Multi-objective Optimization Using Differential Evolution: A Survey of the State-of-the-Art

Differential Evolution is currently one of the most popular heuristics to solve single-objective optimization problems in continuous search spaces. Due to this success, its use has been extended to other types of problems, such as multi-objective optimization. In this chapter, we present a survey of algorithms based on differential evolution which have been used to solve multi-objective optimization problems. Their main features are described and, based precisely on them, we propose a taxonomy of approaches. Some theoretical work found in the specialized literature is also provided. To conclude, based on our findings, we suggest some topics that we consider to be promising paths for future research in this area.

[1]  Jouni Lampinen,et al.  DE’s Selection Rule for Multiobjective Optimization , 2001 .

[2]  C. S. Chang,et al.  Differential evolution based tuning of fuzzy automatic train operation for mass rapid transit system , 2000 .

[3]  Hussein A. Abbass,et al.  Solving Two Multi-Objective Optimization Problems Using Evolutionary Algorithm , 2003 .

[4]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[5]  Arthur C. Sanderson,et al.  Modeling and convergence analysis of a continuous multi-objective differential evolution algorithm , 2005, 2005 IEEE Congress on Evolutionary Computation.

[6]  Bernhard Sendhoff,et al.  On Test Functions for Evolutionary Multi-objective Optimization , 2004, PPSN.

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

[8]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[9]  H. B. Quek,et al.  Pareto-optimal set based multiobjective tuning of fuzzy automatic train operation for mass transit system , 1999 .

[10]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[11]  Kenneth V. Price,et al.  An introduction to differential evolution , 1999 .

[12]  Markus Stumptner,et al.  AI 2001: Advances in Artificial Intelligence , 2002, Lecture Notes in Computer Science.

[13]  Xiaodong Li,et al.  Incorporating directional information within a differential evolution algorithm for multi-objective optimization , 2006, GECCO.

[14]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[15]  Jürgen Teich,et al.  Evolutionary algorithm based exploration of software schedules for digital signal processors , 1999 .

[16]  Xiaodong Li,et al.  Solving Rotated Multi-objective Optimization Problems Using Differential Evolution , 2004, Australian Conference on Artificial Intelligence.

[17]  Thomas Hanne,et al.  On the convergence of multiobjective evolutionary algorithms , 1999, Eur. J. Oper. Res..

[18]  Michael de la Maza,et al.  Book review: Genetic Algorithms + Data Structures = Evolution Programs by Zbigniew Michalewicz (Springer-Verlag, 1992) , 1993 .

[19]  M Reyes Sierra,et al.  Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art , 2006 .

[20]  Julian F. Miller,et al.  Genetic and Evolutionary Computation — GECCO 2003 , 2003, Lecture Notes in Computer Science.

[21]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[22]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[23]  Arthur C. Sanderson,et al.  Multi-objective differential evolution: theory and applications , 2004 .

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

[25]  R. Lyndon While,et al.  A Scalable Multi-objective Test Problem Toolkit , 2005, EMO.

[26]  Arthur C. Sanderson,et al.  Multi-objective differential evolution - algorithm, convergence analysis, and applications , 2005, 2005 IEEE Congress on Evolutionary Computation.

[27]  Lakhmi C. Jain,et al.  Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[28]  Srigiriraju Kishan Chetan,et al.  Noninferior Surface Tracing Evolutionary Algorithm (NSTEA) for Multiobjective optimization , 2000 .

[29]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[30]  L. Lasdon,et al.  On a bicriterion formation of the problems of integrated system identification and system optimization , 1971 .

[31]  Carlos A. Coello Coello,et al.  Solving Hard Multiobjective Optimization Problems Using epsilon-Constraint with Cultured Differential Evolution , 2006, PPSN.

[32]  B. Babu,et al.  Differential evolution for multi-objective optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[33]  Qingfu Zhang,et al.  A Multiobjective Differential Evolution Based on Decomposition for Multiobjective Optimization with Variable Linkages , 2006, PPSN.

[34]  Hussein A. Abbass,et al.  The Pareto Differential Evolution Algorithm , 2002, Int. J. Artif. Intell. Tools.

[35]  Thomas Bäck,et al.  Evolutionary Algorithms in Theory and Practice , 1996 .

[36]  Xin Yao,et al.  Parallel Problem Solving from Nature PPSN VI , 2000, Lecture Notes in Computer Science.

[37]  Edmund K. Burke,et al.  Parallel Problem Solving from Nature - PPSN IX: 9th International Conference, Reykjavik, Iceland, September 9-13, 2006, Proceedings , 2006, PPSN.

[38]  James C. Bean,et al.  Genetic Algorithms and Random Keys for Sequencing and Optimization , 1994, INFORMS J. Comput..

[39]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[40]  Arthur C. Sanderson,et al.  Pareto-based multi-objective differential evolution , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[41]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[42]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

[43]  S. Ranji Ranjithan,et al.  Constraint Method-Based Evolutionary Algorithm (CMEA) for Multiobjective Optimization , 2001, EMO.

[44]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[45]  Carlos A. Coello Coello,et al.  A new proposal for multi-objective optimization using differential evolution and rough sets theory , 2006, GECCO '06.

[46]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[47]  Carlos A. Coello Coello,et al.  Pareto-adaptive -dominance , 2007, Evolutionary Computation.

[48]  Jouni Lampinen,et al.  An Extension of Generalized Differential Evolution for Multi-objective Optimization with Constraints , 2004, PPSN.

[49]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[50]  Xinghuo Yu,et al.  AI 2004: Advances in Artificial Intelligence, 17th Australian Joint Conference on Artificial Intelligence, Cairns, Australia, December 4-6, 2004, Proceedings , 2004, Australian Conference on Artificial Intelligence.

[51]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[52]  Carlos A. Coello Coello,et al.  An Algorithm Based on Differential Evolution for Multi-Objective Problems , 2005 .

[53]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[54]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[55]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[56]  Zbigniew Michalewicz,et al.  Evolutionary Computation 2 , 2000 .

[57]  Jouni Lampinen,et al.  GDE3: the third evolution step of generalized differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[58]  N. Madavan.  Multiobjective optimization using a Pareto differential evolution approach , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[59]  C. Coello,et al.  Cultured differential evolution for constrained optimization , 2006 .

[60]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[61]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[62]  Frank Kursawe,et al.  A Variant of Evolution Strategies for Vector Optimization , 1990, PPSN.

[63]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[64]  Hussein A. Abbass,et al.  A Memetic Pareto Evolutionary Approach to Artificial Neural Networks , 2001, Australian Joint Conference on Artificial Intelligence.

[65]  Dimitris K. Tasoulis,et al.  Vector evaluated differential evolution for multiobjective optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[66]  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).

[67]  Günter Rudolph,et al.  Some Theoretical Properties of Evolutionary Algorithms under Partially Ordered Fitness Values , 2001 .