}, 1433 | "outputs": [], 1434 | "source": [ 1435 | "# Single cut\n", 1436 | "mp_sc = generate_mp()\n", 1437 | "@time Y_sc, Zlb_sc, Zub_sc, T_sc = solve_benders(mp_sc;\n", 1438 | " niter_max=500,\n", 1439 | " seed=0,\n", 1440 | " verbose=20,\n", 1441 | " ϵ_gap=1e-4,\n", 1442 | " time_limit=180,\n", 1443 | " fast_sp=true,\n", 1444 | " root_benders=true,\n", 1445 | " sp_clusters=[collect(1:n)]\n", 1446 | ");\n", 1447 | "niter_sc = length(Y_sc)" 1448 | ] 1449 | }, 1450 | { 1451 | "cell_type": "code", 1452 | "execution_count": null, 1453 | "id": "59be18e4", 1454 | "metadata": {}, 1455 | "outputs": [], 1456 | "source": [ 1457 | "# Aggregated cut\n", 1458 | "mp_ca = generate_mp()\n", 1459 | "@time Y_ca, Zlb_ca, Zub_ca, T_ca = solve_benders(mp_ca;\n", 1460 | " niter_max=500,\n", 1461 | " seed=0,\n", 1462 | " verbose=20,\n", 1463 | " ϵ_gap=1e-4,\n", 1464 | " time_limit=180,\n", 1465 | " fast_sp=true,\n", 1466 | " root_benders=true,\n", 1467 | " sp_clusters=clusters\n", 1468 | ");" 1469 | ] 1470 | }, 1471 | { 1472 | "cell_type": "code", 1473 | "execution_count": null, 1474 | "id": "2c7a3cec", 1475 | "metadata": {}, 1476 | "outputs": [], 1477 | "source": [ 1478 | "plt = plot(\n", 1479 | " legend=:bottomright,\n", 1480 | " xlabel=\"# Benders iteration\",\n", 1481 | " ylabel=\"Bound\"\n", 1482 | ")\n", 1483 | "\n", 1484 | "plot!(plt, Zlb_sc, color=:red, ls=:dash, label=\"LB (single)\")\n", 1485 | "plot!(plt, Zlb_mc, color=:red, ls=:solid, label=\"LB (multi)\")\n", 1486 | "plot!(plt, Zlb_ca, color=:red, ls=:dot, label=\"LB (cluster)\")\n", 1487 | "plot!(plt, Zub_sc, color=:blue, ls=:dash, label=\"UB (single)\")\n", 1488 | "plot!(plt, Zub_mc, color=:blue, ls=:solid, label=\"UB (multi)\")\n", 1489 | "plot!(plt, Zub_ca, color=:blue, ls=:dot, label=\"UB (cluster)\")\n", 1490 | "display(plt)\n", 1491 | "\n", 1492 | "plt = plot(\n", 1493 | " legend=:bottomright,\n", 1494 | " xlabel=\"Time (s)\",\n", 1495 | " ylabel=\"Bound\",\n", 1496 | ")\n", 1497 | "\n", 1498 | "plot!(plt, T_sc, Zlb_sc, color=:red, ls=:dash, label=\"LB (single)\")\n", 1499 | "plot!(plt, T_mc, Zlb_mc, color=:red, ls=:solid, label=\"LB (multi)\")\n", 1500 | "plot!(plt, T_ca, Zlb_ca, color=:red, ls=:dot, label=\"LB (cluster)\")\n", 1501 | "plot!(plt, T_sc, Zub_sc, color=:blue, ls=:dash, label=\"UB (single)\")\n", 1502 | "plot!(plt, T_mc, Zub_mc, color=:blue, ls=:solid, label=\"UB (multi)\")\n", 1503 | "plot!(plt, T_ca, Zub_ca, color=:blue, ls=:dot, label=\"UB (cluster)\")\n", 1504 | "display(plt)\n", 1505 | ";" 1506 | ] 1507 | } 1508 | ], 1509 | "metadata": { 1510 | "kernelspec": { 1511 | "display_name": "Julia 1.8.1", 1512 | "language": "julia", 1513 | "name": "julia-1.8" 1514 | }, 1515 | "language_info": { 1516 | "file_extension": ".jl", 1517 | "mimetype": "application/julia", 1518 | "name": "julia", 1519 | "version": "1.8.1" 1520 | } 1521 | }, 1522 | "nbformat": 4, 1523 | "nbformat_minor": 5 1524 | } 1525 | -------------------------------------------------------------------------------- /benders/acceleration/benders_acceleration.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/mtanneau/or_tutorials/c2b588e4d9af8e390519ba11228d4a7ae69837a0/benders/acceleration/benders_acceleration.pdf -------------------------------------------------------------------------------- /benders/intro/ufl.jl: -------------------------------------------------------------------------------- 1 | using LinearAlgebra 2 | using Printf 3 | using Random 4 | 5 | using JuMP 6 | 7 | using Plots 8 | 9 | struct UFLData 10 | m::Int 11 | n::Int 12 | 13 | Xc::Matrix{Float64} # Customer coordinates 14 | Xf::Matrix{Float64} # Facility coordinates 15 | 16 | f::Vector{Float64} # fixed cost (per facility) 17 | D::Matrix{Float64} # distance matrix 18 | end 19 | 20 | function generate_ufl_instance(m, n; seed::Int=1804, grid_param::Int=1024) 21 | # To ensure reproducibility, always use a seed! 22 | rng = MersenneTwister(seed) 23 | 24 | Xc = rand(rng, 0:grid_param, n, 2) ./ grid_param # Customer coordinates 25 | Xf = rand(rng, -1:21, m, 2) ./ 20 # Facility coordinates 26 | 27 | # Sample fixed building costs 28 | f = rand(10:20, m) 29 | 30 | # Compute distance matrix 31 | D = zeros(Float64, m, n) 32 | for j in 1:n, i in 1:m 33 | D[i, j] = norm(Xf[i, :] - Xc[j, :], 2) 34 | end 35 | # Increase the distances to make the problem a little harder 36 | D .*= 10 37 | 38 | return UFLData(m, n, Xc, Xf, f, D) 39 | end 40 | 41 | """ 42 | plot_ufl(data::UFLData) 43 | 44 | Visualize a UFL instance data. Returns a `Plot` object. 45 | """ 46 | function plot_ufl_instance(ufl::UFLData) 47 | # Since we have coordinates, we can visualize what the instance looks like 48 | plt = plot( 49 | legend=:topleft, 50 | xlim=(-0.1, 1.1), 51 | ylim=(-0.1, 1.33), 52 | ) 53 | 54 | scatter!(plt, ufl.Xf[:, 1], ufl.Xf[:, 2], label="Locations", marker=:rect, ms=8, opacity=0.5) 55 | scatter!(plt, ufl.Xc[:, 1], ufl.Xc[:, 2], label="Customers", marker=:circ, ms=5) 56 | return plt 57 | end 58 | 59 | function plot_ufl_solution(ufl::UFLData, y_, x_) 60 | plt = plot( 61 | legend=:topleft, 62 | ylim=(-0.1, 1.33), 63 | ) 64 | 65 | # Show which customer is served by which facility 66 | for i in 1:ufl.m 67 | for j in 1:ufl.n 68 | if x_[i, j] 69 | # Plot a line between yi and xj 70 | plot!(plt, [ufl.Xc[j, 1], ufl.Xf[i, 1]], [ufl.Xc[j, 2], ufl.Xf[i, 2]], label=nothing, lw=0.5, color=:black) 71 | end 72 | end 73 | end 74 | 75 | # Customers 76 | scatter!(plt, ufl.Xc[:, 1], ufl.Xc[:, 2], label="Customers", marker=:circ, ms=4, color=:red) 77 | 78 | # Facilities (open and closed) 79 | scatter!(plt, [ufl.Xf[.! y_, 1]], [ufl.Xf[.!y_, 2]], 80 | color=:lightblue, 81 | label="Facilities (closed)", 82 | marker=:rect, 83 | ms=6 84 | ) 85 | scatter!(plt, [ufl.Xf[y_, 1]], [ufl.Xf[y_, 2]], 86 | color=:darkblue, 87 | label="Facilities (open)", 88 | marker=:rect, 89 | ms=6 90 | ) 91 | 92 | return plt 93 | end 94 | 95 | function build_ufl_mip(data::UFLData) 96 | model = Model() # You can defined a JuMP model without a solver... 97 | 98 | m, n = data.m, data.n 99 | 100 | # Decision variables 101 | @variable(model, y[1:m], Bin) 102 | @variable(model, x[1:m, 1:n], Bin) 103 | 104 | # Constraints 105 | @constraint(model, customer_served[j in 1:n], sum(x[:, j]) == 1) 106 | @constraint(model, facility_open[i in 1:m, j in 1:n], x[i, j] <= y[i]) 107 | 108 | # Objective function 109 | @objective(model, Min, dot(data.f, y) + dot(data.D, x)) 110 | 111 | return model 112 | end 113 | 114 | function build_ufl_master(ufl::UFLData; optimizer) 115 | mp = Model(optimizer) 116 | 117 | m = ufl.m 118 | n = ufl.n 119 | 120 | @variable(mp, y[1:m], Bin) 121 | @variable(mp, θ[1:n] >= 0) 122 | 123 | @constraint(mp, sum(y) >= 1) 124 | 125 | @objective(mp, Min, dot(ufl.f, y) + sum(θ)) 126 | 127 | return mp 128 | end 129 | 130 | """ 131 | solve_benders_sp(d::AbstractVector, y; kwargs...) 132 | 133 | Solve the Benders sub-problem for customer ``j``. 134 | 135 | # Arguments 136 | * `d::AbstractVector`: the vector of distances between the customer and all locations. 137 | * `y::AbstractVector`: the current master solution. May be integer or fractional. 138 | 139 | # Returns 140 | * `z::Float`: the optimal objective value of the sub-problem 141 | * `λ::Vector{Float64}`: the sub-problem dual solution, used to form the Benders cut 142 | * `x::Vector{Float64}`: the sub-problem primal solution, for information 143 | """ 144 | function solve_benders_sp(d::AbstractVector, y; kwargs...) 145 | m = length(d) 146 | 147 | sp = direct_model(Gurobi.Optimizer(GRBENV)) 148 | 149 | @variable(sp, x[1:m] >= 0) # we don't need the upper bound, because it's implied by sum(x) == 1 150 | @variable(sp, q[1:m]) 151 | 152 | @constraint(sp, sum(x) == 1) 153 | @constraint(sp, benders, q .== y) # Kevin's trick to make your life easier 154 | @constraint(sp, x .<= q) 155 | 156 | @objective(sp, Min, dot(d, x)) 157 | 158 | set_silent(sp) 159 | for (k, v) in kwargs 160 | set_optimizer_attribute(sp, string(k), v) 161 | end 162 | 163 | optimize!(sp) 164 | z = objective_value(sp) 165 | λ = dual.(benders) 166 | x_ = value.(x) 167 | 168 | return z, λ, x_ 169 | end 170 | 171 | function solve_benders_sp_fast(d::AbstractVector, y; kwargs...) 172 | m = length(d) 173 | 174 | # Find the closest facilities... 175 | p = sortperm(d) 176 | # ... then greedily allocate until we hit 1.0 177 | w = 1.0 # we record w == 1 - sum(x) 178 | x_ = zeros(Float64, m) 179 | d_ = Inf # Distance to the furthest facility that serves this customer 180 | z_ = 0.0 # Objective value 181 | for i in p 182 | x_[i] += min(y[i], w) 183 | z_ += x_[i] * d[i] 184 | w -= x_[i] 185 | d_ = y[i] > 0 ? d[i] : d_ 186 | w <= 0 && break 187 | end 188 | 189 | # Now we build the dual solution 190 | λ = zeros(m) 191 | for i in 1:m 192 | λ[i] = (d[i] < d_) * (d[i] - d_) 193 | end 194 | 195 | return z_, λ, x_ 196 | end 197 | -------------------------------------------------------------------------------- /callbacks/Manifest.toml: -------------------------------------------------------------------------------- 1 | # This file is machine-generated - editing it directly is not advised 2 | 3 | [[Adapt]] 4 | deps = ["LinearAlgebra"] 5 | git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f" 6 | uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" 7 | version = "3.3.3" 8 | 9 | [[ArgTools]] 10 | uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" 11 | 12 | [[Artifacts]] 13 | uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" 14 | 15 | [[Base64]] 16 | uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" 17 | 18 | [[BenchmarkTools]] 19 | deps = ["JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"] 20 | git-tree-sha1 = "4c10eee4af024676200bc7752e536f858c6b8f93" 21 | uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" 22 | version = "1.3.1" 23 | 24 | [[Bzip2_jll]] 25 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 26 | git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2" 27 | uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" 28 | version = "1.0.8+0" 29 | 30 | [[Cairo_jll]] 31 | deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] 32 | git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2" 33 | uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" 34 | version = "1.16.1+1" 35 | 36 | [[Calculus]] 37 | deps = ["LinearAlgebra"] 38 | git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad" 39 | uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9" 40 | version = "0.5.1" 41 | 42 | [[ChainRulesCore]] 43 | deps = ["Compat", "LinearAlgebra", "SparseArrays"] 44 | git-tree-sha1 = "9950387274246d08af38f6eef8cb5480862a435f" 45 | uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" 46 | version = "1.14.0" 47 | 48 | [[ChangesOfVariables]] 49 | deps = ["ChainRulesCore", "LinearAlgebra", "Test"] 50 | git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1" 51 | uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0" 52 | version = "0.1.2" 53 | 54 | [[CodecBzip2]] 55 | deps = ["Bzip2_jll", "Libdl", "TranscodingStreams"] 56 | git-tree-sha1 = "2e62a725210ce3c3c2e1a3080190e7ca491f18d7" 57 | uuid = "523fee87-0ab8-5b00-afb7-3ecf72e48cfd" 58 | version = "0.7.2" 59 | 60 | [[CodecZlib]] 61 | deps = ["TranscodingStreams", "Zlib_jll"] 62 | git-tree-sha1 = "ded953804d019afa9a3f98981d99b33e3db7b6da" 63 | uuid = "944b1d66-785c-5afd-91f1-9de20f533193" 64 | version = "0.7.0" 65 | 66 | [[ColorSchemes]] 67 | deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"] 68 | git-tree-sha1 = "12fc73e5e0af68ad3137b886e3f7c1eacfca2640" 69 | uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4" 70 | version = "3.17.1" 71 | 72 | [[ColorTypes]] 73 | deps = ["FixedPointNumbers", "Random"] 74 | git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597" 75 | uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" 76 | version = "0.11.0" 77 | 78 | [[Colors]] 79 | deps = ["ColorTypes", "FixedPointNumbers", "Reexport"] 80 | git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40" 81 | uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" 82 | version = "0.12.8" 83 | 84 | [[CommonSubexpressions]] 85 | deps = ["MacroTools", "Test"] 86 | git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7" 87 | uuid = "bbf7d656-a473-5ed7-a52c-81e309532950" 88 | version = "0.3.0" 89 | 90 | [[Compat]] 91 | deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"] 92 | git-tree-sha1 = "96b0bc6c52df76506efc8a441c6cf1adcb1babc4" 93 | uuid = "34da2185-b29b-5c13-b0c7-acf172513d20" 94 | version = "3.42.0" 95 | 96 | [[CompilerSupportLibraries_jll]] 97 | deps = ["Artifacts", "Libdl"] 98 | uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" 99 | 100 | [[Contour]] 101 | deps = ["StaticArrays"] 102 | git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7" 103 | uuid = "d38c429a-6771-53c6-b99e-75d170b6e991" 104 | version = "0.5.7" 105 | 106 | [[DataAPI]] 107 | git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8" 108 | uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" 109 | version = "1.9.0" 110 | 111 | [[DataStructures]] 112 | deps = ["Compat", "InteractiveUtils", "OrderedCollections"] 113 | git-tree-sha1 = "3daef5523dd2e769dad2365274f760ff5f282c7d" 114 | uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8" 115 | version = "0.18.11" 116 | 117 | [[DataValueInterfaces]] 118 | git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6" 119 | uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464" 120 | version = "1.0.0" 121 | 122 | [[Dates]] 123 | deps = ["Printf"] 124 | uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" 125 | 126 | [[DelimitedFiles]] 127 | deps = ["Mmap"] 128 | uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" 129 | 130 | [[DiffResults]] 131 | deps = ["StaticArrays"] 132 | git-tree-sha1 = "c18e98cba888c6c25d1c3b048e4b3380ca956805" 133 | uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5" 134 | version = "1.0.3" 135 | 136 | [[DiffRules]] 137 | deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"] 138 | git-tree-sha1 = "dd933c4ef7b4c270aacd4eb88fa64c147492acf0" 139 | uuid = "b552c78f-8df3-52c6-915a-8e097449b14b" 140 | version = "1.10.0" 141 | 142 | [[Distributed]] 143 | deps = ["Random", "Serialization", "Sockets"] 144 | uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b" 145 | 146 | [[DocStringExtensions]] 147 | deps = ["LibGit2"] 148 | git-tree-sha1 = "b19534d1895d702889b219c382a6e18010797f0b" 149 | uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" 150 | version = "0.8.6" 151 | 152 | [[Downloads]] 153 | deps = ["ArgTools", "LibCURL", "NetworkOptions"] 154 | uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" 155 | 156 | [[EarCut_jll]] 157 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 158 | git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d" 159 | uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5" 160 | version = "2.2.3+0" 161 | 162 | [[Expat_jll]] 163 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 164 | git-tree-sha1 = "ae13fcbc7ab8f16b0856729b050ef0c446aa3492" 165 | uuid = "2e619515-83b5-522b-bb60-26c02a35a201" 166 | version = "2.4.4+0" 167 | 168 | [[FFMPEG]] 169 | deps = ["FFMPEG_jll"] 170 | git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8" 171 | uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a" 172 | version = "0.4.1" 173 | 174 | [[FFMPEG_jll]] 175 | deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"] 176 | git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f" 177 | uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5" 178 | version = "4.4.0+0" 179 | 180 | [[FixedPointNumbers]] 181 | deps = ["Statistics"] 182 | git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc" 183 | uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93" 184 | version = "0.8.4" 185 | 186 | [[Fontconfig_jll]] 187 | deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"] 188 | git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03" 189 | uuid = "a3f928ae-7b40-5064-980b-68af3947d34b" 190 | version = "2.13.93+0" 191 | 192 | [[Formatting]] 193 | deps = ["Printf"] 194 | git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8" 195 | uuid = "59287772-0a20-5a39-b81b-1366585eb4c0" 196 | version = "0.4.2" 197 | 198 | [[ForwardDiff]] 199 | deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"] 200 | git-tree-sha1 = "1bd6fc0c344fc0cbee1f42f8d2e7ec8253dda2d2" 201 | uuid = "f6369f11-7733-5829-9624-2563aa707210" 202 | version = "0.10.25" 203 | 204 | [[FreeType2_jll]] 205 | deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 206 | git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9" 207 | uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7" 208 | version = "2.10.4+0" 209 | 210 | [[FriBidi_jll]] 211 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 212 | git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91" 213 | uuid = "559328eb-81f9-559d-9380-de523a88c83c" 214 | version = "1.0.10+0" 215 | 216 | [[GLFW_jll]] 217 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"] 218 | git-tree-sha1 = "51d2dfe8e590fbd74e7a842cf6d13d8a2f45dc01" 219 | uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89" 220 | version = "3.3.6+0" 221 | 222 | [[GLPK]] 223 | deps = ["GLPK_jll", "MathOptInterface"] 224 | git-tree-sha1 = "c3cc0a7a4e021620f1c0e67679acdbf1be311eb0" 225 | uuid = "60bf3e95-4087-53dc-ae20-288a0d20c6a6" 226 | version = "1.0.1" 227 | 228 | [[GLPK_jll]] 229 | deps = ["Artifacts", "GMP_jll", "JLLWrappers", "Libdl", "Pkg"] 230 | git-tree-sha1 = "fe68622f32828aa92275895fdb324a85894a5b1b" 231 | uuid = "e8aa6df9-e6ca-548a-97ff-1f85fc5b8b98" 232 | version = "5.0.1+0" 233 | 234 | [[GMP_jll]] 235 | deps = ["Artifacts", "Libdl"] 236 | uuid = "781609d7-10c4-51f6-84f2-b8444358ff6d" 237 | 238 | [[GR]] 239 | deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "RelocatableFolders", "Serialization", "Sockets", "Test", "UUIDs"] 240 | git-tree-sha1 = "9f836fb62492f4b0f0d3b06f55983f2704ed0883" 241 | uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71" 242 | version = "0.64.0" 243 | 244 | [[GR_jll]] 245 | deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"] 246 | git-tree-sha1 = "a6c850d77ad5118ad3be4bd188919ce97fffac47" 247 | uuid = "d2c73de3-f751-5644-a686-071e5b155ba9" 248 | version = "0.64.0+0" 249 | 250 | [[GeometryBasics]] 251 | deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"] 252 | git-tree-sha1 = "83ea630384a13fc4f002b77690bc0afeb4255ac9" 253 | uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326" 254 | version = "0.4.2" 255 | 256 | [[Gettext_jll]] 257 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"] 258 | git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046" 259 | uuid = "78b55507-aeef-58d4-861c-77aaff3498b1" 260 | version = "0.21.0+0" 261 | 262 | [[Glib_jll]] 263 | deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"] 264 | git-tree-sha1 = "a32d672ac2c967f3deb8a81d828afc739c838a06" 265 | uuid = "7746bdde-850d-59dc-9ae8-88ece973131d" 266 | version = "2.68.3+2" 267 | 268 | [[Graphite2_jll]] 269 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 270 | git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011" 271 | uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472" 272 | version = "1.3.14+0" 273 | 274 | [[Grisu]] 275 | git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2" 276 | uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe" 277 | version = "1.0.2" 278 | 279 | [[Gurobi]] 280 | deps = ["Libdl", "MathOptInterface", "Pkg"] 281 | git-tree-sha1 = "d75a6c39ca5bc1a51ac467d1d3084a740b59c7c3" 282 | uuid = "2e9cd046-0924-5485-92f1-d5272153d98b" 283 | version = "0.11.0" 284 | 285 | [[HTTP]] 286 | deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"] 287 | git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a" 288 | uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3" 289 | version = "0.9.17" 290 | 291 | [[HarfBuzz_jll]] 292 | deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"] 293 | git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3" 294 | uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566" 295 | version = "2.8.1+1" 296 | 297 | [[IniFile]] 298 | git-tree-sha1 = "f550e6e32074c939295eb5ea6de31849ac2c9625" 299 | uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f" 300 | version = "0.5.1" 301 | 302 | [[InteractiveUtils]] 303 | deps = ["Markdown"] 304 | uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" 305 | 306 | [[InverseFunctions]] 307 | deps = ["Test"] 308 | git-tree-sha1 = "91b5dcf362c5add98049e6c29ee756910b03051d" 309 | uuid = "3587e190-3f89-42d0-90ee-14403ec27112" 310 | version = "0.1.3" 311 | 312 | [[IrrationalConstants]] 313 | git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151" 314 | uuid = "92d709cd-6900-40b7-9082-c6be49f344b6" 315 | version = "0.1.1" 316 | 317 | [[IterTools]] 318 | git-tree-sha1 = "fa6287a4469f5e048d763df38279ee729fbd44e5" 319 | uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e" 320 | version = "1.4.0" 321 | 322 | [[IteratorInterfaceExtensions]] 323 | git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856" 324 | uuid = "82899510-4779-5014-852e-03e436cf321d" 325 | version = "1.0.0" 326 | 327 | [[JLLWrappers]] 328 | deps = ["Preferences"] 329 | git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1" 330 | uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" 331 | version = "1.4.1" 332 | 333 | [[JSON]] 334 | deps = ["Dates", "Mmap", "Parsers", "Unicode"] 335 | git-tree-sha1 = "3c837543ddb02250ef42f4738347454f95079d4e" 336 | uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" 337 | version = "0.21.3" 338 | 339 | [[JpegTurbo_jll]] 340 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 341 | git-tree-sha1 = "b53380851c6e6664204efb2e62cd24fa5c47e4ba" 342 | uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8" 343 | version = "2.1.2+0" 344 | 345 | [[JuMP]] 346 | deps = ["Calculus", "DataStructures", "ForwardDiff", "LinearAlgebra", "MathOptInterface", "MutableArithmetics", "NaNMath", "OrderedCollections", "Printf", "SparseArrays", "SpecialFunctions"] 347 | git-tree-sha1 = "936e7ebf6c84f0c0202b83bb22461f4ebc5c9969" 348 | uuid = "4076af6c-e467-56ae-b986-b466b2749572" 349 | version = "1.0.0" 350 | 351 | [[LAME_jll]] 352 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 353 | git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c" 354 | uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d" 355 | version = "3.100.1+0" 356 | 357 | [[LERC_jll]] 358 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 359 | git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434" 360 | uuid = "88015f11-f218-50d7-93a8-a6af411a945d" 361 | version = "3.0.0+1" 362 | 363 | [[LZO_jll]] 364 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 365 | git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6" 366 | uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac" 367 | version = "2.10.1+0" 368 | 369 | [[LaTeXStrings]] 370 | git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996" 371 | uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" 372 | version = "1.3.0" 373 | 374 | [[Latexify]] 375 | deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"] 376 | git-tree-sha1 = "4f00cc36fede3c04b8acf9b2e2763decfdcecfa6" 377 | uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316" 378 | version = "0.15.13" 379 | 380 | [[LibCURL]] 381 | deps = ["LibCURL_jll", "MozillaCACerts_jll"] 382 | uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21" 383 | 384 | [[LibCURL_jll]] 385 | deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"] 386 | uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0" 387 | 388 | [[LibGit2]] 389 | deps = ["Base64", "NetworkOptions", "Printf", "SHA"] 390 | uuid = "76f85450-5226-5b5a-8eaa-529ad045b433" 391 | 392 | [[LibSSH2_jll]] 393 | deps = ["Artifacts", "Libdl", "MbedTLS_jll"] 394 | uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8" 395 | 396 | [[Libdl]] 397 | uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" 398 | 399 | [[Libffi_jll]] 400 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 401 | git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290" 402 | uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490" 403 | version = "3.2.2+1" 404 | 405 | [[Libgcrypt_jll]] 406 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"] 407 | git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae" 408 | uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4" 409 | version = "1.8.7+0" 410 | 411 | [[Libglvnd_jll]] 412 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"] 413 | git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf" 414 | uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29" 415 | version = "1.3.0+3" 416 | 417 | [[Libgpg_error_jll]] 418 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 419 | git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9" 420 | uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8" 421 | version = "1.42.0+0" 422 | 423 | [[Libiconv_jll]] 424 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 425 | git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778" 426 | uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531" 427 | version = "1.16.1+1" 428 | 429 | [[Libmount_jll]] 430 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 431 | git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73" 432 | uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9" 433 | version = "2.35.0+0" 434 | 435 | [[Libtiff_jll]] 436 | deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"] 437 | git-tree-sha1 = "c9551dd26e31ab17b86cbd00c2ede019c08758eb" 438 | uuid = "89763e89-9b03-5906-acba-b20f662cd828" 439 | version = "4.3.0+1" 440 | 441 | [[Libuuid_jll]] 442 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 443 | git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066" 444 | uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700" 445 | version = "2.36.0+0" 446 | 447 | [[LinearAlgebra]] 448 | deps = ["Libdl"] 449 | uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 450 | 451 | [[LogExpFunctions]] 452 | deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"] 453 | git-tree-sha1 = "58f25e56b706f95125dcb796f39e1fb01d913a71" 454 | uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688" 455 | version = "0.3.10" 456 | 457 | [[Logging]] 458 | uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" 459 | 460 | [[MacroTools]] 461 | deps = ["Markdown", "Random"] 462 | git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf" 463 | uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" 464 | version = "0.5.9" 465 | 466 | [[Markdown]] 467 | deps = ["Base64"] 468 | uuid = "d6f4376e-aef5-505a-96c1-9c027394607a" 469 | 470 | [[MathOptInterface]] 471 | deps = ["BenchmarkTools", "CodecBzip2", "CodecZlib", "JSON", "LinearAlgebra", "MutableArithmetics", "OrderedCollections", "Printf", "SparseArrays", "Test", "Unicode"] 472 | git-tree-sha1 = "09be99195f42c601f55317bd89f3c6bbaec227dc" 473 | uuid = "b8f27783-ece8-5eb3-8dc8-9495eed66fee" 474 | version = "1.1.1" 475 | 476 | [[MbedTLS]] 477 | deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"] 478 | git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe" 479 | uuid = "739be429-bea8-5141-9913-cc70e7f3736d" 480 | version = "1.0.3" 481 | 482 | [[MbedTLS_jll]] 483 | deps = ["Artifacts", "Libdl"] 484 | uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1" 485 | 486 | [[Measures]] 487 | git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f" 488 | uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e" 489 | version = "0.3.1" 490 | 491 | [[Missings]] 492 | deps = ["DataAPI"] 493 | git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f" 494 | uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28" 495 | version = "1.0.2" 496 | 497 | [[Mmap]] 498 | uuid = "a63ad114-7e13-5084-954f-fe012c677804" 499 | 500 | [[MozillaCACerts_jll]] 501 | uuid = "14a3606d-f60d-562e-9121-12d972cd8159" 502 | 503 | [[MutableArithmetics]] 504 | deps = ["LinearAlgebra", "SparseArrays", "Test"] 505 | git-tree-sha1 = "ba8c0f8732a24facba709388c74ba99dcbfdda1e" 506 | uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0" 507 | version = "1.0.0" 508 | 509 | [[NaNMath]] 510 | git-tree-sha1 = "b086b7ea07f8e38cf122f5016af580881ac914fe" 511 | uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3" 512 | version = "0.3.7" 513 | 514 | [[NetworkOptions]] 515 | uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" 516 | 517 | [[Ogg_jll]] 518 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 519 | git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f" 520 | uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051" 521 | version = "1.3.5+1" 522 | 523 | [[OpenLibm_jll]] 524 | deps = ["Artifacts", "Libdl"] 525 | uuid = "05823500-19ac-5b8b-9628-191a04bc5112" 526 | 527 | [[OpenSSL_jll]] 528 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 529 | git-tree-sha1 = "ab05aa4cc89736e95915b01e7279e61b1bfe33b8" 530 | uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" 531 | version = "1.1.14+0" 532 | 533 | [[OpenSpecFun_jll]] 534 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"] 535 | git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1" 536 | uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e" 537 | version = "0.5.5+0" 538 | 539 | [[Opus_jll]] 540 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 541 | git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720" 542 | uuid = "91d4177d-7536-5919-b921-800302f37372" 543 | version = "1.3.2+0" 544 | 545 | [[OrderedCollections]] 546 | git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c" 547 | uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" 548 | version = "1.4.1" 549 | 550 | [[PCRE_jll]] 551 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 552 | git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488" 553 | uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc" 554 | version = "8.44.0+0" 555 | 556 | [[Parsers]] 557 | deps = ["Dates"] 558 | git-tree-sha1 = "85b5da0fa43588c75bb1ff986493443f821c70b7" 559 | uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0" 560 | version = "2.2.3" 561 | 562 | [[Pixman_jll]] 563 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 564 | git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29" 565 | uuid = "30392449-352a-5448-841d-b1acce4e97dc" 566 | version = "0.40.1+0" 567 | 568 | [[Pkg]] 569 | deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"] 570 | uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" 571 | 572 | [[PlotThemes]] 573 | deps = ["PlotUtils", "Requires", "Statistics"] 574 | git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d" 575 | uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a" 576 | version = "2.0.1" 577 | 578 | [[PlotUtils]] 579 | deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"] 580 | git-tree-sha1 = "bb16469fd5224100e422f0b027d26c5a25de1200" 581 | uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043" 582 | version = "1.2.0" 583 | 584 | [[Plots]] 585 | deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"] 586 | git-tree-sha1 = "90021b03a38f1ae9dbd7bf4dc5e3dcb7676d302c" 587 | uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" 588 | version = "1.27.2" 589 | 590 | [[Preferences]] 591 | deps = ["TOML"] 592 | git-tree-sha1 = "d3538e7f8a790dc8903519090857ef8e1283eecd" 593 | uuid = "21216c6a-2e73-6563-6e65-726566657250" 594 | version = "1.2.5" 595 | 596 | [[Printf]] 597 | deps = ["Unicode"] 598 | uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" 599 | 600 | [[Profile]] 601 | deps = ["Printf"] 602 | uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79" 603 | 604 | [[Qt5Base_jll]] 605 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"] 606 | git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8" 607 | uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1" 608 | version = "5.15.3+0" 609 | 610 | [[REPL]] 611 | deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] 612 | uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" 613 | 614 | [[Random]] 615 | deps = ["Serialization"] 616 | uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" 617 | 618 | [[RecipesBase]] 619 | git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d" 620 | uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01" 621 | version = "1.2.1" 622 | 623 | [[RecipesPipeline]] 624 | deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"] 625 | git-tree-sha1 = "dc1e451e15d90347a7decc4221842a022b011714" 626 | uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c" 627 | version = "0.5.2" 628 | 629 | [[Reexport]] 630 | git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b" 631 | uuid = "189a3867-3050-52da-a836-e630ba90ab69" 632 | version = "1.2.2" 633 | 634 | [[RelocatableFolders]] 635 | deps = ["SHA", "Scratch"] 636 | git-tree-sha1 = "cdbd3b1338c72ce29d9584fdbe9e9b70eeb5adca" 637 | uuid = "05181044-ff0b-4ac5-8273-598c1e38db00" 638 | version = "0.1.3" 639 | 640 | [[Requires]] 641 | deps = ["UUIDs"] 642 | git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7" 643 | uuid = "ae029012-a4dd-5104-9daa-d747884805df" 644 | version = "1.3.0" 645 | 646 | [[SHA]] 647 | uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" 648 | 649 | [[Scratch]] 650 | deps = ["Dates"] 651 | git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda" 652 | uuid = "6c6a2e73-6563-6170-7368-637461726353" 653 | version = "1.1.0" 654 | 655 | [[Serialization]] 656 | uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" 657 | 658 | [[SharedArrays]] 659 | deps = ["Distributed", "Mmap", "Random", "Serialization"] 660 | uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383" 661 | 662 | [[Showoff]] 663 | deps = ["Dates", "Grisu"] 664 | git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de" 665 | uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f" 666 | version = "1.0.3" 667 | 668 | [[Sockets]] 669 | uuid = "6462fe0b-24de-5631-8697-dd941f90decc" 670 | 671 | [[SortingAlgorithms]] 672 | deps = ["DataStructures"] 673 | git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508" 674 | uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c" 675 | version = "1.0.1" 676 | 677 | [[SparseArrays]] 678 | deps = ["LinearAlgebra", "Random"] 679 | uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" 680 | 681 | [[SpecialFunctions]] 682 | deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"] 683 | git-tree-sha1 = "5ba658aeecaaf96923dce0da9e703bd1fe7666f9" 684 | uuid = "276daf66-3868-5448-9aa4-cd146d93841b" 685 | version = "2.1.4" 686 | 687 | [[StaticArrays]] 688 | deps = ["LinearAlgebra", "Random", "Statistics"] 689 | git-tree-sha1 = "4f6ec5d99a28e1a749559ef7dd518663c5eca3d5" 690 | uuid = "90137ffa-7385-5640-81b9-e52037218182" 691 | version = "1.4.3" 692 | 693 | [[Statistics]] 694 | deps = ["LinearAlgebra", "SparseArrays"] 695 | uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" 696 | 697 | [[StatsAPI]] 698 | deps = ["LinearAlgebra"] 699 | git-tree-sha1 = "c3d8ba7f3fa0625b062b82853a7d5229cb728b6b" 700 | uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0" 701 | version = "1.2.1" 702 | 703 | [[StatsBase]] 704 | deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"] 705 | git-tree-sha1 = "8977b17906b0a1cc74ab2e3a05faa16cf08a8291" 706 | uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" 707 | version = "0.33.16" 708 | 709 | [[StructArrays]] 710 | deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"] 711 | git-tree-sha1 = "57617b34fa34f91d536eb265df67c2d4519b8b98" 712 | uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a" 713 | version = "0.6.5" 714 | 715 | [[TOML]] 716 | deps = ["Dates"] 717 | uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76" 718 | 719 | [[TableTraits]] 720 | deps = ["IteratorInterfaceExtensions"] 721 | git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39" 722 | uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c" 723 | version = "1.0.1" 724 | 725 | [[Tables]] 726 | deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"] 727 | git-tree-sha1 = "5ce79ce186cc678bbb5c5681ca3379d1ddae11a1" 728 | uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c" 729 | version = "1.7.0" 730 | 731 | [[Tar]] 732 | deps = ["ArgTools", "SHA"] 733 | uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" 734 | 735 | [[Test]] 736 | deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] 737 | uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" 738 | 739 | [[TranscodingStreams]] 740 | deps = ["Random", "Test"] 741 | git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c" 742 | uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa" 743 | version = "0.9.6" 744 | 745 | [[URIs]] 746 | git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355" 747 | uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4" 748 | version = "1.3.0" 749 | 750 | [[UUIDs]] 751 | deps = ["Random", "SHA"] 752 | uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" 753 | 754 | [[Unicode]] 755 | uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" 756 | 757 | [[UnicodeFun]] 758 | deps = ["REPL"] 759 | git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf" 760 | uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1" 761 | version = "0.4.1" 762 | 763 | [[Unzip]] 764 | git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670" 765 | uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d" 766 | version = "0.1.2" 767 | 768 | [[Wayland_jll]] 769 | deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"] 770 | git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23" 771 | uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89" 772 | version = "1.19.0+0" 773 | 774 | [[Wayland_protocols_jll]] 775 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 776 | git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da" 777 | uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91" 778 | version = "1.25.0+0" 779 | 780 | [[XML2_jll]] 781 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"] 782 | git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a" 783 | uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a" 784 | version = "2.9.12+0" 785 | 786 | [[XSLT_jll]] 787 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"] 788 | git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a" 789 | uuid = "aed1982a-8fda-507f-9586-7b0439959a61" 790 | version = "1.1.34+0" 791 | 792 | [[Xorg_libX11_jll]] 793 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"] 794 | git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527" 795 | uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc" 796 | version = "1.6.9+4" 797 | 798 | [[Xorg_libXau_jll]] 799 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 800 | git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e" 801 | uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec" 802 | version = "1.0.9+4" 803 | 804 | [[Xorg_libXcursor_jll]] 805 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"] 806 | git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd" 807 | uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724" 808 | version = "1.2.0+4" 809 | 810 | [[Xorg_libXdmcp_jll]] 811 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 812 | git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4" 813 | uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05" 814 | version = "1.1.3+4" 815 | 816 | [[Xorg_libXext_jll]] 817 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 818 | git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3" 819 | uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3" 820 | version = "1.3.4+4" 821 | 822 | [[Xorg_libXfixes_jll]] 823 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 824 | git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4" 825 | uuid = "d091e8ba-531a-589c-9de9-94069b037ed8" 826 | version = "5.0.3+4" 827 | 828 | [[Xorg_libXi_jll]] 829 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"] 830 | git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246" 831 | uuid = "a51aa0fd-4e3c-5386-b890-e753decda492" 832 | version = "1.7.10+4" 833 | 834 | [[Xorg_libXinerama_jll]] 835 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"] 836 | git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123" 837 | uuid = "d1454406-59df-5ea1-beac-c340f2130bc3" 838 | version = "1.1.4+4" 839 | 840 | [[Xorg_libXrandr_jll]] 841 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"] 842 | git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631" 843 | uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484" 844 | version = "1.5.2+4" 845 | 846 | [[Xorg_libXrender_jll]] 847 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 848 | git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96" 849 | uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa" 850 | version = "0.9.10+4" 851 | 852 | [[Xorg_libpthread_stubs_jll]] 853 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 854 | git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb" 855 | uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74" 856 | version = "0.1.0+3" 857 | 858 | [[Xorg_libxcb_jll]] 859 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"] 860 | git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6" 861 | uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b" 862 | version = "1.13.0+3" 863 | 864 | [[Xorg_libxkbfile_jll]] 865 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 866 | git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2" 867 | uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a" 868 | version = "1.1.0+4" 869 | 870 | [[Xorg_xcb_util_image_jll]] 871 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] 872 | git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97" 873 | uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b" 874 | version = "0.4.0+1" 875 | 876 | [[Xorg_xcb_util_jll]] 877 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"] 878 | git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1" 879 | uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5" 880 | version = "0.4.0+1" 881 | 882 | [[Xorg_xcb_util_keysyms_jll]] 883 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] 884 | git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00" 885 | uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7" 886 | version = "0.4.0+1" 887 | 888 | [[Xorg_xcb_util_renderutil_jll]] 889 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] 890 | git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e" 891 | uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e" 892 | version = "0.3.9+1" 893 | 894 | [[Xorg_xcb_util_wm_jll]] 895 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] 896 | git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67" 897 | uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361" 898 | version = "0.4.1+1" 899 | 900 | [[Xorg_xkbcomp_jll]] 901 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"] 902 | git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b" 903 | uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4" 904 | version = "1.4.2+4" 905 | 906 | [[Xorg_xkeyboard_config_jll]] 907 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"] 908 | git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d" 909 | uuid = "33bec58e-1273-512f-9401-5d533626f822" 910 | version = "2.27.0+4" 911 | 912 | [[Xorg_xtrans_jll]] 913 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 914 | git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845" 915 | uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" 916 | version = "1.4.0+3" 917 | 918 | [[Zlib_jll]] 919 | deps = ["Libdl"] 920 | uuid = "83775a58-1f1d-513f-b197-d71354ab007a" 921 | 922 | [[Zstd_jll]] 923 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 924 | git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927" 925 | uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" 926 | version = "1.5.2+0" 927 | 928 | [[libass_jll]] 929 | deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 930 | git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" 931 | uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" 932 | version = "0.15.1+0" 933 | 934 | [[libfdk_aac_jll]] 935 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 936 | git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" 937 | uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" 938 | version = "2.0.2+0" 939 | 940 | [[libpng_jll]] 941 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 942 | git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" 943 | uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" 944 | version = "1.6.38+0" 945 | 946 | [[libvorbis_jll]] 947 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] 948 | git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" 949 | uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" 950 | version = "1.3.7+1" 951 | 952 | [[nghttp2_jll]] 953 | deps = ["Artifacts", "Libdl"] 954 | uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" 955 | 956 | [[p7zip_jll]] 957 | deps = ["Artifacts", "Libdl"] 958 | uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" 959 | 960 | [[x264_jll]] 961 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 962 | git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" 963 | uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" 964 | version = "2021.5.5+0" 965 | 966 | [[x265_jll]] 967 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 968 | git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" 969 | uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" 970 | version = "3.5.0+0" 971 | 972 | [[xkbcommon_jll]] 973 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] 974 | git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6" 975 | uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" 976 | version = "0.9.1+5" 977 | -------------------------------------------------------------------------------- /callbacks/Project.toml: -------------------------------------------------------------------------------- 1 | [deps] 2 | GLPK = "60bf3e95-4087-53dc-ae20-288a0d20c6a6" 3 | Gurobi = "2e9cd046-0924-5485-92f1-d5272153d98b" 4 | JuMP = "4076af6c-e467-56ae-b986-b466b2749572" 5 | LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 6 | Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" 7 | Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" 8 | Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" 9 | -------------------------------------------------------------------------------- /callbacks/callbacks_intro.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "f494cf5d", 6 | "metadata": { 7 | "slideshow": { 8 | "slide_type": "slide" 9 | } 10 | }, 11 | "source": [ 12 | "# Callbacks 101" 13 | ] 14 | }, 15 | { 16 | "cell_type": "code", 17 | "execution_count": 1, 18 | "id": "85e97467", 19 | "metadata": { 20 | "slideshow": { 21 | "slide_type": "skip" 22 | } 23 | }, 24 | "outputs": [], 25 | "source": [ 26 | "def fsum(X, f=None):\n", 27 | " \"\"\"Compute the sum of `f(x)` for each element in `X`.\n", 28 | "\n", 29 | " Args:\n", 30 | " X: A sequence of integers\n", 31 | " f: A function with signature `f(x)`, where `x` is an integer.\n", 32 | " `f(x)` should return a number.\n", 33 | " If `f` is not specified, it defaults to the identity function.\n", 34 | " \"\"\"\n", 35 | " res = 0\n", 36 | " for (i, x) in enumerate(X):\n", 37 | " if f is not None:\n", 38 | " res += f(x)\n", 39 | " else:\n", 40 | " res += x\n", 41 | " \n", 42 | " return res" 43 | ] 44 | }, 45 | { 46 | "cell_type": "markdown", 47 | "id": "2c31b731", 48 | "metadata": { 49 | "slideshow": { 50 | "slide_type": "subslide" 51 | } 52 | }, 53 | "source": [ 54 | "Someone defined a function called `fsum`..." 55 | ] 56 | }, 57 | { 58 | "cell_type": "code", 59 | "execution_count": 2, 60 | "id": "f190b103", 61 | "metadata": { 62 | "slideshow": { 63 | "slide_type": "fragment" 64 | } 65 | }, 66 | "outputs": [ 67 | { 68 | "name": "stdout", 69 | "output_type": "stream", 70 | "text": [ 71 | "Help on function fsum in module __main__:\n", 72 | "\n", 73 | "fsum(X, f=None)\n", 74 | " Compute the sum of `f(x)` for each element in `X`.\n", 75 | " \n", 76 | " Args:\n", 77 | " X: A sequence of integers\n", 78 | " f: A function with signature `f(x)`, where `x` is an integer.\n", 79 | " `f(x)` should return a number.\n", 80 | " If `f` is not specified, it defaults to the identity function.\n", 81 | "\n" 82 | ] 83 | } 84 | ], 85 | "source": [ 86 | "help(fsum)" 87 | ] 88 | }, 89 | { 90 | "cell_type": "code", 91 | "execution_count": 3, 92 | "id": "7c324c2b", 93 | "metadata": { 94 | "slideshow": { 95 | "slide_type": "fragment" 96 | } 97 | }, 98 | "outputs": [ 99 | { 100 | "data": { 101 | "text/plain": [ 102 | "10" 103 | ] 104 | }, 105 | "execution_count": 3, 106 | "metadata": {}, 107 | "output_type": "execute_result" 108 | } 109 | ], 110 | "source": [ 111 | "fsum([1, 2, 3, 4])" 112 | ] 113 | }, 114 | { 115 | "cell_type": "markdown", 116 | "id": "1616d10c", 117 | "metadata": { 118 | "slideshow": { 119 | "slide_type": "subslide" 120 | } 121 | }, 122 | "source": [ 123 | "> `fsum(X, f=None)`\n", 124 | "\n", 125 | "The extra argument `f` is a function..." 126 | ] 127 | }, 128 | { 129 | "cell_type": "code", 130 | "execution_count": 4, 131 | "id": "de424da3", 132 | "metadata": { 133 | "slideshow": { 134 | "slide_type": "fragment" 135 | } 136 | }, 137 | "outputs": [], 138 | "source": [ 139 | "def my_callback(x):\n", 140 | " print(f'I am in a callback! (BTW, x={x})')\n", 141 | " return x" 142 | ] 143 | }, 144 | { 145 | "cell_type": "markdown", 146 | "id": "02085ab6", 147 | "metadata": { 148 | "slideshow": { 149 | "slide_type": "fragment" 150 | } 151 | }, 152 | "source": [ 153 | "... and this function is called during the execution of `fsum`" 154 | ] 155 | }, 156 | { 157 | "cell_type": "code", 158 | "execution_count": 5, 159 | "id": "5e4f295f", 160 | "metadata": { 161 | "slideshow": { 162 | "slide_type": "fragment" 163 | } 164 | }, 165 | "outputs": [ 166 | { 167 | "name": "stdout", 168 | "output_type": "stream", 169 | "text": [ 170 | "I am in a callback! (BTW, x=1)\n", 171 | "I am in a callback! (BTW, x=2)\n", 172 | "I am in a callback! (BTW, x=3)\n", 173 | "I am in a callback! (BTW, x=4)\n", 174 | "result = 10\n" 175 | ] 176 | } 177 | ], 178 | "source": [ 179 | "res = fsum([1, 2, 3, 4], my_callback)\n", 180 | "print(f'result = {res}')" 181 | ] 182 | }, 183 | { 184 | "cell_type": "markdown", 185 | "id": "7f59024c", 186 | "metadata": { 187 | "slideshow": { 188 | "slide_type": "subslide" 189 | } 190 | }, 191 | "source": [ 192 | "### Fancier examples\n", 193 | "\n", 194 | "What if we want to sum only _odd_ or _even_ integers?" 195 | ] 196 | }, 197 | { 198 | "cell_type": "code", 199 | "execution_count": 6, 200 | "id": "2f1ffda1", 201 | "metadata": { 202 | "slideshow": { 203 | "slide_type": "fragment" 204 | } 205 | }, 206 | "outputs": [], 207 | "source": [ 208 | "X_all = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n", 209 | "\n", 210 | "# Explicitly keep only odd / even integers\n", 211 | "X_odd = [1, 3, 5, 7, 9]\n", 212 | "X_even = [2, 4, 6, 8, 10] " 213 | ] 214 | }, 215 | { 216 | "cell_type": "code", 217 | "execution_count": 7, 218 | "id": "96b22d65", 219 | "metadata": { 220 | "slideshow": { 221 | "slide_type": "fragment" 222 | } 223 | }, 224 | "outputs": [ 225 | { 226 | "name": "stdout", 227 | "output_type": "stream", 228 | "text": [ 229 | "sum(all) : 55\n", 230 | "sum(odd) : 25\n", 231 | "sum(even) : 30\n" 232 | ] 233 | } 234 | ], 235 | "source": [ 236 | "print(\"sum(all) :\", fsum(X_all))\n", 237 | "print(\"sum(odd) :\", fsum(X_odd))\n", 238 | "print(\"sum(even) :\", fsum(X_even))" 239 | ] 240 | }, 241 | { 242 | "cell_type": "markdown", 243 | "id": "8e9ee4e5", 244 | "metadata": { 245 | "slideshow": { 246 | "slide_type": "subslide" 247 | } 248 | }, 249 | "source": [ 250 | "Could we do that without creating new lists?" 251 | ] 252 | }, 253 | { 254 | "cell_type": "markdown", 255 | "id": "dae1fb69", 256 | "metadata": { 257 | "slideshow": { 258 | "slide_type": "fragment" 259 | } 260 | }, 261 | "source": [ 262 | "Yes! Just define a callback that skips odd/even integers" 263 | ] 264 | }, 265 | { 266 | "cell_type": "code", 267 | "execution_count": 8, 268 | "id": "9d660d55", 269 | "metadata": { 270 | "slideshow": { 271 | "slide_type": "fragment" 272 | } 273 | }, 274 | "outputs": [], 275 | "source": [ 276 | "def even_only(x): \n", 277 | " if (x % 2 == 1):\n", 278 | " print(f'Callback #1: skipping odd element x={x}.')\n", 279 | " return 0\n", 280 | " \n", 281 | " return x\n", 282 | " \n", 283 | "def odd_only(x):\n", 284 | " if (x % 2 == 0):\n", 285 | " print(f'Callback #1: skipping even element x={x}.')\n", 286 | " return 0\n", 287 | " \n", 288 | " return x" 289 | ] 290 | }, 291 | { 292 | "cell_type": "code", 293 | "execution_count": 9, 294 | "id": "51bb9818", 295 | "metadata": { 296 | "slideshow": { 297 | "slide_type": "subslide" 298 | } 299 | }, 300 | "outputs": [ 301 | { 302 | "name": "stdout", 303 | "output_type": "stream", 304 | "text": [ 305 | "Callback #1: skipping odd element x=1.\n", 306 | "Callback #1: skipping odd element x=3.\n", 307 | "Callback #1: skipping odd element x=5.\n", 308 | "Callback #1: skipping odd element x=7.\n", 309 | "Callback #1: skipping odd element x=9.\n", 310 | "sum(even) : 30\n" 311 | ] 312 | } 313 | ], 314 | "source": [ 315 | "res = fsum(X_all, even_only)\n", 316 | "print(f'sum(even) : {res}')" 317 | ] 318 | }, 319 | { 320 | "cell_type": "code", 321 | "execution_count": 10, 322 | "id": "23982e8b", 323 | "metadata": { 324 | "slideshow": { 325 | "slide_type": "fragment" 326 | } 327 | }, 328 | "outputs": [ 329 | { 330 | "name": "stdout", 331 | "output_type": "stream", 332 | "text": [ 333 | "Callback #1: skipping even element x=2.\n", 334 | "Callback #1: skipping even element x=4.\n", 335 | "Callback #1: skipping even element x=6.\n", 336 | "Callback #1: skipping even element x=8.\n", 337 | "Callback #1: skipping even element x=10.\n", 338 | "sum(odd) : 25\n" 339 | ] 340 | } 341 | ], 342 | "source": [ 343 | "res = fsum(X_all, odd_only)\n", 344 | "print(f'sum(odd) : {res}')" 345 | ] 346 | }, 347 | { 348 | "cell_type": "markdown", 349 | "id": "3407a615", 350 | "metadata": { 351 | "slideshow": { 352 | "slide_type": "slide" 353 | } 354 | }, 355 | "source": [ 356 | "# Closures 101\n", 357 | "\n", 358 | "MIP callbacks in Julia and python use so-called _closures_." 359 | ] 360 | }, 361 | { 362 | "cell_type": "markdown", 363 | "id": "2ac7fcc1", 364 | "metadata": { 365 | "slideshow": { 366 | "slide_type": "fragment" 367 | } 368 | }, 369 | "source": [ 370 | " > A closure is a record storing a function together with an environment" 371 | ] 372 | }, 373 | { 374 | "cell_type": "markdown", 375 | "id": "cd24f607", 376 | "metadata": { 377 | "slideshow": { 378 | "slide_type": "fragment" 379 | } 380 | }, 381 | "source": [ 382 | "In English: you can define a function that captures a variable defined _outside_ the function." 383 | ] 384 | }, 385 | { 386 | "cell_type": "markdown", 387 | "id": "6d380d7e", 388 | "metadata": { 389 | "slideshow": { 390 | "slide_type": "subslide" 391 | } 392 | }, 393 | "source": [ 394 | "### `lambda` functions are closures!" 395 | ] 396 | }, 397 | { 398 | "cell_type": "code", 399 | "execution_count": 11, 400 | "id": "1ce18a86", 401 | "metadata": { 402 | "slideshow": { 403 | "slide_type": "fragment" 404 | } 405 | }, 406 | "outputs": [], 407 | "source": [ 408 | "a = 1\n", 409 | "g = lambda x: (a+x)" 410 | ] 411 | }, 412 | { 413 | "cell_type": "code", 414 | "execution_count": 12, 415 | "id": "df51b727", 416 | "metadata": { 417 | "slideshow": { 418 | "slide_type": "fragment" 419 | } 420 | }, 421 | "outputs": [ 422 | { 423 | "data": { 424 | "text/plain": [ 425 | "2" 426 | ] 427 | }, 428 | "execution_count": 12, 429 | "metadata": {}, 430 | "output_type": "execute_result" 431 | } 432 | ], 433 | "source": [ 434 | "g(1)" 435 | ] 436 | }, 437 | { 438 | "cell_type": "code", 439 | "execution_count": 13, 440 | "id": "b08650e3", 441 | "metadata": { 442 | "slideshow": { 443 | "slide_type": "fragment" 444 | } 445 | }, 446 | "outputs": [ 447 | { 448 | "data": { 449 | "text/plain": [ 450 | "4" 451 | ] 452 | }, 453 | "execution_count": 13, 454 | "metadata": {}, 455 | "output_type": "execute_result" 456 | } 457 | ], 458 | "source": [ 459 | "a = 3\n", 460 | "g(1)" 461 | ] 462 | }, 463 | { 464 | "cell_type": "code", 465 | "execution_count": 14, 466 | "id": "160a9770", 467 | "metadata": { 468 | "slideshow": { 469 | "slide_type": "fragment" 470 | } 471 | }, 472 | "outputs": [ 473 | { 474 | "ename": "TypeError", 475 | "evalue": "can only concatenate str (not \"int\") to str", 476 | "output_type": "error", 477 | "traceback": [ 478 | "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", 479 | "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", 480 | "\u001b[0;32m/tmp/ipykernel_17827/1195662531.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"hello\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", 481 | "\u001b[0;32m/tmp/ipykernel_17827/3526735162.py\u001b[0m in \u001b[0;36m\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", 482 | "\u001b[0;31mTypeError\u001b[0m: can only concatenate str (not \"int\") to str" 483 | ] 484 | } 485 | ], 486 | "source": [ 487 | "a = \"hello\"\n", 488 | "g(1)" 489 | ] 490 | }, 491 | { 492 | "cell_type": "markdown", 493 | "id": "37775f8c", 494 | "metadata": { 495 | "slideshow": { 496 | "slide_type": "subslide" 497 | } 498 | }, 499 | "source": [ 500 | "### Closures within a function" 501 | ] 502 | }, 503 | { 504 | "cell_type": "code", 505 | "execution_count": 15, 506 | "id": "9d580b94", 507 | "metadata": { 508 | "slideshow": { 509 | "slide_type": "fragment" 510 | } 511 | }, 512 | "outputs": [], 513 | "source": [ 514 | "def modulo_sum(X):\n", 515 | " # `n` and `U` are defined within `modulo_sum`\n", 516 | " n = 0\n", 517 | " U = []\n", 518 | " \n", 519 | " # The definition of `f` \"captures\" the variables `n` and `U`\n", 520 | " # This allows us to modify `U` within the callback\n", 521 | " def f(x):\n", 522 | " U.append(x)\n", 523 | " return x ** (n)\n", 524 | " \n", 525 | " for k in range(1, 4):\n", 526 | " n = k # <-- this implicitly changes f!\n", 527 | " res = fsum(X, f) # <-- will modify U\n", 528 | " \n", 529 | " print(f'Σ(x^{k}) = {res}')\n", 530 | " \n", 531 | " return U" 532 | ] 533 | }, 534 | { 535 | "cell_type": "code", 536 | "execution_count": 16, 537 | "id": "234e2236", 538 | "metadata": { 539 | "slideshow": { 540 | "slide_type": "fragment" 541 | } 542 | }, 543 | "outputs": [ 544 | { 545 | "name": "stdout", 546 | "output_type": "stream", 547 | "text": [ 548 | "Σ(x^1) = 6\n", 549 | "Σ(x^2) = 14\n", 550 | "Σ(x^3) = 36\n", 551 | "U = [1, 2, 3, 1, 2, 3, 1, 2, 3]\n" 552 | ] 553 | } 554 | ], 555 | "source": [ 556 | "X = range(1, 4)\n", 557 | "U = modulo_sum(X)\n", 558 | "print('U = ', U)" 559 | ] 560 | }, 561 | { 562 | "cell_type": "markdown", 563 | "id": "8fa3bcdb", 564 | "metadata": { 565 | "slideshow": { 566 | "slide_type": "subslide" 567 | } 568 | }, 569 | "source": [ 570 | "## When is this useful / needed?\n", 571 | "\n", 572 | "* To monitor a lower / upper bound within the optimization\n", 573 | "* To keep track of all feasible solution (or just the best)\n", 574 | "* To access user-defined data structures\n", 575 | " --> e.g., a Benders' subproblem" 576 | ] 577 | } 578 | ], 579 | "metadata": { 580 | "celltoolbar": "Slideshow", 581 | "kernelspec": { 582 | "display_name": "Python 3 (ipykernel)", 583 | "language": "python", 584 | "name": "python3" 585 | }, 586 | "language_info": { 587 | "codemirror_mode": { 588 | "name": "ipython", 589 | "version": 3 590 | }, 591 | "file_extension": ".py", 592 | "mimetype": "text/x-python", 593 | "name": "python", 594 | "nbconvert_exporter": "python", 595 | "pygments_lexer": "ipython3", 596 | "version": "3.9.5" 597 | } 598 | }, 599 | "nbformat": 4, 600 | "nbformat_minor": 5 601 | } 602 | -------------------------------------------------------------------------------- /callbacks/tsp_iterative_35.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/mtanneau/or_tutorials/c2b588e4d9af8e390519ba11228d4a7ae69837a0/callbacks/tsp_iterative_35.gif 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