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1 | # Awesome Multi-Objective Optimization [](https://awesome.re)
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6 | A curated list of awesome multi-objective optimization research resources. Inspired by [awesome-360-vision](https://github.com/hsientzucheng/awesome-360-vision), [awesome-architecture-search](https://github.com/markdtw/awesome-architecture-search), [awesome-deep-vision](https://github.com/kjw0612/awesome-deep-vision), [awesome-adversarial-machine-learning](https://github.com/yenchenlin/awesome-adversarial-machine-learning) and [awesome-deep-learning-papers](https://github.com/terryum/awesome-deep-learning-papers). Still working on it, any suggestions of missing reference are welcome.
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8 |
9 | ## Table of Contents
10 |
11 | - [Papers](#papers)
12 | - [Reinforcement Learning](#reinforcement-learning)
13 | - [Single Policy](#single-policy)
14 | - [Multiple Policy](#multiple-policy)
15 | - [Evolutionary Algorithms](#evolutionary-algorithms)
16 | - [Dominance Based](#dominance-based)
17 | - [Aggregation Based](#aggregation-based)
18 | - [Indicator Based](#indicator-based)
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21 |
22 |
23 | ## Papers
24 |
25 | ### Reinforcement Learning
26 | #### Survey
27 | - A survey of multi-objective sequential decision-making. [[pdf]](https://arxiv.org/pdf/1402.0590)
28 | - Roijers, Diederik M., et al. *JAIR 2013*
29 | - Multiobjective reinforcement learning: A comprehensive overview. [[pdf]](https://arxiv.org/pdf/1402.0590)
30 | - C. Liu, X. Xu, D. Hu *IEEE SMC 2015*
31 |
32 | #### Single Policy
33 | ##### Weighted-Sum Approach
34 | - Learning to solve multiple goals. [[pdf]](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.37.8338&rep=rep1&type=pdf)
35 | - J. Karlsson.
36 | - Multiple-goal reinforcement learning with modular sarsa (0). [[pdf]](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.37.8338&rep=rep1&type=pdf)
37 | - N. Sprague, D. Ballard. *IJCAI 2003*
38 | - A multiple goal reinforcement learn-ing method for complex vehicle overtaking maneuver. [[pdf]](https://hub.hku.hk/bitstream/10722/137287/1/Content.pdf?accept=1)
39 | - DCK Ngai, NHC Yung. *WCICA 2010*
40 | - Self-adaptive multi-objective optimization method design based on agent reinforcement learning for elevator group control systems. [[pdf]](https://ieeexplore.ieee.org/abstract/document/5554696/)
41 | - F. Zeng, Q. Zong, Z. Sun, L. Dou. *IEEE Trans. Intell. Trans. Syst 2011*
42 | - Managing power consumption and performance of computing systems using reinforcement learning. [[pdf]](http://papers.nips.cc/paper/3251-managing-power-consumption-and-performance-of-computing-systems-using-reinforcement-learning.pdf)
43 | - Tesauro, Gerald, et al. *NIPS 2018*
44 |
45 | ##### W-Learning Approach
46 | - Action selection methods using reinforcement learning. [[pdf]](http://cogprints.org/447/2/g.SAB96.ps)
47 | - M Humphrys.
48 | ##### Analytic Hierarchy Process Approach
49 | - A multi-objective optimization genetic algorithm incorporating preference information. [[pdf]](http://en.cnki.com.cn/Article_en/CJFDTOTAL-XXYK200706016.htm)
50 | - X Shen, Y Guo, Q Chen, W Hu.
51 | - Multi-objective reinforcement learning algorithm for MOSDMP in unknown environment. [[pdf]](http://en.cnki.com.cn/Article_en/CJFDTOTAL-XXYK200706016.htm)
52 | - Zhao, Yun, Qingwei Chen, and Weili Hu. *WCICA 2010*
53 | ##### Ranking Approach
54 | - Multi-criteria reinforcement learning. [[pdf]](http://www.academia.edu/download/3406069/multi98.ps.pdf)
55 | - Z Gábor, Z Kalmár, C Szepesvári. *ICML 1998*
56 | - Reinforcement learning with bounded risk. [[pdf]](http://peter-geibel.de/OnlineArticles/icml01.pdf)
57 | - P Geibel. *ICML 2001*
58 | - Multi-objective reinforcement learning based routing in cognitive radio networks: Walking in a random maze. [[pdf]](http://peter-geibel.de/OnlineArticles/icml01.pdf)
59 | - K. Zheng, H. Li, RC. Qiu, S. Gong. *ICNC 2012*
60 | ##### Geometric Approach
61 | - A geometric approach to multi-criterion reinforcement learning. [[pdf]](http://www.jmlr.org/papers/volume5/mannor04a/mannor04a.pdf)
62 | - S. Mannor, N. Shimkin. *JMLR 2014*
63 | - The steering approach for multi-criteria reinforcement learning. [[pdf]](http://papers.nips.cc/paper/1986-the-steering-approach-for-multi-criteria-reinforcement-learning.pdf)
64 | - S. Mannor, N. Shimkin. *NIPS 2002*
65 |
66 | #### Multiple Policy
67 | ##### Convex Hull Approach
68 | - Learning all optimal policies with multiple criteria. [[pdf]](http://www1.icsi.berkeley.edu/~snarayan/icml.pdf)
69 | - Barrett, Leon, and Srini Narayanan. *ICML 2008*
70 | ##### Varying Parameter Approach
71 | - Importance sampling for reinforcement learning with multiple objectives. [[pdf]](https://dspace.mit.edu/bitstream/handle/1721.1/5568/AITR-2001-003.pdf?sequence=2)
72 | - CR Shelton.
73 |
74 |
114 |
115 | ### Evolutionary Algorithms
116 | #### Survey
117 | - Multiobjective evolutionary algorithms: A survey of the state of the art [[pdf]](https://dl.acm.org/ft_gateway.cfm?ftid=1627892&id=2792984)
118 | - Zhou, Aimin, et al.
119 | - Many-Objective Evolutionary Algorithms: A Survey [[pdf]](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.465.9199&rep=rep1&type=pdf)
120 | - B Li, J Li, K Tang, X Yao. *CSUR 2015*
121 | #### Dominance Based
122 | - A fast and elitist multiobjective genetic algorithm: NSGA-II [[pdf]](https://ieeexplore.ieee.org/document/996017/) [[Official]](https://www.iitk.ac.in/kangal/codes.shtml) [[python]](https://github.com/haris989/NSGA-II) [[C++]](https://github.com/dojeda/nsga2-cpp) [[Java]](https://github.com/onclave/NSGA-II)
123 | - K. Deb, A. Pratap, S. Agarwal, T. Meyarivan. *IEEE Transactions on Evolutionary Computation 2012*
124 | - SPEA2: Improving the Strength Pareto Evolutionary Algorithm [[pdf]](https://pdfs.semanticscholar.org/6672/8d01f9ebd0446ab346a855a44d2b138fd82d.pdf) [[official]](http://www.cleveralgorithms.com/nature-inspired/evolution/spea.html)
125 | - E. Zitzler, M. Laumanns, L. Thiele. *TIK-report 2001*
126 | - ISPEA: improvement for the strength Pareto evolutionary algorithm for multiobjective optimization with immunity [[pdf]](https://ieeexplore.ieee.org/abstract/document/1238153/)
127 | - M. Hongyun, L. Sanyang. *ICCIMA 2003*
128 | - Applications of Vector Evaluated Genetic Algorithms (VEGA) in Ultimate Limit State Based Ship Structural Design [[pdf]](http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1911976)
129 | - O. Hughes, M. Ma, JK. Paik. *ASME 2014*
130 | - Shift-based density estimation for Pareto-based algorithms in many-objective optimization [[pdf]](https://bura.brunel.ac.uk/bitstream/2438/12061/1/Fulltext.pdf)
131 | - M Li, S Yang, X Liu. *IEEE Transactions on Evolutionary Computation 2014*
132 | - The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation (PAES) [[pdf]](https://ieeexplore.ieee.org/document/781913/)
133 | - Knowles, Joshua, and David Corne. *CEC 1999*
134 |
135 | #### Aggregation Based
136 | - MOEA/D: A multiobjective evolutionary algorithm based on decomposition [[pdf]](http://web.xidian.edu.cn/xlwang/files/20150312_174546.pdf) [[R]](https://github.com/fcampelo/MOEADr) [[python]](https://github.com/mbelmadani/moead-py) [[java]](https://github.com/jMetal/jMetal/blob/master/jmetal-algorithm/src/main/java/org/uma/jmetal/algorithm/multiobjective/moead/MOEAD.java)
137 | - Q Zhang, H Li. *IEEE Transactions on Evolutionary Computation 2007*
138 | - Normal-boundary intersection: A new method for generating the pareto surface in nonlinear multicriteria optimization problems [[pdf]](https://scholarship.rice.edu/bitstream/handle/1911/101880/TR96-19.pdf?sequence=1)
139 | - I Das, JE Dennis. *SIAM Journal on Optimization 1998*
140 | - Many-objective directed evolutionary line search [[pdf]](http://www.whitehorseradar.co.uk/PublicationsUPDAT/conf_2011_GECCO_models.pdf)
141 | - Hughes, E. James. *GECCO 2011*
142 | - Ranking methods for many-objective optimization [[pdf]](http://delta.cs.cinvestav.mx/~ccoello/EMOO/fabre09.pdf.gz)
143 | - M. Garza-Fabre, GT Pulido, CAC Coello. *MICAI 2009*
144 | - A decomposition based evolutionary algorithm for many objective optimization with systematic sampling and adaptive epsilon control [[pdf]](https://pdfs.semanticscholar.org/8f71/35ba677fa47371688b3b1b77a18b1137c3ad.pdf)
145 | - Asafuddoula, Md, Tapabrata Ray, and Ruhul Sarker. *EMO 2013*
146 | - Ranking-dominance and many-objective optimization [[pdf]](https://www.researchgate.net/profile/J_Lampinen/publication/224301953_Ranking-Dominance_and_Many-Objective_Optimization/links/0912f509b37511a19c000000/Ranking-Dominance-and-Many-Objective-Optimization.pdf)
147 | - Kukkonen, Saku, and Jouni Lampinen. *CEC 2017*
148 |
149 | #### Indicator Based
150 | - HypE: An algorithm for fast hypervolume-based many-objective optimization [[pdf]](https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/12187/1/eth-30945-01.pdf)
151 | - J. Bader, E. Zitzler.
152 | - An EMO algorithm using the hypervolume measure as selection criterion [[pdf]](https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/12187/1/eth-30945-01.pdf)
153 | - M. Emmerich, N. Beume, B. Naujoks. *EMO 2015*
154 | - Approximation-guided evolutionary multi-objective optimization. [[pdf]](http://www.aaai.org/ocs/index.php/IJCAI/IJCAI11/paper/viewFile/2929/3419)
155 | - Bringmann, Karl, et al. *IJCAI 2011*
156 | - On the properties of the R2 indicator. [[pdf]](https://hal.archives-ouvertes.fr/docs/00/72/20/60/PDF/pap486s1-brockhoffAuthorVersion.pdf)
157 | - Brockhoff, Dimo, T. Wagner, and H. Trautmann. *GECCO 2012*
158 | - MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator. [[pdf]](http://delta.cs.cinvestav.mx/~ccoello/EMOO/hernandez13.pdf.gz)
159 | - Gómez, Raquel Hernández, and Carlos A. Coello Coello. *CEC 2013*
160 | - A ranking method based on the R2 indicator for many-objective optimization. [[pdf]](https://www.cs.cinvestav.mx/~EVOCINV/publications/2013/conferences/cec2013-alan-final.pdf.gz)
161 | - Díaz-Manríquez, Alan, et al. *CEC 2013*
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163 |
167 |
168 | ## License
169 |
170 | [](https://creativecommons.org/publicdomain/zero/1.0/)
171 |
172 | To the extent possible under law, [Anjie Zheng](http://anjie.me/) has waived all copyright and related or neighboring rights to this work.
173 |
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