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  1 | # Awesome Multi-Objective Optimization [![Awesome](https://awesome.re/badge.svg)](https://awesome.re)
  2 | <p align="center">
  3 |   <img width="250" src="https://camo.githubusercontent.com/1131548cf666e1150ebd2a52f44776d539f06324/68747470733a2f2f63646e2e7261776769742e636f6d2f73696e647265736f726875732f617765736f6d652f6d61737465722f6d656469612f6c6f676f2e737667" "Awesome!">
  4 | </p>
  5 | 
  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.
  7 | 
  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)
 19 | 
 20 | 
 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 | <!---
 75 | #### FQI(fitted Q-iteration) Extension
 76 | 
 77 | ### TBC
 78 | - Tree-based fitted q-iteration for multi-objective markov decision problems. [[pdf]](https://re.public.polimi.it/bitstream/11311/690408/1/06252759.pdf)
 79 |   - A. Castelletti, F. Pianosi, M. Restelli. *IJCNN 2012*
 80 | 
 81 | - Multi-objective optimization by reinforcement learning (Store in elite list)
 82 | 
 83 | - Solving multi-objective reinforcement learning problems by EDA-RL-acquisition of various strategies (SP:Estimation of distribution)
 84 | 
 85 | - Multi-criteria reinforcement learning based on goal-directed exploration and its application to bipedal walking robot(SP:α-domination strategy+goal-directed bias)
 86 | 
 87 | - Multi-objective reinforcement learning algo-rithm and its improved convergency method(SP:parallel genetic algo+perturbation stochastic approximation)
 88 | 
 89 | - Parallel reinforcement learn-ing for weighted multi-criteria model with adaptive margin(SP:Adaptive margin)
 90 | 
 91 | - Multiobjective reinforcement learning based on multiple value functions(SP:Actor critic)
 92 | 
 93 | - Multi-objective fitted Q-iteration: Pareto frontier approximation in one single run(SP:FQI angain:))
 94 | 
 95 | - Computing optimal stationary policies for multi-objective Markov decision processes(SP:CON-MODP value iter algo)
 96 | 
 97 | - Policy gradient approaches for multi-objective sequential decision making
 98 | 
 99 | - Model-based multi-objective reinforcement learning
100 | 
101 | - Hypervolume-based multi-objective reinforcement learning
102 | 
103 | - Multi-objective reinforcement learning using sets of pareto dominating policies
104 | 
105 | - Scalarized Multi-Objective Reinforcement Learning: Novel Design Techniques
106 | 
107 | - Many-objective stochastic path finding using reinforcement learning
108 | 
109 | - Multi-objective reinforcement learning through continuous pareto manifold approximation
110 | 
111 | - Softmax exploration strategies for multiobjective reinforcement learning
112 | 
113 | -->
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*
162 | 
163 | <!---
164 | ### Bradient Based
165 | ### Others
166 | -->
167 | 
168 | ## License
169 | 
170 | [![PDM](https://licensebuttons.net/p/mark/1.0/88x31.png)](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 | 
174 | 


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