Cooperative Differential Evolution With Multiple Populations for Multiobjective Optimization

This paper presents a cooperative differential evolution (DE) with multiple populations for multiobjective optimization. The proposed algorithm has M single-objective optimization subpopulations and an archive population for an M-objective optimization problem. An adaptive DE is applied to each subpopulation to optimize the corresponding objective of the multiobjective optimization problem (MOP). The archive population is also optimized by an adaptive DE. The archive population is used not only to maintain all nondominated solutions found so far but also to guide each subpopulation to search along the whole Pareto front. These (M + 1) populations cooperate to optimize all objectives of the MOP by using adaptive DEs. Simulation results on benchmark problems with two, three, and many objectives show that the proposed algorithm is better than some state-of-the-art multiobjective DE algorithms and other popular multiobjective evolutionary algorithms. The online search behavior and parameter sensitivity of the proposed algorithm are also investigated.

[1]  Hussein A. Abbass,et al.  MOCCA-II: A multi-objective co-operative co-evolutionary algorithm , 2014, Appl. Soft Comput..

[2]  María José del Jesús,et al.  KEEL: a software tool to assess evolutionary algorithms for data mining problems , 2008, Soft Comput..

[3]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[4]  Konstantinos E. Parsopoulos,et al.  MULTIOBJECTIVE OPTIMIZATION USING PARALLEL VECTOR EVALUATED PARTICLE SWARM OPTIMIZATION , 2003 .

[5]  Millie Pant,et al.  An efficient Differential Evolution based algorithm for solving multi-objective optimization problems , 2011, Eur. J. Oper. Res..

[6]  H. Abbass,et al.  PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[7]  Pascal Bouvry,et al.  Multi-objective Cooperative Coevolutionary Evolutionary Algorithms for Continuous and Combinatorial Optimization , 2011, Intelligent Decision Systems in Large-Scale Distributed Environments.

[8]  Self-adaptive differential evolution algorithm with α-constrained-domination principle for constrained multi-objective optimization , 2012, Soft Comput..

[9]  Mietek A. Brdys,et al.  Grid Implementation of a Parallel Multiobjective Genetic Algorithm for Optimized Allocation of Chlorination Stations in Drinking Water Distribution Systems: Chojnice Case Study , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[10]  Shengxiang Yang,et al.  Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[11]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[12]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[13]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[14]  Carlos A. Coello Coello,et al.  Multi-objective Optimization Using Differential Evolution: A Survey of the State-of-the-Art , 2008 .

[15]  Carlos A. Coello Coello,et al.  A coevolutionary multi-objective evolutionary algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[16]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[17]  Kay Chen Tan,et al.  A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design , 2010, Eur. J. Oper. Res..

[18]  Qingfu Zhang,et al.  Distributed evolutionary algorithms and their models: A survey of the state-of-the-art , 2015, Appl. Soft Comput..

[19]  Jie Chen,et al.  Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[20]  Gexiang Zhang,et al.  Multi-objective Differential Evolution : a Recent Survey , 2013 .

[21]  Jiannong Cao,et al.  Multiple Populations for Multiple Objectives: A Coevolutionary Technique for Solving Multiobjective Optimization Problems , 2013, IEEE Transactions on Cybernetics.

[22]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[23]  Gexiang Zhang,et al.  Enhancing distributed differential evolution with multicultural migration for global numerical optimization , 2013, Inf. Sci..

[24]  Qingfu Zhang,et al.  Are All the Subproblems Equally Important? Resource Allocation in Decomposition-Based Multiobjective Evolutionary Algorithms , 2016, IEEE Transactions on Evolutionary Computation.

[25]  Lotfi A. Zadeh,et al.  Applied Soft Computing - Foreword , 2001, Appl. Soft Comput..

[26]  Yiqiao Cai,et al.  Differential evolution with hybrid linkage crossover , 2015, Inf. Sci..

[27]  Cheng-Nan Chen,et al.  Parameter control mechanisms in differential evolution: A tutorial review and taxonomy , 2013, 2013 IEEE Symposium on Differential Evolution (SDE).

[28]  Yang Yang,et al.  A distributed cooperative coevolutionary algorithm for multiobjective optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[29]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[30]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[31]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[32]  Joshua D. Knowles,et al.  ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems , 2006, IEEE Transactions on Evolutionary Computation.

[33]  Yiqiao Cai,et al.  Differential Evolution Enhanced With Multiobjective Sorting-Based Mutation Operators , 2014, IEEE Transactions on Cybernetics.

[34]  David Naso,et al.  Compact Differential Evolution , 2011, IEEE Transactions on Evolutionary Computation.

[35]  Carlos A. Coello Coello,et al.  Use of cooperative coevolution for solving large scale multiobjective optimization problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[36]  Habibollah Haron,et al.  The review of multiple evolutionary searches and multi-objective evolutionary algorithms , 2013, Artificial Intelligence Review.

[37]  César Hervás-Martínez,et al.  Multi-objective cooperative coevolution of artificial neural networks (multi-objective cooperative networks) , 2002, Neural Networks.

[38]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[39]  Wenyin Gong,et al.  Adaptive Ranking Mutation Operator Based Differential Evolution for Constrained Optimization , 2015, IEEE Transactions on Cybernetics.

[40]  Xiaodong Li,et al.  A Cooperative Coevolutionary Multiobjective Algorithm Using Non-dominated Sorting , 2004, GECCO.

[41]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[42]  Yaonan Wang,et al.  Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure , 2010, Soft Comput..

[43]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[44]  Kay Chen Tan,et al.  A Competitive-Cooperative Coevolutionary Paradigm for Dynamic Multiobjective Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[45]  Xiaodong Li,et al.  Cooperative Co-Evolution With Differential Grouping for Large Scale Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[46]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[47]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[48]  Gary G. Yen,et al.  PSO-Based Multiobjective Optimization With Dynamic Population Size and Adaptive Local Archives , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[49]  Ville Tirronen,et al.  Recent advances in differential evolution: a survey and experimental analysis , 2010, Artificial Intelligence Review.

[50]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..