Adaptive differential evolution algorithm for multiobjective optimization problems
In this paper, a new adaptive differential evolution algorithm (ADEA) is proposed for multiobjective optimization problems. In ADEA, the variable parameter F based on the number of the current Pareto-front and the diversity of the current solutions is given for adjusting search size in every generat...
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| Veröffentlicht in: | Applied mathematics and computation Jg. 201; H. 1; S. 431 - 440 |
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15.07.2008
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| Abstract | In this paper, a new adaptive differential evolution algorithm (ADEA) is proposed for multiobjective optimization problems. In ADEA, the variable parameter
F based on the number of the current Pareto-front and the diversity of the current solutions is given for adjusting search size in every generation to find Pareto solutions in mutation operator, and the select operator combines the advantages of DE with the mechanisms of Pareto-based ranking and crowding distance sorting. ADEA is implemented on five classical multiobjective problems, the results illustrate that ADEA efficiently achieves two goals of multiobjective optimization problems: find the solutions converge to the true Pareto-front and uniform spread along the front. |
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| AbstractList | In this paper, a new adaptive differential evolution algorithm (ADEA) is proposed for multiobjective optimization problems. In ADEA, the variable parameter
F based on the number of the current Pareto-front and the diversity of the current solutions is given for adjusting search size in every generation to find Pareto solutions in mutation operator, and the select operator combines the advantages of DE with the mechanisms of Pareto-based ranking and crowding distance sorting. ADEA is implemented on five classical multiobjective problems, the results illustrate that ADEA efficiently achieves two goals of multiobjective optimization problems: find the solutions converge to the true Pareto-front and uniform spread along the front. |
| Author | Qian, Weiyi li, Ajun |
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| Keywords | Multiobjective optimization problems Select operator Differential evolution algorithm Adaptive Numerical analysis Adaptive algorithm Applied mathematics Optimization method Implementation Sorting |
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| References | Madavan (bib7) 2002; vol. 2 Tea Rolič, Bogdan Filipic˘, in: C.A. Coello, et al. (Eds.), DEMO: Differential Evolution for Multiobjective Optimization, EMO 2005, LNCS 3410, 2005, pp. 520–533. Deb, Pratap, Agarwal, Meyarivan (bib1) 2002; 6 Abbass (bib6) 2002; vol. 1 Knowles, Corne (bib3) 1999 Abbass, Sarker, Newton (bib5) 2001; vol. 2 Goldberg (bib10) 1989 Price, Storn (bib4) 1997; 22 J. Lampinen, A bibliography of differential evolution algorithm. . Xue, Sanderson, Graves (bib2) 2003; vol. 2 Price (10.1016/j.amc.2007.12.052_bib4) 1997; 22 Deb (10.1016/j.amc.2007.12.052_bib1) 2002; 6 Knowles (10.1016/j.amc.2007.12.052_bib3) 1999 Abbass (10.1016/j.amc.2007.12.052_bib5) 2001; vol. 2 Madavan (10.1016/j.amc.2007.12.052_bib7) 2002; vol. 2 Xue (10.1016/j.amc.2007.12.052_bib2) 2003; vol. 2 10.1016/j.amc.2007.12.052_bib9 Abbass (10.1016/j.amc.2007.12.052_bib6) 2002; vol. 1 10.1016/j.amc.2007.12.052_bib8 Goldberg (10.1016/j.amc.2007.12.052_bib10) 1989 |
| References_xml | – year: 1989 ident: bib10 article-title: Genetic Algorithms in Search, Optimization, and Machine Learning – volume: vol. 2 start-page: 971 year: 2001 end-page: 978 ident: bib5 article-title: PDE: A Pareto-frontier differential evolution approach for multi-objective optimization problems publication-title: Proceedings of the Congress on Evolutionary Computation 2001 (CEC’2001) – volume: vol. 1 start-page: 831 year: 2002 end-page: 836 ident: bib6 article-title: The self-adaptive Pareto differential evolution algorithm publication-title: Proceedings of the Congress on Evolutionary Computation (CEC’2002) – volume: vol. 2 start-page: 862 year: 2003 end-page: 869 ident: bib2 article-title: Pareto-based multi-objective differential evolution publication-title: Proceedings of the 2003 Congress on Evolutionary Computation (CEC’2003) – volume: 6 start-page: 182 year: 2002 end-page: 197 ident: bib1 article-title: A fast and elitist multiobjective genetic algorithm: NSGA-II publication-title: IEEE Transactions on Evolutionary Computation – volume: 22 start-page: 18 year: 1997 end-page: 24 ident: bib4 article-title: Differential evolution-a simple evolution strategy for fast optimization publication-title: Dr. Dobb’s Journal – reference: J. Lampinen, A bibliography of differential evolution algorithm. – start-page: 98 year: 1999 end-page: 105 ident: bib3 article-title: The Pareto archived evolution strategy: a new baseline algorithm for multiobjective optimization publication-title: Proceedings of the 1999 Congress on Evolutionary Computation – volume: vol. 2 start-page: 1145 year: 2002 end-page: 1150 ident: bib7 article-title: Multiobjective optimization using a Pareto differential evolution approach publication-title: Proceeding of the Congress on Evolutionary Computation (CEC’2002) – reference: Tea Rolič, Bogdan Filipic˘, in: C.A. Coello, et al. (Eds.), DEMO: Differential Evolution for Multiobjective Optimization, EMO 2005, LNCS 3410, 2005, pp. 520–533. – reference: . – ident: 10.1016/j.amc.2007.12.052_bib8 doi: 10.1007/978-3-540-31880-4_36 – volume: 22 start-page: 18 year: 1997 ident: 10.1016/j.amc.2007.12.052_bib4 article-title: Differential evolution-a simple evolution strategy for fast optimization publication-title: Dr. Dobb’s Journal – volume: 6 start-page: 182 year: 2002 ident: 10.1016/j.amc.2007.12.052_bib1 article-title: A fast and elitist multiobjective genetic algorithm: NSGA-II publication-title: IEEE Transactions on Evolutionary Computation doi: 10.1109/4235.996017 – start-page: 98 year: 1999 ident: 10.1016/j.amc.2007.12.052_bib3 article-title: The Pareto archived evolution strategy: a new baseline algorithm for multiobjective optimization – volume: vol. 2 start-page: 862 year: 2003 ident: 10.1016/j.amc.2007.12.052_bib2 article-title: Pareto-based multi-objective differential evolution – volume: vol. 1 start-page: 831 year: 2002 ident: 10.1016/j.amc.2007.12.052_bib6 article-title: The self-adaptive Pareto differential evolution algorithm – ident: 10.1016/j.amc.2007.12.052_bib9 – volume: vol. 2 start-page: 1145 year: 2002 ident: 10.1016/j.amc.2007.12.052_bib7 article-title: Multiobjective optimization using a Pareto differential evolution approach – year: 1989 ident: 10.1016/j.amc.2007.12.052_bib10 – volume: vol. 2 start-page: 971 year: 2001 ident: 10.1016/j.amc.2007.12.052_bib5 article-title: PDE: A Pareto-frontier differential evolution approach for multi-objective optimization problems |
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| SubjectTerms | Adaptive Differential evolution algorithm Exact sciences and technology Global analysis, analysis on manifolds Mathematical analysis Mathematics Multiobjective optimization problems Numerical analysis Numerical analysis. Scientific computation Sciences and techniques of general use Select operator Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| Title | Adaptive differential evolution algorithm for multiobjective optimization problems |
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