Adaptive ε-Ranking on many-objective problems
This work proposes Adaptive ε-Ranking to enhance Pareto based selection, aiming to develop effective many -objective evolutionary optimization algorithms. ε-Ranking fine grains ranking of solutions after they have been ranked by Pareto dominance, using a randomized sampling procedure combined with ε...
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| Vydané v: | Evolutionary intelligence Ročník 2; číslo 4; s. 183 - 206 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Springer-Verlag
01.12.2009
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| ISSN: | 1864-5909, 1864-5917 |
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| Abstract | This work proposes Adaptive ε-Ranking to enhance Pareto based selection, aiming to develop effective
many
-objective evolutionary optimization algorithms. ε-Ranking fine grains ranking of solutions after they have been ranked by Pareto dominance, using a randomized sampling procedure combined with ε-dominance to favor a good distribution of the samples. In the proposed method, sampled solutions keep their initial rank and solutions located within the virtually expanded ε-dominance regions of the sampled solutions are demoted to an inferior rank. The parameter ε that determines the expanded regions of dominance of the sampled solutions is adapted at each generation so that the number of best-ranked solutions is kept close to a desired number that is expressed as a fraction of the population size. We enhance NSGA-II with the proposed method and analyze its performance on MNK-Landscapes, showing that the adaptive method works effectively and that compared to NSGA-II convergence and diversity of solutions can be improved remarkably on MNK-Landscapes with 3 ≤
M
≤ 10 objectives. Also, we compare the performance of Adaptive ε-Ranking with two representative many-objective evolutionary algorithms on DTLZ continuous functions. Results on DTLZ functions with 3 ≤
M
≤ 10 objectives suggest that the three many-objective approaches emphasize different areas of objective space and could be used as complementary strategies to produce a better approximation of the Pareto front. |
|---|---|
| AbstractList | This work proposes Adaptive ε-Ranking to enhance Pareto based selection, aiming to develop effective
many
-objective evolutionary optimization algorithms. ε-Ranking fine grains ranking of solutions after they have been ranked by Pareto dominance, using a randomized sampling procedure combined with ε-dominance to favor a good distribution of the samples. In the proposed method, sampled solutions keep their initial rank and solutions located within the virtually expanded ε-dominance regions of the sampled solutions are demoted to an inferior rank. The parameter ε that determines the expanded regions of dominance of the sampled solutions is adapted at each generation so that the number of best-ranked solutions is kept close to a desired number that is expressed as a fraction of the population size. We enhance NSGA-II with the proposed method and analyze its performance on MNK-Landscapes, showing that the adaptive method works effectively and that compared to NSGA-II convergence and diversity of solutions can be improved remarkably on MNK-Landscapes with 3 ≤
M
≤ 10 objectives. Also, we compare the performance of Adaptive ε-Ranking with two representative many-objective evolutionary algorithms on DTLZ continuous functions. Results on DTLZ functions with 3 ≤
M
≤ 10 objectives suggest that the three many-objective approaches emphasize different areas of objective space and could be used as complementary strategies to produce a better approximation of the Pareto front. |
| Author | Aguirre, Hernán Tanaka, Kiyoshi |
| Author_xml | – sequence: 1 givenname: Hernán surname: Aguirre fullname: Aguirre, Hernán email: ahernan@shinshu-u.ac.jp organization: International Young Researcher Empowerment Center, Faculty of Engineering, Shinshu University – sequence: 2 givenname: Kiyoshi surname: Tanaka fullname: Tanaka, Kiyoshi organization: Faculty of Engineering, Shinshu University |
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| CitedBy_id | crossref_primary_10_1016_j_neucom_2011_03_053 crossref_primary_10_1109_TSMC_2022_3143657 crossref_primary_10_1109_TEVC_2016_2587749 crossref_primary_10_1002_int_23016 crossref_primary_10_1016_j_eij_2025_100733 |
| Cites_doi | 10.1007/978-1-4757-5184-0 10.1007/11844297_54 10.1109/CEC.2002.1007032 10.1109/CEC.2005.1554688 10.1109/CEC.2006.1688440 10.1109/CEC.2007.4424990 10.1007/978-3-540-70928-2_54 10.1007/978-3-540-70928-2_56 10.1007/978-3-540-31880-4_25 10.1007/3-540-36970-8_35 10.1007/978-3-540-70928-2_8 10.1007/978-3-540-89694-4_43 10.1109/CEC.2007.4424988 10.1093/oso/9780195079517.001.0001 10.1162/106365602760234108 10.1007/3-540-36970-8_37 10.1007/978-3-540-31880-4_5 10.1109/CEC.2004.1330857 10.1007/BF00932614 10.1007/3-540-36970-8_2 10.1007/3-540-45356-3_83 10.1109/CEC.2008.4631121 10.1007/978-3-540-70928-2_55 10.1007/3-540-36605-9_13 10.1007/978-3-540-30549-1_74 10.1016/j.ejor.2006.08.004 |
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| Keywords | Epistasis Many-objective optimization Selection ε-Ranking Adaptation |
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| References | Salomon R (1996) Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms, vol 39, no.3. Byosystems, Elsevier, pp 263–278 Kukkonen S, Lampinen J (2007) Ranking-dominance and many objective optimization. In: Proceedings of 2007 IEEE congress on evolutionary computation (CEC 2007), pp 3983–3990 Sulflow A, Drechsler N, Drechsler R (2007) Robust multi-objective optimization in high dimensional spaces. In: Proceedings of 4th international conference on evolutionary multi-criterion optimization, vol 4403. LNCS (Springer), pp 715–726 Bleuler S, Laumanns M, Thiele L, Zitzler E (2003) PISA—a platform and programming language independent interface for search algorithms. In: Proceedings of 2nd international conference on evolutionary multi-criterion optimization, vol 2632. LNCS (Springer), pp 494–508 Deb K, Saxena K (2006) Searching for pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. In: Proceedings of 2006 IEEE congress on evolutionary computation (CEC 2006), pp 3353–3360 Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. PhD thesis, Swiss Federal Institute of Technology, Zurich Hughes EJ (2005, September) evolutionary many-objective optimisation: many once or one many? In: Proceedings of 2005 IEEE congress on evolutionary computation, vol 1. IEEE Service Center, pp 222–227 CoelloCVan VeldhuizenDLamontGEvolutionary algorithms for solving multi-objective problems2002BostonKluwer1130.90002 Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. KanGAL report 200001 Iorio A.W., Li X (2004) Solving rotated multi-objective optimization problems using differential evolution. In: Proceedings of 17th Australian joint conference on artificial intelligence 2004, vol 3339. LNAI (Springer), pp 861–872 Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. In: Proceedings of IEEE congress on evolutionary computation (CEC 2008). IEEE Press, pp 2424–2431 Koppen M, Yoshida K (2007) Substitute distance assignments in NSGA-II for handling many-objective optimization problems. In: Proceedings of 4th international conference on evolutionary multi-criterion optimzation, vol 4403. LNCS (Springer), pp 727–741 Deb K, Sundar J (2006) Preference point based multi-objective optimization using evolutionary algorithms. In: Proceedings of 2006 genetic and evolutionary computation conference (GECCO 2006), pp 635–642 Knowles J, Corne D (2002) On metrics for comparing non-dominated sets. In: Proceedings of 2002 congress on evolutionary computation. IEEE Press, pp 711–716 Brockhoff D, Zitzler E (2006) Are all objectives necessary? On dimensionality reduction in evolutionary multi-objective optimization. In: Parallel problem solving from nature, PPSN IX, vol 4193. LNCS (Springer), pp 533–542 Wagner T, Beume N, Naujoks B (2007) Pareto-, aggregation, and indicator-based methods in many-objective optimization. In: Proceedings of 4th international conference on evolutionary multi-criterion optimization, vol 4403. LNCS (Springer), pp 742–756 Hughes EJ (2003) Multiple single objective pareto sampling. In: Proceedings of 2003 IEEE congress on evolutionary computation. IEEE Service Center Emmerich M, Beume N., Naujoks B (2005) An EMO algorithm using the hypervolume measure as selection criterion. In: Proceedings of 3rd international conference on evolutionary multi-criterion optimization, vol 3410, LNCS (Springer), pp 62–76 Fonseca C, Paquete L, López-Ibáñez M (2006) An improved dimension-sweep algorithm for the hypervolume indicator. In: Proceedings of 2006 IEEE congress on evolutionary computation, IEEE Service Center, pp 1157–1163 Aguirre H, Tanaka K (2008) Robust optimization by ε-Ranking on high dimensional objective spaces. In: Proceedings of 7th international conference on simulated evolution and learning, vol 5361. LNCS (Springer), pp 421–431 KauffmanSAThe origins of order: self-organization and selection in evolution1993New YorkOxford University Press Ishibuchi H, Nojima Y (2007) Optimization of scalarizing functions through evolutionary multi-objective optimization. In: Proceedings of 4th international conference on evolutionary multi-criterion optimization (EMO 2007), vol 4403. LNCS (Springer), pp 51–65 Zitzler E, Kunzli S (2004) Indicator based selection in multi-objective search. In: Proceedings of conference on parallel problem solving from nature (PPSN VIII). Springer, pp. 832–842 Fleischer M (2003) The measure of pareto optima: applications to multi-objective metaheuristics. In: 2nd International conference on evolutionary multi-criterion optimization, Lecture Notes in Computer Science, vol 2632. Springer, pp 519–533 Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multi-objective optimization test problems. In: Proceedings of 2002 congress on evolutionary computation. IEEE Service Center, pp 825–830 Purshouse RC, Fleming PJ (2003, April) Conflict, harmony, and independence: relationships in evolutionary multi-criterion optimization. In: Proceedings of 2nd international conference on evolutionary multi-criterion optimization, vol 2632. LNCS (Springer), pp16–30 Ishibuchi H, Tsukamoto N, Nojima Y (2007) Iterative approach to indicator-based multi-objective optimization. In: Proceedings of 2007 IEEE congress on evolutionary computation (CEC 2007), pp 3697–3704 DebKMulti-objective optimization using evolutionary algorithms2001ChichesterWiley0970.90091 LaumannsMThieleLDebKZitzlerECombining convergence and diversity in evolutionary multi-objective optimizationEvol Comput200210326328210.1162/106365602760234108(Fall) Aguirre H, Tanaka K (2003) Genetic algorithms on NK-landscapes: effects of selection, drift, mutation, and recombination. In: Proceedings of 3rd European workshop on evolutionary computation in combinatorial optimization (EvoCOP 2003), vol 2611. LNCS (Springer), pp 131–142 Aguirre H, Tanaka K (2004) Insights on properties of multi-objective MNK-landscapes. In: Proceedings of 2004 IEEE congress on evolutionary computation. IEEE Service Center, pp.196–203 Aguirre H, Tanaka K (2005) Selection, drift, recombination, and mutation in multi-objective evolutionary algorithms on scalable MNK-landscapes. In: Proceedings of 3rd international conference on evolutionary multi-criterion optimization, vol. 3410. LNCS (Springer), pp 355–369 AguirreHTanakaKWorking principles, behavior, and performance of MOEAs on MNK-landscapesEur J Oper Res Elsevier20071813167016901123.9006310.1016/j.ejor.2006.08.004 Corne D, Knowles J (2007) Techniques for highly multi-objective optimization: some non-dominated points are better than others. In: Proceedings of 2007 genetic and evolutionary computation conference (GECCO 2007), pp 773–780 YuPLCone convexity, cone extreme points, and nondominated solutions in decision problems with multi-objectivesJ Optim Theory Appl19741433193770268.9005710.1007/BF00932614 31_CR16 31_CR15 31_CR18 31_CR17 SA Kauffman (31_CR26) 1993 31_CR12 31_CR34 31_CR11 31_CR33 31_CR14 31_CR13 31_CR35 31_CR19 PL Yu (31_CR24) 1974; 14 31_CR30 31_CR10 M Laumanns (31_CR25) 2002; 10 31_CR32 31_CR31 31_CR5 31_CR27 31_CR4 31_CR7 31_CR29 31_CR6 31_CR28 31_CR23 31_CR22 31_CR3 31_CR9 K Deb (31_CR1) 2001 C Coello (31_CR2) 2002 31_CR21 31_CR20 H Aguirre (31_CR8) 2007; 181 |
| References_xml | – reference: Ishibuchi H, Nojima Y (2007) Optimization of scalarizing functions through evolutionary multi-objective optimization. In: Proceedings of 4th international conference on evolutionary multi-criterion optimization (EMO 2007), vol 4403. LNCS (Springer), pp 51–65 – reference: Salomon R (1996) Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms, vol 39, no.3. Byosystems, Elsevier, pp 263–278 – reference: Hughes EJ (2005, September) evolutionary many-objective optimisation: many once or one many? In: Proceedings of 2005 IEEE congress on evolutionary computation, vol 1. IEEE Service Center, pp 222–227 – reference: Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. PhD thesis, Swiss Federal Institute of Technology, Zurich – reference: Koppen M, Yoshida K (2007) Substitute distance assignments in NSGA-II for handling many-objective optimization problems. In: Proceedings of 4th international conference on evolutionary multi-criterion optimzation, vol 4403. LNCS (Springer), pp 727–741 – reference: DebKMulti-objective optimization using evolutionary algorithms2001ChichesterWiley0970.90091 – reference: LaumannsMThieleLDebKZitzlerECombining convergence and diversity in evolutionary multi-objective optimizationEvol Comput200210326328210.1162/106365602760234108(Fall) – reference: Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. In: Proceedings of IEEE congress on evolutionary computation (CEC 2008). IEEE Press, pp 2424–2431 – reference: YuPLCone convexity, cone extreme points, and nondominated solutions in decision problems with multi-objectivesJ Optim Theory Appl19741433193770268.9005710.1007/BF00932614 – reference: Purshouse RC, Fleming PJ (2003, April) Conflict, harmony, and independence: relationships in evolutionary multi-criterion optimization. In: Proceedings of 2nd international conference on evolutionary multi-criterion optimization, vol 2632. LNCS (Springer), pp16–30 – reference: Aguirre H, Tanaka K (2008) Robust optimization by ε-Ranking on high dimensional objective spaces. In: Proceedings of 7th international conference on simulated evolution and learning, vol 5361. LNCS (Springer), pp 421–431 – reference: Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multi-objective optimization test problems. In: Proceedings of 2002 congress on evolutionary computation. IEEE Service Center, pp 825–830 – reference: Hughes EJ (2003) Multiple single objective pareto sampling. In: Proceedings of 2003 IEEE congress on evolutionary computation. IEEE Service Center – reference: Brockhoff D, Zitzler E (2006) Are all objectives necessary? On dimensionality reduction in evolutionary multi-objective optimization. In: Parallel problem solving from nature, PPSN IX, vol 4193. LNCS (Springer), pp 533–542 – reference: CoelloCVan VeldhuizenDLamontGEvolutionary algorithms for solving multi-objective problems2002BostonKluwer1130.90002 – reference: Zitzler E, Kunzli S (2004) Indicator based selection in multi-objective search. In: Proceedings of conference on parallel problem solving from nature (PPSN VIII). Springer, pp. 832–842 – reference: Sulflow A, Drechsler N, Drechsler R (2007) Robust multi-objective optimization in high dimensional spaces. In: Proceedings of 4th international conference on evolutionary multi-criterion optimization, vol 4403. LNCS (Springer), pp 715–726 – reference: Iorio A.W., Li X (2004) Solving rotated multi-objective optimization problems using differential evolution. In: Proceedings of 17th Australian joint conference on artificial intelligence 2004, vol 3339. LNAI (Springer), pp 861–872 – reference: Corne D, Knowles J (2007) Techniques for highly multi-objective optimization: some non-dominated points are better than others. In: Proceedings of 2007 genetic and evolutionary computation conference (GECCO 2007), pp 773–780 – reference: Ishibuchi H, Tsukamoto N, Nojima Y (2007) Iterative approach to indicator-based multi-objective optimization. In: Proceedings of 2007 IEEE congress on evolutionary computation (CEC 2007), pp 3697–3704 – reference: Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. KanGAL report 200001 – reference: AguirreHTanakaKWorking principles, behavior, and performance of MOEAs on MNK-landscapesEur J Oper Res Elsevier20071813167016901123.9006310.1016/j.ejor.2006.08.004 – reference: Aguirre H, Tanaka K (2003) Genetic algorithms on NK-landscapes: effects of selection, drift, mutation, and recombination. In: Proceedings of 3rd European workshop on evolutionary computation in combinatorial optimization (EvoCOP 2003), vol 2611. LNCS (Springer), pp 131–142 – reference: Knowles J, Corne D (2002) On metrics for comparing non-dominated sets. In: Proceedings of 2002 congress on evolutionary computation. IEEE Press, pp 711–716 – reference: Deb K, Sundar J (2006) Preference point based multi-objective optimization using evolutionary algorithms. In: Proceedings of 2006 genetic and evolutionary computation conference (GECCO 2006), pp 635–642 – reference: Fleischer M (2003) The measure of pareto optima: applications to multi-objective metaheuristics. In: 2nd International conference on evolutionary multi-criterion optimization, Lecture Notes in Computer Science, vol 2632. Springer, pp 519–533 – reference: Fonseca C, Paquete L, López-Ibáñez M (2006) An improved dimension-sweep algorithm for the hypervolume indicator. In: Proceedings of 2006 IEEE congress on evolutionary computation, IEEE Service Center, pp 1157–1163 – reference: Bleuler S, Laumanns M, Thiele L, Zitzler E (2003) PISA—a platform and programming language independent interface for search algorithms. In: Proceedings of 2nd international conference on evolutionary multi-criterion optimization, vol 2632. LNCS (Springer), pp 494–508 – reference: Aguirre H, Tanaka K (2005) Selection, drift, recombination, and mutation in multi-objective evolutionary algorithms on scalable MNK-landscapes. In: Proceedings of 3rd international conference on evolutionary multi-criterion optimization, vol. 3410. LNCS (Springer), pp 355–369 – reference: Emmerich M, Beume N., Naujoks B (2005) An EMO algorithm using the hypervolume measure as selection criterion. In: Proceedings of 3rd international conference on evolutionary multi-criterion optimization, vol 3410, LNCS (Springer), pp 62–76 – reference: Aguirre H, Tanaka K (2004) Insights on properties of multi-objective MNK-landscapes. In: Proceedings of 2004 IEEE congress on evolutionary computation. IEEE Service Center, pp.196–203 – reference: Wagner T, Beume N, Naujoks B (2007) Pareto-, aggregation, and indicator-based methods in many-objective optimization. In: Proceedings of 4th international conference on evolutionary multi-criterion optimization, vol 4403. LNCS (Springer), pp 742–756 – reference: KauffmanSAThe origins of order: self-organization and selection in evolution1993New YorkOxford University Press – reference: Deb K, Saxena K (2006) Searching for pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. In: Proceedings of 2006 IEEE congress on evolutionary computation (CEC 2006), pp 3353–3360 – reference: Kukkonen S, Lampinen J (2007) Ranking-dominance and many objective optimization. In: Proceedings of 2007 IEEE congress on evolutionary computation (CEC 2007), pp 3983–3990 – volume-title: Evolutionary algorithms for solving multi-objective problems year: 2002 ident: 31_CR2 doi: 10.1007/978-1-4757-5184-0 – ident: 31_CR16 doi: 10.1007/11844297_54 – ident: 31_CR32 – ident: 31_CR27 doi: 10.1109/CEC.2002.1007032 – ident: 31_CR28 – ident: 31_CR7 doi: 10.1109/CEC.2005.1554688 – ident: 31_CR31 doi: 10.1109/CEC.2006.1688440 – ident: 31_CR13 doi: 10.1109/CEC.2007.4424990 – ident: 31_CR11 – ident: 31_CR17 doi: 10.1007/978-3-540-70928-2_54 – ident: 31_CR19 doi: 10.1007/978-3-540-70928-2_56 – ident: 31_CR6 doi: 10.1007/978-3-540-31880-4_25 – ident: 31_CR35 doi: 10.1007/3-540-36970-8_35 – ident: 31_CR15 doi: 10.1007/978-3-540-70928-2_8 – ident: 31_CR22 doi: 10.1007/978-3-540-89694-4_43 – ident: 31_CR5 – ident: 31_CR10 – ident: 31_CR14 doi: 10.1109/CEC.2007.4424988 – volume-title: The origins of order: self-organization and selection in evolution year: 1993 ident: 31_CR26 doi: 10.1093/oso/9780195079517.001.0001 – volume: 10 start-page: 263 issue: 3 year: 2002 ident: 31_CR25 publication-title: Evol Comput doi: 10.1162/106365602760234108 – ident: 31_CR30 doi: 10.1007/3-540-36970-8_37 – ident: 31_CR29 – volume-title: Multi-objective optimization using evolutionary algorithms year: 2001 ident: 31_CR1 – ident: 31_CR9 doi: 10.1007/978-3-540-31880-4_5 – ident: 31_CR4 doi: 10.1109/CEC.2004.1330857 – volume: 14 start-page: 319 issue: 3 year: 1974 ident: 31_CR24 publication-title: J Optim Theory Appl doi: 10.1007/BF00932614 – ident: 31_CR12 – ident: 31_CR3 doi: 10.1007/3-540-36970-8_2 – ident: 31_CR21 doi: 10.1007/3-540-45356-3_83 – ident: 31_CR23 doi: 10.1109/CEC.2008.4631121 – ident: 31_CR18 doi: 10.1007/978-3-540-70928-2_55 – ident: 31_CR20 – ident: 31_CR33 doi: 10.1007/3-540-36605-9_13 – ident: 31_CR34 doi: 10.1007/978-3-540-30549-1_74 – volume: 181 start-page: 1670 issue: 3 year: 2007 ident: 31_CR8 publication-title: Eur J Oper Res Elsevier doi: 10.1016/j.ejor.2006.08.004 |
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| Snippet | This work proposes Adaptive ε-Ranking to enhance Pareto based selection, aiming to develop effective
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-objective evolutionary optimization algorithms.... |
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| Title | Adaptive ε-Ranking on many-objective problems |
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