├── .gitignore
├── project
    └── project.exe
├── .idea
    ├── untitled.iml
    ├── misc.xml
    ├── .gitignore
    ├── vcs.xml
    └── modules.xml
├── CMakeLists.txt
├── main.cpp
├── README.md
├── Optimization.h
├── Optimization.cpp
├── LICENSE
└── flowshop-test-10-student.txt


/.gitignore:
--------------------------------------------------------------------------------
1 | # 项目排除路径
2 | /cmake-build-debug/
3 | /cmake-build-release/
4 | /.idea/
5 | 


--------------------------------------------------------------------------------
/project/project.exe:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gzh0821/Optimization_project/HEAD/project/project.exe


--------------------------------------------------------------------------------
/.idea/untitled.iml:
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1 | <?xml version="1.0" encoding="UTF-8"?>
2 | <module classpath="CMake" type="CPP_MODULE" version="4" />


--------------------------------------------------------------------------------
/.idea/misc.xml:
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1 | <?xml version="1.0" encoding="UTF-8"?>
2 | <project version="4">
3 |   <component name="CMakeWorkspace" PROJECT_DIR="$PROJECT_DIR$" />
4 | </project>


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/.idea/.gitignore:
--------------------------------------------------------------------------------
1 | # 默认忽略的文件
2 | /shelf/
3 | /workspace.xml
4 | # 基于编辑器的 HTTP 客户端请求
5 | /httpRequests/
6 | # Datasource local storage ignored files
7 | /dataSources/
8 | /dataSources.local.xml
9 | 


--------------------------------------------------------------------------------
/.idea/vcs.xml:
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1 | <?xml version="1.0" encoding="UTF-8"?>
2 | <project version="4">
3 |   <component name="VcsDirectoryMappings">
4 |     <mapping directory="$PROJECT_DIR$" vcs="Git" />
5 |   </component>
6 | </project>


--------------------------------------------------------------------------------
/CMakeLists.txt:
--------------------------------------------------------------------------------
1 | cmake_minimum_required(VERSION 3.22)
2 | project(Optimization_project)
3 | 
4 | set(CMAKE_CXX_STANDARD 17)
5 | set (CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -static-libstdc++ -static-libgcc")
6 | 
7 | add_executable(Optimization_project main.cpp Optimization.h Optimization.cpp)
8 | 


--------------------------------------------------------------------------------
/.idea/modules.xml:
--------------------------------------------------------------------------------
1 | <?xml version="1.0" encoding="UTF-8"?>
2 | <project version="4">
3 |   <component name="ProjectModuleManager">
4 |     <modules>
5 |       <module fileurl="file://$PROJECT_DIR$/.idea/untitled.iml" filepath="$PROJECT_DIR$/.idea/untitled.iml" />
6 |     </modules>
7 |   </component>
8 | </project>


--------------------------------------------------------------------------------
/main.cpp:
--------------------------------------------------------------------------------
 1 | //    Copyright 2022 Gzh0821/Gaozih
 2 | //
 3 | //    Licensed under the Apache License, Version 2.0 (the "License");
 4 | //    you may not use this file except in compliance with the License.
 5 | //    You may obtain a copy of the License at
 6 | //
 7 | //      http://www.apache.org/licenses/LICENSE-2.0
 8 | //
 9 | //    Unless required by applicable law or agreed to in writing, software
10 | //    distributed under the License is distributed on an "AS IS" BASIS,
11 | //    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 | //    See the License for the specific language governing permissions and
13 | //    limitations under the License.
14 | 
15 | #include "Optimization.h"
16 | #include <iostream>
17 | #include <thread>
18 | #include <chrono>
19 | //主函数
20 | using namespace std;
21 | using namespace chrono;
22 | 
23 | int cal_func(Solution &&s, int compare_ans) {
24 |     auto startTime = system_clock::now();
25 |     int ans = s.SA(make_tuple(250, 5, 0.95, 25));//SA算法,参数设置分别为起始温度,温度阈值,退火速度和允许相同数
26 |     //int ans = s.HCS();//HCS算法
27 |     auto endTime = system_clock::now();
28 |     if (ans <= compare_ans) {//若结果比上一次优，输出
29 |         cout << ans << endl;
30 |         for (auto &i: s.next_order)
31 |             cout << i << ',';
32 |         cout << endl << "Time:" << duration_cast<milliseconds>(endTime - startTime).count() << endl;//时间
33 |     }
34 |     return min(ans, compare_ans);
35 | }
36 | 
37 | int main(int argc, char *argv[]) {
38 |     int id, last_ans = INT_MAX;
39 |     if (argc == 1)
40 |         cin >> id;
41 |     else
42 |         id = strtol(argv[1], nullptr, 10);
43 |     Solution sol;
44 |     sol.setup(id);//设置id
45 |     auto startTime = system_clock::now();
46 |     for (int i = 0; i < 20; ++i) {
47 |         Solution s(sol);//复制构造Solution对象
48 |         last_ans = cal_func(move(s), last_ans);//计算
49 |     }
50 |     auto endTime = system_clock::now();
51 |     cout << endl << "TotalTime:" << duration_cast<milliseconds>(endTime - startTime).count() << endl;//输出总时间
52 |     cout << "Press any button to exit." << endl;
53 | }
54 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | # SA and HCS Optimization Project
 2 | 
 3 | 一个使用模拟退火算法和登山算法解决流水车间调度问题的最优化实验。
 4 | 
 5 | 基于`C++ 17`标准库。
 6 | 
 7 | ![](https://img.shields.io/badge/author-Gaozih-%2366ccff)
 8 | ![](https://img.shields.io/github/license/Gzh0821/Optimization_project)
 9 | ![](https://img.shields.io/github/stars/Gzh0821/Optimization_project)
10 | 
11 | 
12 | ## 简介
13 | - 本项目来源于最优化方法课程的大作业。
14 | 
15 | - 本项目实现了使用`HCS`（登山算法）和`SA`（模拟退火算法）解决流水车间调度问题。
16 | 
17 | - 仅使用C++17标准库，可直接编译运行。
18 | 
19 | - 代码重要处均附有注释，易于复现和修改。
20 | 
21 | ## 项目结构
22 | - `Optimization.h`为项目头文件，包含解决方案类声明，算法参数格式声明和随机数生成器。
23 | - `Optimization.cpp`为项目解决方案文件，包含`SA`算法，`HCS`算法的实现及文件预处理方法。
24 | - `main.cpp`为主文件，包含项目入口`main`函数和调用算法的`cal_func`函数。
25 | 
26 | ## 选择数据集
27 | - 本项目使用给出的数据集`flowshop-test-10-student.txt`，包含11组原始数据。
28 | - 执行程序时，需输入数字0-10选择要处理的数据组。
29 | - 或调用程序时直接输入数字参数。
30 | 
31 | ## 简易的复现
32 | ### 直接运行
33 | - 本项目已使用默认参数（SA算法，起始温度=250,温度阈值=5,退火速度=0.95,允许相同数=2），重复20次,
34 | 构建了`exe`可执行文件（`Windows`平台），可在`project`目录下，打开`cmd`命令行窗口，输入`.\project.exe`运行程序。
35 | 
36 | ### 使用CMake构建（建议）
37 | - 使用项目内`CMakeLists.txt`配置文件即可。
38 | 
39 | ### 使用GNU-g++
40 | 
41 | - 使用g++编译文件。
42 | ```
43 | g++ main.cpp Optimization.cpp -O3 -std=c++17 -o Test.exe
44 | ```
45 | - 将生成的`Test.exe`置入项目的`project`目录下，并在`project`目录下打开命令行窗口，输入`.\Test.exe`运行程序。
46 | 
47 | ## 计算结果
48 | - 程序会打印每次算出的最优（最短时间）结果，仅需查看最后一次输出的结果即可。
49 | - 输出结果格式如下（以第0组数据为例）：
50 | ```
51 | 7038
52 | 7,4,8,2,6,1,0,3,10,9,5,
53 | Time:59
54 | ```
55 | - 第一行为计算出的最短时间，即工件最优顺序的总加工时间为7038。
56 | - 第二行为此时间对应的工件加工顺序。工件编号按原始数据顺序。从0号开始。
57 | - 第三行为此次计算所耗费的时间，单位为毫秒（ms）。
58 | 
59 | ## 修改算法和参数
60 | - 若需修改每次执行程序时算法的执行次数，只需修改`main.cpp`中的`main`函数：
61 | ```cpp
62 |     for (int i = 0; i < 20; ++i) {
63 |         Solution s(sol);//复制构造Solution对象
64 |         last_ans = cal_func(move(s), last_ans);//计算
65 |     }
66 | ```
67 | - 将`i < 20`中的20修改为需要的值即可。
68 | ---------
69 | - 若需修改使用的算法或参数，只需修改`main.cpp`中的`cal_func`函数：
70 | ```cpp
71 |     int ans = s.SA(make_tuple(250, 5, 0.95, 25));//SA算法,参数设置分别为起始温度,温度阈值,退火速度和允许相同数
72 |     //int ans = s.HCS();//HCS算法
73 | ```
74 | - 若需修改`SA`算法的参数，修改`make_tuple()`内的四个参数即可。
75 | - 若需使用`HCS`算法，将`s.SA`所在行注释掉，并解除`s.HCS`所在行注释即可。
76 | 


--------------------------------------------------------------------------------
/Optimization.h:
--------------------------------------------------------------------------------
 1 | //    Copyright 2022 Gzh0821/Gaozih
 2 | //
 3 | //    Licensed under the Apache License, Version 2.0 (the "License");
 4 | //    you may not use this file except in compliance with the License.
 5 | //    You may obtain a copy of the License at
 6 | //
 7 | //      http://www.apache.org/licenses/LICENSE-2.0
 8 | //
 9 | //    Unless required by applicable law or agreed to in writing, software
10 | //    distributed under the License is distributed on an "AS IS" BASIS,
11 | //    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 | //    See the License for the specific language governing permissions and
13 | //    limitations under the License.
14 | 
15 | #pragma once
16 | //最优化头文件
17 | #include <vector>
18 | #include <tuple>
19 | #include <random>
20 | #include <set>
21 | #include <memory>
22 | #include <ctime>
23 | 
24 | using para_format = std::tuple<double, double, double, int>;//SA参数格式
25 | 
26 | class random_num_engine {//随机数生成引擎
27 |     std::random_device rand_source;//随机熵源
28 |     std::mt19937_64 rand_eng;//64位梅森环绕生成器
29 | public:
30 |     random_num_engine() : rand_source(), rand_eng(time(nullptr) + rand_source()) {};
31 |     //下为函数对象定义
32 |     int operator()(int max) {//生成0-max的随机整数
33 |         rand_eng.seed(rand_eng() ^ time(nullptr) + rand_source());
34 |         return std::uniform_int_distribution<>(0, max - 1)(rand_eng);
35 |     }
36 | 
37 |     double operator()(double start = 0.0, double end = 1.0) {//生成start-end的随机浮点数
38 |         rand_eng.seed(rand_eng() ^ time(nullptr) + rand_source());
39 |         return std::uniform_real_distribution<>(start, end)(rand_eng);
40 |     }
41 | 
42 | };
43 | 
44 | class Solution {//解决方案类
45 | public:
46 |     static constexpr double e_v = 2.71828;//编译常量e
47 | 
48 |     Solution() : order_record(std::make_unique<std::set<std::vector<int>>>()), machines(0), workpieces(0) {}
49 | 
50 |     Solution(const Solution &other) : machines(other.machines), workpieces(other.workpieces),
51 |                                       cost_table(other.cost_table),
52 |                                       order_record(std::make_unique<std::set<std::vector<int>>>()) {}
53 | 
54 |     ~Solution() {
55 |         order_record.reset();
56 |     }
57 | 
58 |     void setup(int id);
59 | 
60 |      [[maybe_unused, nodiscard]]  int HCS();
61 | 
62 |     [[maybe_unused, nodiscard]] int SA(para_format input_para);
63 | 
64 |     friend int cal_func(Solution &&,int);
65 | private:
66 |     random_num_engine get_random_num;//随机数模块
67 |     int machines, workpieces;     //机器数量和工件数量
68 |     std::vector<int> last_order, order, next_order;//当前序列
69 |     std::vector<std::vector<int>> cost_table;//工件耗时表
70 |     std::unique_ptr<std::set<std::vector<int>>> order_record;//独占指针指向存储序列的红黑树
71 | 
72 | 
73 |     inline void change_random_order();//随机换序
74 | 
75 |     inline void change_adjacent_order(int wa);//相邻两点调换
76 | 
77 |     int calc_order_time();//计算函数模块
78 | };


--------------------------------------------------------------------------------
/Optimization.cpp:
--------------------------------------------------------------------------------
  1 | //    Copyright 2022 Gzh0821/Gaozih
  2 | //
  3 | //    Licensed under the Apache License, Version 2.0 (the "License");
  4 | //    you may not use this file except in compliance with the License.
  5 | //    You may obtain a copy of the License at
  6 | //
  7 | //      http://www.apache.org/licenses/LICENSE-2.0
  8 | //
  9 | //    Unless required by applicable law or agreed to in writing, software
 10 | //    distributed under the License is distributed on an "AS IS" BASIS,
 11 | //    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 12 | //    See the License for the specific language governing permissions and
 13 | //    limitations under the License.
 14 | 
 15 | #include "Optimization.h"
 16 | #include <fstream>
 17 | #include <algorithm>
 18 | //最优化实现
 19 | using namespace std;
 20 | 
 21 | void Solution::setup(int id) //预处理数据读入
 22 | {
 23 |     string line;
 24 |     int id_now;
 25 |     ifstream fin("../flowshop-test-10-student.txt");
 26 |     if (!fin.is_open()) {
 27 |         throw ios_base::failure("unable to open file!");
 28 |     }
 29 |     while (getline(fin, line)) {
 30 |         if(line.front()!='+')
 31 |             continue;
 32 |         fin >> line >> id_now;
 33 |         if (id_now == id)
 34 |         {
 35 |             fin >> workpieces >> machines;//存入工件与机器数量
 36 |             cost_table.resize(workpieces);
 37 |             int _;
 38 |             for (auto &&i: cost_table) {
 39 |                 i.resize(machines);
 40 |                 for (int &j: i)
 41 |                     fin >> _ >> j;//写入工件耗时表
 42 |             }
 43 |             fin.close();
 44 |             return;
 45 |         }
 46 |     }
 47 | }
 48 | 
 49 | void Solution::change_random_order() {
 50 |     int a = get_random_num(workpieces), b = get_random_num(workpieces);
 51 |     swap(order[a], order[b]);//随机交换
 52 | }
 53 | 
 54 | void Solution::change_adjacent_order(int wa) {
 55 |     if (wa < workpieces - 1 && wa >= 0) {
 56 |         swap(order[wa], order[wa + 1]);//交换相邻两项
 57 |     } else
 58 |         throw out_of_range("Out of range in order!");
 59 | }
 60 | 
 61 | 
 62 | int Solution::calc_order_time() {
 63 |     vector<int> order_time_dp(workpieces); //记录每个工件在当前步骤机器上加工结束时的时间
 64 |     order_time_dp.front() = cost_table[order.front()].front();
 65 |     for (int i = 1; i < workpieces; ++i)
 66 |         order_time_dp[i] = order_time_dp[i - 1] + cost_table[order[i]][0];
 67 |     for (int i = 1; i < machines; ++i) {
 68 |         order_time_dp[0] += cost_table[order[0]][i];
 69 |         for (int j = 1; j < workpieces; ++j) {
 70 |             int res = max(order_time_dp[j - 1], order_time_dp[j]);
 71 |             order_time_dp[j] = res + cost_table[order[j]][i]; //动态规划计算当前序列耗时
 72 |         }
 73 |     }
 74 |     return order_time_dp[workpieces - 1];
 75 | }
 76 | 
 77 | [[maybe_unused]] int Solution::HCS() {
 78 |     int last = INT_MAX; //上一次计算结果
 79 |     next_order.reserve(workpieces);
 80 |     order.reserve(workpieces);
 81 |     last_order.reserve(workpieces);//预分配空间
 82 |     for (int i = 0; i < workpieces; ++i)
 83 |         order.emplace_back(i);
 84 |     for (int i = 0; i < workpieces; ++i) //随机化初始顺序
 85 |         change_random_order();
 86 |     int res = calc_order_time();
 87 |     next_order = order;
 88 |     while (last > res) //邻域内所有解均小于上次迭代解则结束迭代
 89 |     {
 90 |         int now_min = res;
 91 |         last = res;
 92 |         last_order = order;
 93 |         for (int i = 0; i < workpieces - 1; i++) //计算邻域，即交换相邻位置，并取最小值
 94 |         {
 95 |             change_adjacent_order(i);
 96 |             res = calc_order_time();
 97 |             if (res < now_min) {
 98 |                 now_min = res;
 99 |                 next_order = order;
100 |             }
101 |             order = last_order; //还原初始序列，继续迭代
102 |         }
103 |         res = now_min;//存储结果
104 |         order = next_order;
105 |     }
106 |     return res;
107 | }
108 | 
109 | [[maybe_unused]] int Solution::SA(para_format input_para) //模拟退火算法
110 | {
111 |     auto &&[T, T_ed, velocity, same_threshold] = input_para;//参数元组，分别为起始温度,温度阈值,退火速度和允许相同数
112 |     next_order.reserve(workpieces);
113 |     order.reserve(workpieces);
114 |     last_order.reserve(workpieces);
115 |     int last = INT_MAX, res; //last用于记录上次迭代结果
116 |     for (int i = 0; i < workpieces; ++i)
117 |         order.emplace_back(i);
118 |     for (int i = 0; i < workpieces; ++i)
119 |         change_random_order();
120 |     last_order = order;
121 |     while (T > T_ed) //温度低于阈值时推出
122 |     {
123 |         int count_same = 0, count_cycle = 1; //记录循环次数和相同解重复次数
124 |         T *= velocity; //降温
125 |         do {
126 |             res = calc_order_time();
127 |             if (res < last) {
128 |                 last = res;
129 |                 count_same = 0;
130 |                 next_order = order;
131 |             } else if (res == last)
132 |                 ++count_same;
133 |             else
134 |             {
135 |                 double randtmp = get_random_num(), threshold = pow(e_v, ((last - res) / T)); // log(count_cycle+2)用于规避临近值反复
136 |                 if (randtmp < threshold) {
137 |                     last = res;
138 |                     count_same = 0;
139 |                     next_order = order;
140 |                 } else {
141 |                     ++count_same;
142 |                     order = last_order;
143 |                 }//使用Metropolis准则判断是否接受
144 |             }
145 |             order_record->emplace(order);//记录当前序列
146 |             last_order = order;
147 |             do {
148 |                 change_random_order();//获得从未出现的序列
149 |             } while (order_record->count(order));
150 | 
151 |             ++count_cycle;
152 |         } while (count_same < same_threshold &&
153 |                  count_cycle < workpieces * 250); //结束迭代,count_cycle为了防止出现循环跳跃
154 |     }
155 |     order_record->clear();//清除集合内的序列
156 |     return last;
157 | }
158 | 
159 | 


--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
  1 |                                  Apache License
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--------------------------------------------------------------------------------
/flowshop-test-10-student.txt:
--------------------------------------------------------------------------------
  1 | +++++++++++++++++++++++++++++
  2 | instance 0
  3 | 11 5
  4 | 0 375 1  12 2 142 3 245 4 412
  5 | 0 632 1 452 2 758 3 278 4 398
  6 | 0  12 1 876 2 124 3 534 4 765
  7 | 0 460 1 542 2 523 3 120 4 499
  8 | 0 528 1 101 2 789 3 124 4 999
  9 | 0 796 1 245 2 632 3 375 4 123
 10 | 0 532 1 230 2 543 3 896 4 452
 11 | 0  14 1 124 2 214 3 543 4 785
 12 | 0 257 1 527 2 753 3 210 4 463
 13 | 0 896 1 896 2 214 3 258 4 259
 14 | 0 532 1 302 2 501 3 765 4 988
 15 | +++++++++++++++++++++++++++++
 16 | instance 1
 17 | 8 8
 18 | 0 456 1 654 2 852 3 145 4 632 5 425 6 214 7 654
 19 | 0 789 1 123 2 369 3 678 4 581 5 396 6 123 7 789
 20 | 0 654 1 123 2 632 3 965 4 475 5 325 6 456 7 654
 21 | 0 321 1 456 2 581 3 421 4  32 5 147 6 789 7 123
 22 | 0 456 1 789 2 472 3 365 4 536 5 852 6 654 7 123
 23 | 0 789 1 654 2 586 3 824 4 325 5  12 6 321 7 456
 24 | 0 654 1 321 2 320 3 758 4 863 5 452 6 456 7 789
 25 | 0 789 1 147 2 120 3 639 4  21 5 863 6 789 7 654
 26 | +++++++++++++++++++++++++++++
 27 | instance 2
 28 | 13 4
 29 | 0 654 1 147 2 345 3 447
 30 | 0 321 1 520 2 789 3 702
 31 | 0  12 1 147 2 630 3 255
 32 | 0 345 1 586 2 214 3 866
 33 | 0 678 1 532 2 275 3 332
 34 | 0 963 1 145 2 302 3 225
 35 | 0  25 1  24 2 142 3 589
 36 | 0 874 1 517 2  24 3 996
 37 | 0 114 1 896 2 520 3 541
 38 | 0 785 1 543 2 336 3 234
 39 | 0 203 1 210 2 699 3 784
 40 | 0 696 1 784 2 855 3 512
 41 | 0 302 1 512 2 221 3 345
 42 | +++++++++++++++++++++++++++++
 43 | instance 3
 44 | 12 5
 45 | 0 210 1 145 2 114 3 401 4 876
 46 | 0 123 1 214 2 332 3 856 4 543
 47 | 0 124 1 247 2 753 3 214 4 543
 48 | 0 210 1 785 2 966 3 147 4 876
 49 | 0 543 1 532 2 100 3 321 4 789
 50 | 0 876 1 632 2 588 3 896 4 456
 51 | 0 789 1 854 2 225 3 528 4 123
 52 | 0 876 1 698 2 322 3 546 4 456
 53 | 0 543 1 145 2 669 3 325 4 789
 54 | 0 456 1 752 2 144 3 321 4 210
 55 | 0 789 1 143 2 755 3 427 4 123
 56 | 0 456 1 537 2 123 3 214 4 234
 57 | +++++++++++++++++++++++++++++
 58 | instance 4
 59 | 14 4
 60 | 0 456 1 856 2 963 3 696
 61 | 0 789 1 930 2  21 3 320
 62 | 0 630 1 214 2 475 3 142
 63 | 0 214 1 257 2 320 3 753
 64 | 0 573 1 896 2 124 3 214
 65 | 0 218 1 532 2 752 3 528
 66 | 0 653 1 142 2 147 3 653
 67 | 0 214 1 547 2 532 3 214
 68 | 0 204 1 865 2 145 3 527
 69 | 0 785 1 321 2 763 3 536
 70 | 0 696 1 124 2 214 3 214
 71 | 0 532 1  12 2 257 3 528
 72 | 0  12 1 345 2 854 3 888
 73 | 0 457 1 678 2 123 3 999
 74 | +++++++++++++++++++++++++++++
 75 | instance 5
 76 | 10 6
 77 | 0 333 1 991 2 996 3 123 4 145 5 234
 78 | 0 333 1 111 2 663 3 456 4 785 5 532
 79 | 0 252 1 222 2 222 3 789 4 214 5 586
 80 | 0 222 1 204 2 114 3 876 4 752 5 532
 81 | 0 255 1 477 2 123 3 543 4 143 5 142
 82 | 0 555 1 566 2 456 3 210 4 698 5 573
 83 | 0 558 1 899 2 789 3 124 4 532 5  12
 84 | 0 888 1 965 2 876 3 537 4 145 5  14
 85 | 0 889 1 588 2 543 3 854 4 247 5 527
 86 | 0 999 1 889 2 210 3 632 4 451 5 856
 87 | +++++++++++++++++++++++++++++
 88 | instance 6
 89 | 20 10
 90 | 0  96  1  80  2  56  3  48  4  14  5  88  6  50  7  15  8  67  9  65
 91 | 0  25  1  44  2  10  3  41  4  64  5  52  6  19  7  28  8  72  9  27
 92 | 0  76  1  62  2  48  3  54  4  47  5  35  6  72  7  54  8  27  9  56
 93 | 0  41  1   6  2   3  3  33  4  77  5  44  6  43  7  50  8  19  9  43
 94 | 0  65  1  91  2  75  3  30  4  47  5  55  6  51  7   1  8  36  9  73
 95 | 0  81  1  69  2  65  3  93  4  61  5   3  6  44  7  17  8   6  9  14
 96 | 0  49  1   9  2  12  3  54  4  75  5  66  6  34  7  12  8  32  9   6
 97 | 0  93  1  89  2  31  3  14  4  37  5  57  6  33  7  96  8  32  9  45
 98 | 0  39  1  83  2  55  3  32  4  18  5   9  6  93  7  65  8  75  9  73
 99 | 0  52  1  46  2  64  3  13  4  54  5  62  6  45  7  80  8  19  9  65
100 | 0  72  1   4  2  29  3  94  4  85  5  51  6  29  7  65  8  50  9  16
101 | 0  55  1  43  2  47  3  32  4  87  5  97  6  41  7  86  8  17  9  30
102 | 0   8  1  91  2  81  3  93  4  14  5  86  6  64  7  42  8  70  9   3
103 | 0  27  1  11  2  94  3  38  4  33  5  67  6   8  7  55  8  99  9  18
104 | 0  34  1  86  2  87  3  10  4  64  5  30  6  47  7  51  8  69  9  26
105 | 0  15  1   5  2  39  3  23  4  16  5   1  6  57  7  55  8  62  9  35
106 | 0  59  1  55  2  43  3  49  4  23  5  25  6  51  7  72  8   9  9   1
107 | 0  93  1   4  2  43  3   5  4  84  5  55  6  22  7  78  8  31  9  11
108 | 0  20  1  91  2  73  3  41  4 100  5  38  6  75  7   9  8  76  9  71
109 | 0  59  1  13  2  93  3  26  4  11  5   7  6  66  7  42  8  54  9  99
110 | +++++++++++++++++++++++++++++
111 | instance 7
112 | 20 15
113 | 0  60  1  70  2  51  3  74  4   6  5   4  6  27  7   5  8  30  9  79 10  58 11  49 12  91 13  20 14  63
114 | 0  79  1  53  2  74  3  87  4  18  5  16  6  44  7  95  8  41  9   3 10  20 11  59 12  74 13  33 14  42
115 | 0  94  1  57  2  19  3  77  4  70  5  90  6  36  7  73  8  37  9  24 10  28 11  23 12  16 13  97 14  75
116 | 0  23  1   3  2  82  3  87  4  45  5  54  6  76  7  60  8  61  9  98 10  68 11  14 12  10 13  17 14   9
117 | 0  38  1  32  2  68  3   7  4  49  5  49  6  72  7  31  8  70  9   8 10  26 11  81 12  86 13  60 14  74
118 | 0  27  1  14  2  77  3  20  4  92  5  74  6  33  7  44  8  43  9  52 10  10 11  81 12  30 13  93 14  71
119 | 0  23  1  55  2  67  3   6  4  64  5  68  6  19  7  73  8  92  9  96 10   3 11  21 12  51 13   3 14  25
120 | 0  41  1  91  2  90  3  43  4  37  5  96  6  99  7  46  8  41  9  51 10  33 11  49 12  17 13  64 14  68
121 | 0  92  1  44  2  12  3  37  4  75  5  20  6  14  7  43  8  26  9  64 10  85 11  14 12  54 13  54 14  97
122 | 0  69  1  69  2  71  3  54  4  36  5  96  6   3  7  27  8  16  9  61 10  94 11  96 12  85 13  34 14  34
123 | 0  16  1  38  2  36  3  48  4  92  5  20  6  55  7  89  8  75  9  57 10  89 11  62 12  36 13  36 14  69
124 | 0  37  1  19  2  55  3   2  4  96  5  10  6  81  7  29  8   2  9  34 10  83 11   1 12  45 13  23 14  64
125 | 0   4  1  57  2  26  3  29  4  91  5  94  6  21  7  30  8  30  9  51 10  31 11  62 12  53 13  29 14  51
126 | 0  55  1  65  2  21  3  99  4  27  5  53  6  42  7  78  8  63  9  25 10  86 11  60 12  64 13  76 14  69
127 | 0  17  1  70  2  33  3  81  4  24  5  35  6  77  7  21  8  83  9  19 10  44 11  70 12  90 13  34 14  90
128 | 0  76  1  94  2  54  3  34  4  12  5  28  6  24  7   5  8  59  9   4 10  46 11  93 12  32 13  78 14  48
129 | 0  81  1  49  2  83  3  72  4  31  5  72  6  91  7   8  8  40  9  93 10  84 11  63 12  67 13  36 14  84
130 | 0  63  1  70  2  14  3  85  4  66  5  41  6  64  7  54  8  10  9  65 10  26 11  58 12  20 13  64 14  41
131 | 0  98  1  39  2  91  3   5  4  55  5  28  6  43  7  97  8  35  9  23 10  50 11  99 12  59 13  63 14  95
132 | 0  47  1  48  2  89  3  33  4  99  5  10  6  54  7  94  8  52  9  44 10  73 11  67 12  44 13  36 14  98
133 | +++++++++++++++++++++++++++++
134 | instance 8
135 | 20  5
136 | 0  34  1   6  2  63  3  85  4  60
137 | 0  11  1  65  2   4  3   1  4  73
138 | 0  63  1  67  2   3  3  73  4 100
139 | 0  22  1  46  2  88  3   1  4  66
140 | 0  76  1   4  2  34  3   9  4  76
141 | 0  20  1  22  2   7  3   3  4  28
142 | 0  44  1  30  2  55  3  68  4  92
143 | 0  29  1  89  2  12  3  96  4  71
144 | 0  54  1  12  2  21  3  74  4   2
145 | 0  62  1  96  2  61  3  79  4  53
146 | 0  50  1  13  2  48  3  40  4  37
147 | 0  89  1  69  2  57  3   1  4  70
148 | 0  50  1  56  2   8  3  67  4  46
149 | 0  32  1  24  2  23  3  87  4  62
150 | 0  12  1  88  2  64  3  14  4  13
151 | 0  59  1  78  2  95  3  59  4  48
152 | 0  41  1  20  2  83  3  65  4  20
153 | 0  94  1  48  2  26  3  93  4   3
154 | 0  28  1  59  2  10  3  81  4  20
155 | 0  66  1  33  2  34  3   8  4   5
156 | +++++++++++++++++++++++++++++
157 | instance 9
158 | 20 15
159 | 0  59  1  11  2   4  3  79  4  94  5  31  6  74  7  82  8  53  9  51 10  19 11  31 12  46 13  47 14  10
160 | 0  72  1  54  2  36  3   3  4  59  5  23  6  40  7  59  8  89  9  37 10  85 11  67 12  39 13  65 14  60
161 | 0  92  1  26  2  15  3  81  4  86  5  56  6  92  7  47  8  93  9  21 10  40 11  77 12  84 13  10 14  91
162 | 0  49  1  27  2  99  3  64  4  30  5  51  6  26  7  89  8  40  9  64 10  60 11  67 12  67 13 100 14   3
163 | 0  42  1  12  2  55  3  62  4  37  5  24  6  24  7  42  8  41  9  88 10  14 11  33 12  85 13   4 14  20
164 | 0  21  1  61  2  52  3  49  4  44  5  98  6  26  7  68  8  61  9  25 10   6 11  46 12  75 13  37 14   5
165 | 0  80  1  99  2  88  3  83  4  11  5  93  6  47  7  80  8 100  9  87 10  84 11  17 12  43 13  93 14  58
166 | 0   4  1  54  2  43  3  63  4  44  5  78  6  44  7  39  8  76  9  99 10  29 11  38 12  14 13  75 14  25
167 | 0  46  1  23  2  54  3  77  4  60  5  53  6  42  7  72  8  90  9  11 10  22 11  68 12  94 13  24 14  14
168 | 0  23  1  84  2  92  3  94  4   8  5  10  6  77  7  58  8  64  9  95 10  55 11  15 12  19 13  62 14  67
169 | 0  53  1  91  2  80  3   8  4  41  5  89  6   3  7  87  8  57  9  75 10  37 11   8 12  23 13  88 14  65
170 | 0  72  1  17  2  53  3  36  4   9  5  24  6  80  7   9  8  28  9  60 10  94 11  99 12  67 13  10 14  44
171 | 0   5  1  44  2  96  3  37  4  21  5  44  6  49  7  13  8  86  9  74 10  89 11   3 12  82 13  85 14  61
172 | 0  80  1  19  2  73  3  95  4  78  5  78  6  31  7  13  8  50  9  93 10  98 11  80 12  46 13   9 14  37
173 | 0   7  1  16  2  46  3  82  4  97  5  82  6  41  7  21  8  11  9  50 10   5 11  28 12  95 13  84 14  45
174 | 0  68  1  73  2  57  3   4  4  66  5  71  6  87  7  43  8  60  9  56 10  30 11  21 12  14 13  37 14  61
175 | 0  77  1   2  2   1  3  82  4   2  5  49  6  89  7  27  8  34  9  52 10  85 11  26 12  80 13  87 14  58
176 | 0  17  1  86  2  32  3  35  4   6  5  50  6  53  7  39  8  94  9  89 10  22 11  75 12  59 13  74 14  27
177 | 0  61  1  14  2  70  3  58  4  24  5  36  6  70  7  57  8  31  9 100 10  21 11  76 12  54 13  94 14  57
178 | 0  29  1   6  2   6  3  12  4  78  5  28  6  40  7  13  8  61  9  19 10  39 11  98 12  69 13  14 14   3
179 | +++++++++++++++++++++++++++++
180 | instance 10
181 | 50 10
182 | 0 100  1  72  2  76  3 100  4  16  5   9  6   5  7  87  8  34  9  15
183 | 0  19  1   3  2  19  3  68  4  29  5  22  6  16  7  13  8  87  9  70
184 | 0  70  1  56  2  39  3  71  4  29  5  91  6 100  7  86  8  88  9  99
185 | 0  50  1  93  2 100  3  71  4  84  5  64  6  67  7  29  8  28  9  81
186 | 0  80  1  97  2   3  3  10  4  14  5  32  6  92  7  67  8  72  9  68
187 | 0  47  1  59  2  29  3   3  4  26  5  20  6  50  7  26  8   1  9  70
188 | 0  40  1  63  2  69  3  21  4  56  5  73  6  56  7  10  8  46  9  40
189 | 0  84  1  80  2  68  3  82  4   4  5  45  6 100  7  96  8  29  9  67
190 | 0  85  1  46  2  59  3  35  4  68  5  84  6  89  7  18  8  97  9  58
191 | 0  60  1  60  2   2  3  50  4  90  5  20  6  78  7  56  8  62  9  27
192 | 0  78  1  64  2  21  3   5  4  85  5  55  6  15  7  23  8  36  9  87
193 | 0  98  1  31  2  42  3  73  4  83  5  48  6  71  7  49  8  72  9  30
194 | 0   4  1  57  2  30  3  11  4  67  5   4  6  82  7  77  8  98  9  21
195 | 0  45  1  45  2  25  3  45  4   7  5  59  6  88  7  42  8  57  9  81
196 | 0  73  1  94  2  83  3  59  4   1  5  72  6  65  7  62  8  45  9  76
197 | 0  77  1  84  2  11  3  82  4  10  5   9  6  67  7  27  8  43  9   8
198 | 0  22  1  66  2   5  3  77  4  97  5  28  6  61  7  82  8  62  9  96
199 | 0  90  1  51  2  87  3  27  4  65  5  76  6  67  7  20  8  75  9  67
200 | 0  12  1  92  2  43  3  21  4  92  5  64  6  94  7  67  8  60  9  46
201 | 0   9  1  76  2  62  3  46  4  71  5  65  6  76  7  65  8  30  9  38
202 | 0  29  1  12  2  71  3  70  4  46  5  96  6  12  7  70  8  76  9  19
203 | 0  83  1  15  2  73  3  32  4  51  5   6  6   3  7  29  8   3  9  24
204 | 0  83  1  95  2  87  3  29  4  46  5  67  6  89  7  73  8  69  9  33
205 | 0  83  1  46  2  82  3   2  4  55  5  54  6  85  7   3  8  20  9  57
206 | 0  11  1  32  2  15  3  27  4   2  5  43  6  23  7  79  8  28  9  29
207 | 0  10  1  74  2  73  3  99  4  54  5  89  6  83  7   5  8  28  9  90
208 | 0  73  1  40  2   4  3  20  4  51  5  18  6  37  7  18  8  61  9  75
209 | 0  85  1  30  2  58  3  89  4  48  5  15  6  82  7  77  8   2  9   3
210 | 0  56  1  63  2  26  3  87  4  53  5   8  6  80  7  46  8   5  9  62
211 | 0  59  1  67  2  73  3  65  4  60  5  61  6  94  7  86  8  38  9   1
212 | 0  70  1  66  2  80  3  32  4  93  5  56  6  26  7  41  8  21  9   9
213 | 0   4  1  66  2  79  3  43  4  39  5  83  6  55  7  25  8  62  9  13
214 | 0  51  1  42  2  90  3  85  4  84  5  29  6  73  7   8  8  95  9  57
215 | 0  18  1  30  2  61  3  67  4  57  5  60  6  25  7  10  8  20  9  95
216 | 0  61  1   9  2   3  3   2  4  61  5  18  6  44  7  78  8  38  9  74
217 | 0  25  1  91  2  31  3   2  4  14  5  97  6  91  7  84  8  88  9  26
218 | 0  84  1   8  2  95  3  61  4  85  5  41  6  88  7   4  8  86  9  51
219 | 0  74  1   2  2  24  3  42  4  33  5  24  6  62  7  13  8  62  9  10
220 | 0  33  1   7  2  62  3  68  4  42  5  41  6  78  7  67  8  99  9   6
221 | 0  38  1  43  2   2  3   4  4  62  5  95  6  76  7  91  8  67  9  78
222 | 0  43  1  98  2  28  3  51  4  43  5  84  6  13  7  71  8  64  9  81
223 | 0  15  1  19  2  50  3  30  4  75  5  90  6  94  7  35  8  51  9  83
224 | 0  75  1  98  2  42  3  67  4  24  5  63  6  15  7  45  8  92  9  44
225 | 0  29  1  60  2  80  3  86  4  70  5  13  6 100  7  86  8  88  9   6
226 | 0  14  1  49  2  78  3  93  4  45  5  94  6  35  7  46  8  18  9  85
227 | 0  29  1  20  2  27  3  66  4  70  5  95  6   7  7  11  8  75  9  52
228 | 0  73  1  19  2  33  3  36  4  93  5  21  6  44  7  51  8   4  9  24
229 | 0  87  1  79  2  52  3  85  4  24  5  89  6  50  7   4  8  37  9  50
230 | 0  86  1  99  2  31  3  25  4  78  5  10  6  41  7  66  8  35  9   1
231 | 0   2  1  41  2  41  3  88  4   6  5  77  6  89  7  80  8  21  9  54
232 | +++++++++++++++++++++++++++++
233 | 


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