Skip to main content

2016 | OriginalPaper | Buchkapitel

23. Multiobjective Optimization

verfasst von : Ke-Lin Du, M. N. S. Swamy

Erschienen in: Search and Optimization by Metaheuristics

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Multiobjective optimization problems (MOPs) involve several conflicting objectives to be optimized simultaneously. The challenge is to find a Pareto set involving nondominated solutions that are evenly distributed along the Pareto Front. Metaheuristics for multiobjective optimization have been established as efficient approaches to solve MOPs.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Abbass HA, Sarker R, Newton C. PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of IEEE congress on evolutionary computation (CEC), Seoul, South Korea, May 2001. p. 971–978. Abbass HA, Sarker R, Newton C. PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of IEEE congress on evolutionary computation (CEC), Seoul, South Korea, May 2001. p. 971–978.
2.
Zurück zum Zitat Abbass HA. The self-adaptive pareto differential evolution algorithm. In: Proceedings of IEEE congress on evolutionary computation (CEC), Honolulu, HI, USA, May 2002. p. 831–836. Abbass HA. The self-adaptive pareto differential evolution algorithm. In: Proceedings of IEEE congress on evolutionary computation (CEC), Honolulu, HI, USA, May 2002. p. 831–836.
3.
Zurück zum Zitat Agrawal S, Panigrahi BK, Tiwari MK. Multiobjective particle swarm algorithm with fuzzy clustering for electrical power dispatch. IEEE Trans Evol Comput. 2008;12(5):529–41.CrossRef Agrawal S, Panigrahi BK, Tiwari MK. Multiobjective particle swarm algorithm with fuzzy clustering for electrical power dispatch. IEEE Trans Evol Comput. 2008;12(5):529–41.CrossRef
4.
Zurück zum Zitat Asafuddoula M, Ray T, Sarker R. A decomposition-based evolutionary algorithm for many objective optimization. IEEE Trans Evol Comput. 2015;19(3):445–60.CrossRef Asafuddoula M, Ray T, Sarker R. A decomposition-based evolutionary algorithm for many objective optimization. IEEE Trans Evol Comput. 2015;19(3):445–60.CrossRef
5.
Zurück zum Zitat Auger A, Bader J, Brockhoff D, Zitzler E. Theory of the hypervolume indicator: optimal \(\mu \)-distributions and the choice of the reference point. In: Proceedings of the 10th ACM SIGEVO workshop on foundations of genetic algorithms (FOGA), Orlando, FL, USA, Jan 2009. p. 87–102. Auger A, Bader J, Brockhoff D, Zitzler E. Theory of the hypervolume indicator: optimal \(\mu \)-distributions and the choice of the reference point. In: Proceedings of the 10th ACM SIGEVO workshop on foundations of genetic algorithms (FOGA), Orlando, FL, USA, Jan 2009. p. 87–102.
6.
Zurück zum Zitat Babbar M, Lakshmikantha A, Goldberg DE. A modified NSGA-II to solve noisy multi-objective problems. In: Proceedings of genetic and evolutionary computation conference (GECCO), Chicago, IL, USA, July 2003. p. 21–27. Babbar M, Lakshmikantha A, Goldberg DE. A modified NSGA-II to solve noisy multi-objective problems. In: Proceedings of genetic and evolutionary computation conference (GECCO), Chicago, IL, USA, July 2003. p. 21–27.
7.
Zurück zum Zitat Bader J, Zitzler E. HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput. 2011;19(1):45–76.CrossRef Bader J, Zitzler E. HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput. 2011;19(1):45–76.CrossRef
8.
Zurück zum Zitat Bandyopadhyay S, Mukherjee A. An algorithm for many-objective optimization with reduced objective computations: a study in differential evolution. IEEE Trans Evol Comput. 2015;19(3):400–13.CrossRef Bandyopadhyay S, Mukherjee A. An algorithm for many-objective optimization with reduced objective computations: a study in differential evolution. IEEE Trans Evol Comput. 2015;19(3):400–13.CrossRef
9.
Zurück zum Zitat Bandyopadhyay S, Saha S, Maulik U, Deb K. A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Trans Evol Comput. 2008;12(3):269–83.CrossRef Bandyopadhyay S, Saha S, Maulik U, Deb K. A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Trans Evol Comput. 2008;12(3):269–83.CrossRef
10.
Zurück zum Zitat Bastos-Filho CJA, Guimaraes ACS. Multi-objective fish school search. Int J Swarm Intell Res. 2015;6(1):18p. Bastos-Filho CJA, Guimaraes ACS. Multi-objective fish school search. Int J Swarm Intell Res. 2015;6(1):18p.
11.
Zurück zum Zitat Beausoleil RP. Moss: multiobjective scatter search applied to nonlinear multiple criteria optimization. Eur J Oper Res. 2006;169(2):426–49.MathSciNetMATHCrossRef Beausoleil RP. Moss: multiobjective scatter search applied to nonlinear multiple criteria optimization. Eur J Oper Res. 2006;169(2):426–49.MathSciNetMATHCrossRef
12.
Zurück zum Zitat Bosman PAN, Thierens D. The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Trans Evol Comput. 2003;7(2):174–88.CrossRef Bosman PAN, Thierens D. The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Trans Evol Comput. 2003;7(2):174–88.CrossRef
13.
Zurück zum Zitat Bosman PAN, Thierens D. The naive MIDEA: a baseline multi-objective EA. In: Proceedings of the 3rd international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 428–442. Bosman PAN, Thierens D. The naive MIDEA: a baseline multi-objective EA. In: Proceedings of the 3rd international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 428–442.
14.
Zurück zum Zitat Branke J, Mostaghim S. About selecting the personal best in multiobjective particle swarm optimization. In: Proceedings of conference on parallel problem solving from nature (PPSN IX), Reykjavik, Iceland, Sept 2006. Berlin: Springer; 2006. p. 523–532. Branke J, Mostaghim S. About selecting the personal best in multiobjective particle swarm optimization. In: Proceedings of conference on parallel problem solving from nature (PPSN IX), Reykjavik, Iceland, Sept 2006. Berlin: Springer; 2006. p. 523–532.
15.
Zurück zum Zitat Branke J, Greco S, Slowinski R, Zielniewicz P. Learning value functions in interactive evolutionary multiobjective optimization. IEEE Trans Evol Comput. 2015;19(1):88–102.MATHCrossRef Branke J, Greco S, Slowinski R, Zielniewicz P. Learning value functions in interactive evolutionary multiobjective optimization. IEEE Trans Evol Comput. 2015;19(1):88–102.MATHCrossRef
16.
Zurück zum Zitat Brockhoff D, Zitzler E. Objective reduction in evolutionary multiobjective optimization: theory and applications. Evol Comput. 2009;17(2):135–66.CrossRef Brockhoff D, Zitzler E. Objective reduction in evolutionary multiobjective optimization: theory and applications. Evol Comput. 2009;17(2):135–66.CrossRef
18.
Zurück zum Zitat Bui LT, Liu J, Bender A, Barlow M, Wesolkowski S, Abbass HA. DMEA: a direction-based multiobjective evolutionary algorithm. Memetic Comput. 2011;3:271–85.CrossRef Bui LT, Liu J, Bender A, Barlow M, Wesolkowski S, Abbass HA. DMEA: a direction-based multiobjective evolutionary algorithm. Memetic Comput. 2011;3:271–85.CrossRef
19.
Zurück zum Zitat Cai L, Qu S, Yuan Y, Yao X. A clustering-ranking method for many-objective optimization. Appl Soft Comput. 2015;35:681–94.CrossRef Cai L, Qu S, Yuan Y, Yao X. A clustering-ranking method for many-objective optimization. Appl Soft Comput. 2015;35:681–94.CrossRef
20.
Zurück zum Zitat Camara M, de Toro F, Ortega J. An analysis of multiobjective evolutionary algorithms for optimization problems with time constraints. Appl Artif Intell. 2013;27:851–79.CrossRef Camara M, de Toro F, Ortega J. An analysis of multiobjective evolutionary algorithms for optimization problems with time constraints. Appl Artif Intell. 2013;27:851–79.CrossRef
21.
Zurück zum Zitat Camara M, Ortega J, de Toro F. A single front genetic algorithm for parallel multi-objective optimization in dynamic environments. Neurocomputing. 2009;72:3570–9.CrossRef Camara M, Ortega J, de Toro F. A single front genetic algorithm for parallel multi-objective optimization in dynamic environments. Neurocomputing. 2009;72:3570–9.CrossRef
22.
Zurück zum Zitat Chen Q, Guan S-U. Incremental multiple objective genetic algorithms. IEEE Trans Syst Man Cybern Part B. 2004;34(3):1325–34.MathSciNetCrossRef Chen Q, Guan S-U. Incremental multiple objective genetic algorithms. IEEE Trans Syst Man Cybern Part B. 2004;34(3):1325–34.MathSciNetCrossRef
23.
Zurück zum Zitat Clymont KM, Keedwell E. Deductive sort and climbing sort: new methods for non-dominated sorting. Evol Comput. 2012;20(1):1–26.CrossRef Clymont KM, Keedwell E. Deductive sort and climbing sort: new methods for non-dominated sorting. Evol Comput. 2012;20(1):1–26.CrossRef
24.
Zurück zum Zitat Coello CAC, Becerra RL. Evolutionary multiobjective optimization using a cultural algorithm. In: Proceedings of IEEE swarm intelligence symposium, Indianapolis, IN, USA, April 2003. p. 6–13. Coello CAC, Becerra RL. Evolutionary multiobjective optimization using a cultural algorithm. In: Proceedings of IEEE swarm intelligence symposium, Indianapolis, IN, USA, April 2003. p. 6–13.
25.
Zurück zum Zitat Coello CAC, Cortes NC. Solving multiobjective optimization problems using an artificial immune system. Genet Program Evolvable Mach. 2005;6:163–90.CrossRef Coello CAC, Cortes NC. Solving multiobjective optimization problems using an artificial immune system. Genet Program Evolvable Mach. 2005;6:163–90.CrossRef
26.
Zurück zum Zitat Coello CAC, Lechuga MS. MOPSO: a proposal for multiple objective particle swarm optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), Honolulu, HI, USA, May 2002. p. 1051–1056. Coello CAC, Lechuga MS. MOPSO: a proposal for multiple objective particle swarm optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), Honolulu, HI, USA, May 2002. p. 1051–1056.
27.
Zurück zum Zitat Coello CAC, Pulido GT. A micro-genetic algorithm for multiobjective optimization. In: Proceedings of the 1st international conference on evolutionary multi-criterion optimization (EMO), Zurich, Switzerland, March 2001. p. 126–140. Coello CAC, Pulido GT. A micro-genetic algorithm for multiobjective optimization. In: Proceedings of the 1st international conference on evolutionary multi-criterion optimization (EMO), Zurich, Switzerland, March 2001. p. 126–140.
28.
Zurück zum Zitat Coello CAC, Pulido GT, Lechuga MS. Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput. 2004;8(3):256–79.CrossRef Coello CAC, Pulido GT, Lechuga MS. Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput. 2004;8(3):256–79.CrossRef
29.
Zurück zum Zitat Corne DW, Jerram NR, Knowles JD, Oates MJ. PESA-II: region-based selection in evolutionary multiobjective optimization. In: Proceedings of genetic and evolutionary computation conference (GECCO), San Francisco, CA, USA, July 2001. p. 283–290. Corne DW, Jerram NR, Knowles JD, Oates MJ. PESA-II: region-based selection in evolutionary multiobjective optimization. In: Proceedings of genetic and evolutionary computation conference (GECCO), San Francisco, CA, USA, July 2001. p. 283–290.
30.
Zurück zum Zitat Corne DW, Knowles JD. Techniques for highly multiobjective optimization: some nondominated points are better than others. In: Proceedings of the 9th ACM genetic and evolutionary computation conference (GECCO), London, UK, July 2007. p. 773–780. Corne DW, Knowles JD. Techniques for highly multiobjective optimization: some nondominated points are better than others. In: Proceedings of the 9th ACM genetic and evolutionary computation conference (GECCO), London, UK, July 2007. p. 773–780.
31.
Zurück zum Zitat Corne DW, Knowles JD, Oates MJ. The pareto envelope-based selection algorithm for multiobjective optimisation. In: Proceedings of the 6th international conference on parallel problem solving from nature (PPSN VI), Paris, France, Sept 2000. Berlin: Springer; 2000. p. 839–848. Corne DW, Knowles JD, Oates MJ. The pareto envelope-based selection algorithm for multiobjective optimisation. In: Proceedings of the 6th international conference on parallel problem solving from nature (PPSN VI), Paris, France, Sept 2000. Berlin: Springer; 2000. p. 839–848.
32.
Zurück zum Zitat Costa M, Minisci E. MOPED: a multi-objective Parzen-based estimation of distribution algorithm for continuous problems. In: Proceedings of the 2nd international conference on evolutionary multi-criterion optimization (EMO), Faro, Portugal, April 2003. p. 282–294. Costa M, Minisci E. MOPED: a multi-objective Parzen-based estimation of distribution algorithm for continuous problems. In: Proceedings of the 2nd international conference on evolutionary multi-criterion optimization (EMO), Faro, Portugal, April 2003. p. 282–294.
33.
Zurück zum Zitat Costa e Silva MA, Coelho LDS, Lebensztajn L. Multiobjective biogeography-based optimization based on predator-prey approach. IEEE Trans Magn. 2012;48(2):951–954. Costa e Silva MA, Coelho LDS, Lebensztajn L. Multiobjective biogeography-based optimization based on predator-prey approach. IEEE Trans Magn. 2012;48(2):951–954.
34.
Zurück zum Zitat Dai X, Yuan X, Zhang Z. A self-adaptive multi-objective harmony search algorithm based on harmony memory variance. Appl Soft Comput. 2015;35:541–57.CrossRef Dai X, Yuan X, Zhang Z. A self-adaptive multi-objective harmony search algorithm based on harmony memory variance. Appl Soft Comput. 2015;35:541–57.CrossRef
35.
Zurück zum Zitat Deb K. Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol Comput. 1999;7(3):205–30.CrossRef Deb K. Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol Comput. 1999;7(3):205–30.CrossRef
36.
Zurück zum Zitat Deb K. Multi-objective optimization using evolutionary algorithms. Chichester: Wiley; 2001.MATH Deb K. Multi-objective optimization using evolutionary algorithms. Chichester: Wiley; 2001.MATH
37.
Zurück zum Zitat Deb K, Agrawal S, Pratap A, Meyarivan T. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of the 6th international conference on parallel problem solving from nature (PPSN VI), Paris, France, Sept 2000. Berlin: Springer; 2000. p. 849–858. Deb K, Agrawal S, Pratap A, Meyarivan T. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of the 6th international conference on parallel problem solving from nature (PPSN VI), Paris, France, Sept 2000. Berlin: Springer; 2000. p. 849–858.
38.
Zurück zum Zitat Deb K, Jain H. An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part i: solving problems with box constraints. IEEE Trans Evol Comput. 2013;18(4):577–601. Deb K, Jain H. An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part i: solving problems with box constraints. IEEE Trans Evol Comput. 2013;18(4):577–601.
39.
Zurück zum Zitat Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput. 2002;6(2):182–97.CrossRef Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput. 2002;6(2):182–97.CrossRef
40.
Zurück zum Zitat Deb K, Saxena DK. On finding Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. KanGAL Report, No.2005011. 2005. Deb K, Saxena DK. On finding Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. KanGAL Report, No.2005011. 2005.
41.
Zurück zum Zitat Deb K, Sinha A, Kukkonen S. Multi-objective test problems, linkages, and evolutionary methodologies. In: Proceedings of genetic and evolutinary computation conference (GECCO), Seattle, WA, USA, July 2006. p. 1141–1148. Deb K, Sinha A, Kukkonen S. Multi-objective test problems, linkages, and evolutionary methodologies. In: Proceedings of genetic and evolutinary computation conference (GECCO), Seattle, WA, USA, July 2006. p. 1141–1148.
42.
Zurück zum Zitat Deb K, Sundar J. Reference point based multiobjective optimization using evolutionary algorithms. In: Proceedings of the 8th genetic and evolutionary computation conference (GECCO), Seattle, WA, USA, July 2006. p. 635–642. Deb K, Sundar J. Reference point based multiobjective optimization using evolutionary algorithms. In: Proceedings of the 8th genetic and evolutionary computation conference (GECCO), Seattle, WA, USA, July 2006. p. 635–642.
43.
Zurück zum Zitat Depolli M, Trobec R, Filipic B. Asynchronous master-slave parallelization of differential evolution for multi-objective optimization. Evol Comput. 2013;21(2):261–91.CrossRef Depolli M, Trobec R, Filipic B. Asynchronous master-slave parallelization of differential evolution for multi-objective optimization. Evol Comput. 2013;21(2):261–91.CrossRef
44.
Zurück zum Zitat di Pierro F, Khu S-T, Savic DA. An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Trans Evol Comput. 2007;11(1):17–45.CrossRef di Pierro F, Khu S-T, Savic DA. An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Trans Evol Comput. 2007;11(1):17–45.CrossRef
45.
Zurück zum Zitat Elhossini A, Areibi S, Dony R. Strength Pareto particle swarm optimization and hybrid EA-PSO for multi-objective optimization. Evol Comput. 2010;18(1):127–56.CrossRef Elhossini A, Areibi S, Dony R. Strength Pareto particle swarm optimization and hybrid EA-PSO for multi-objective optimization. Evol Comput. 2010;18(1):127–56.CrossRef
46.
Zurück zum Zitat Erickson M, Mayer A, Horn J. The niched pareto genetic algorithm 2 applied to the design of groundwater remediation systems. In: Proceedings of the 1st international conference on evolutionary multi-criterion optimization (EMO), Zurich, Switzerland, March 2001. p. 681–695. Erickson M, Mayer A, Horn J. The niched pareto genetic algorithm 2 applied to the design of groundwater remediation systems. In: Proceedings of the 1st international conference on evolutionary multi-criterion optimization (EMO), Zurich, Switzerland, March 2001. p. 681–695.
47.
Zurück zum Zitat Fang H, Wang Q, Tu Y-C, Horstemeyer MF. An efficient non-dominated sorting method for evolutionary algorithms. Evol Comput. 2008;16(3):355–84.CrossRef Fang H, Wang Q, Tu Y-C, Horstemeyer MF. An efficient non-dominated sorting method for evolutionary algorithms. Evol Comput. 2008;16(3):355–84.CrossRef
48.
Zurück zum Zitat Farina M, Amato P. On the optimal solution definition for many-criteria optimization problems. In: Proceedings of the annual meeting of the North American fuzzy information processing society (NAFIPS), New Orleans, LA, USA, June 2002. p. 233–238. Farina M, Amato P. On the optimal solution definition for many-criteria optimization problems. In: Proceedings of the annual meeting of the North American fuzzy information processing society (NAFIPS), New Orleans, LA, USA, June 2002. p. 233–238.
49.
Zurück zum Zitat Fleming PJ, Purshouse RC, Lygoe RJ. Many-objective optimization: an engineering design perspective. In: Proceedings of international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 14–32. Fleming PJ, Purshouse RC, Lygoe RJ. Many-objective optimization: an engineering design perspective. In: Proceedings of international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 14–32.
50.
Zurück zum Zitat Fonseca CM, Fleming PJ. Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Forrest S, editor. Proceedings of the 5th international conference on genetic algorithms, July 1993. San Francisco, CA: Morgan Kaufmann; 1993. p. 416–423. Fonseca CM, Fleming PJ. Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Forrest S, editor. Proceedings of the 5th international conference on genetic algorithms, July 1993. San Francisco, CA: Morgan Kaufmann; 1993. p. 416–423.
51.
Zurück zum Zitat Fonseca CM, Fleming PJ. Multiobjective optimization and multiple constraint handling with evolutionary algorithms—Part i: a unified formulation; Part ii: application example. IEEE Trans Syst Man Cybern Part A. 1998;28(1):26–37, 38–47. Fonseca CM, Fleming PJ. Multiobjective optimization and multiple constraint handling with evolutionary algorithms—Part i: a unified formulation; Part ii: application example. IEEE Trans Syst Man Cybern Part A. 1998;28(1):26–37, 38–47.
52.
Zurück zum Zitat Freschi F, Repetto M. Multiobjective optimization by a modified artificial immune system algorithm. In: Proceedings of the 4th international conference on artificial immune systems (ICARIS), Banff, Alberta, Canada, Aug 2005. pp. 248–261. Freschi F, Repetto M. Multiobjective optimization by a modified artificial immune system algorithm. In: Proceedings of the 4th international conference on artificial immune systems (ICARIS), Banff, Alberta, Canada, Aug 2005. pp. 248–261.
53.
Zurück zum Zitat Garcia-Martinez C, Cordon O, Herrera F. A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. Eur J Oper Res. 2007;180(1):116–48.MATHCrossRef Garcia-Martinez C, Cordon O, Herrera F. A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. Eur J Oper Res. 2007;180(1):116–48.MATHCrossRef
54.
Zurück zum Zitat Ghasemi M, Ghavidel S, Ghanbarian MM, Gitizadeh M. Multi-objective optimal electric power planning in the power system using Gaussian bare-bones imperialist competitive algorithm. Inf Sci. 2015;294:286–304.MathSciNetCrossRef Ghasemi M, Ghavidel S, Ghanbarian MM, Gitizadeh M. Multi-objective optimal electric power planning in the power system using Gaussian bare-bones imperialist competitive algorithm. Inf Sci. 2015;294:286–304.MathSciNetCrossRef
55.
Zurück zum Zitat Giagkiozis I, Purshouse RC, Fleming PJ. Generalized decomposition and cross entropy methods for many-objective optimization. Inf Sci. 2014;282:363–87.MathSciNetCrossRef Giagkiozis I, Purshouse RC, Fleming PJ. Generalized decomposition and cross entropy methods for many-objective optimization. Inf Sci. 2014;282:363–87.MathSciNetCrossRef
56.
Zurück zum Zitat Goh C-K, Tan KC. A competitive-cooperative coevolutionary paradigm for dynamic multiobjective optimization. IEEE Trans Evol Comput. 2009;13(1):103–27.CrossRef Goh C-K, Tan KC. A competitive-cooperative coevolutionary paradigm for dynamic multiobjective optimization. IEEE Trans Evol Comput. 2009;13(1):103–27.CrossRef
57.
Zurück zum Zitat Goh CK, Tan KC, Liu DS, Chiam SC. A competitive and cooperative coevolutionary approach to multi-objective particle swarm optimization algorithm design. Eur J Oper Res. 2010;202(1):42–54.MATHCrossRef Goh CK, Tan KC, Liu DS, Chiam SC. A competitive and cooperative coevolutionary approach to multi-objective particle swarm optimization algorithm design. Eur J Oper Res. 2010;202(1):42–54.MATHCrossRef
58.
Zurück zum Zitat Goldberg DE. Genetic algorithms in search, optimization, and machine learning. Reading, MA, USA: Addison-Wesley; 1989.MATH Goldberg DE. Genetic algorithms in search, optimization, and machine learning. Reading, MA, USA: Addison-Wesley; 1989.MATH
59.
Zurück zum Zitat Gong M, Jiao L, Du H, Bo L. Multiobjective immune algorithm with nondominated neighbor-based selection. Evol Comput. 2008;16(2):225–55.CrossRef Gong M, Jiao L, Du H, Bo L. Multiobjective immune algorithm with nondominated neighbor-based selection. Evol Comput. 2008;16(2):225–55.CrossRef
60.
Zurück zum Zitat Guevara-Souza M, Vallejo EE. Using a simulated Wolbachia infection mechanism to improve multi-objective evolutionary algorithms. Nat Comput. 2015;14:157–67.MathSciNetCrossRef Guevara-Souza M, Vallejo EE. Using a simulated Wolbachia infection mechanism to improve multi-objective evolutionary algorithms. Nat Comput. 2015;14:157–67.MathSciNetCrossRef
61.
Zurück zum Zitat Guzman MA, Delgado A, De Carvalho J. A novel multi-objective optimization algorithm based on bacterial chemotaxis. Eng Appl Artif Intell. 2010;23:292–301.CrossRef Guzman MA, Delgado A, De Carvalho J. A novel multi-objective optimization algorithm based on bacterial chemotaxis. Eng Appl Artif Intell. 2010;23:292–301.CrossRef
62.
Zurück zum Zitat Hadka D, Reed P. Diagnostic assessment of search controls and failure modes in many-objective evolutionary optimization. Evol Comput. 2012;20(3):423–52.CrossRef Hadka D, Reed P. Diagnostic assessment of search controls and failure modes in many-objective evolutionary optimization. Evol Comput. 2012;20(3):423–52.CrossRef
63.
Zurück zum Zitat Hadka D, Reed P. Borg: an auto-adaptive many-objective evolutionary computing framework. Evol Comput. 2013;21:231–59.CrossRef Hadka D, Reed P. Borg: an auto-adaptive many-objective evolutionary computing framework. Evol Comput. 2013;21:231–59.CrossRef
64.
Zurück zum Zitat Hansen MP, Jaszkiewicz A. Evaluating the quality of approximations to the non-dominated set. Technical Report IMM-REP-1998-7, Institute of Mathematical Modeling, Technical University of Denmark, Denmark; 1998. Hansen MP, Jaszkiewicz A. Evaluating the quality of approximations to the non-dominated set. Technical Report IMM-REP-1998-7, Institute of Mathematical Modeling, Technical University of Denmark, Denmark; 1998.
65.
Zurück zum Zitat He X-S, Li N, Yang X-S. Non-dominated sorting cuckoo search for multiobjective optimization. In: Proceedings of IEEE symposium on swarm intelligence (SIS), Orlando, FL, USA, Dec 2014. p. 1–7. He X-S, Li N, Yang X-S. Non-dominated sorting cuckoo search for multiobjective optimization. In: Proceedings of IEEE symposium on swarm intelligence (SIS), Orlando, FL, USA, Dec 2014. p. 1–7.
66.
Zurück zum Zitat He Z, Yen GG. Many-objective evolutionary algorithm: objective space reduction and diversity improvement. IEEE Trans Evol Comput. 2016;20(1):145–60.CrossRef He Z, Yen GG. Many-objective evolutionary algorithm: objective space reduction and diversity improvement. IEEE Trans Evol Comput. 2016;20(1):145–60.CrossRef
67.
Zurück zum Zitat Hu X, Eberhart RC. Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Proceedings of congress on evolutinary computation (CEC), Honolulu, HI, USA, May 2002. p. 1677–1681. Hu X, Eberhart RC. Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Proceedings of congress on evolutinary computation (CEC), Honolulu, HI, USA, May 2002. p. 1677–1681.
68.
Zurück zum Zitat Hu X, Eberhart RC, Shi Y. Particle swarm with extended memory for multiobjective optimization. In: Proceedings of IEEE swarm intelligence symposium, Indianapolis, IN, USA, April 2003. p. 193–197. Hu X, Eberhart RC, Shi Y. Particle swarm with extended memory for multiobjective optimization. In: Proceedings of IEEE swarm intelligence symposium, Indianapolis, IN, USA, April 2003. p. 193–197.
69.
70.
Zurück zum Zitat Huo Y, Zhuang Y, Gu J, Ni S. Elite-guided multi-objective artificial bee colony algorithm. Appl Soft Comput. 2015;32:199–210.CrossRef Huo Y, Zhuang Y, Gu J, Ni S. Elite-guided multi-objective artificial bee colony algorithm. Appl Soft Comput. 2015;32:199–210.CrossRef
71.
Zurück zum Zitat Horn J, Nafpliotis N, Goldberg DE. A niched pareto genetic algorithm for multiobjective optimization. In: Proceedings of the 1st IEEE conference on evolutionary computation, Orlando, FL, USA, June 1994. p. 82–87. Horn J, Nafpliotis N, Goldberg DE. A niched pareto genetic algorithm for multiobjective optimization. In: Proceedings of the 1st IEEE conference on evolutionary computation, Orlando, FL, USA, June 1994. p. 82–87.
72.
Zurück zum Zitat Ikeda K, Kita H, Kobayashi S. Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? In: Proceedings of congress on evolutionary computation (CEC), Seoul, Korea, May 2001. p. 957–962. Ikeda K, Kita H, Kobayashi S. Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? In: Proceedings of congress on evolutionary computation (CEC), Seoul, Korea, May 2001. p. 957–962.
73.
Zurück zum Zitat Iorio AW, Li X. A cooperative coevolutionary multiobjective algorithm using non-dominated sorting. In: Proceedings of genetic and evolutionary computation conference (GECCO), Seattle, WA, USA, June 2004. p. 537–548. Iorio AW, Li X. A cooperative coevolutionary multiobjective algorithm using non-dominated sorting. In: Proceedings of genetic and evolutionary computation conference (GECCO), Seattle, WA, USA, June 2004. p. 537–548.
74.
Zurück zum Zitat Ishibuchi H, Murata T. Multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans Syst Man Cybern Part C. 1998;28(3):392–403.CrossRef Ishibuchi H, Murata T. Multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans Syst Man Cybern Part C. 1998;28(3):392–403.CrossRef
75.
Zurück zum Zitat Jaimes AL, Coello CAC, Barrientos JEU. Online objective reduction to deal with many-objective problems. In: Proceedings of the 5th international conference on evolutionary multi-criterion optimization (EMO), Nantes, France, April 2009. p. 423–437. Jaimes AL, Coello CAC, Barrientos JEU. Online objective reduction to deal with many-objective problems. In: Proceedings of the 5th international conference on evolutionary multi-criterion optimization (EMO), Nantes, France, April 2009. p. 423–437.
76.
Zurück zum Zitat Jain H, Deb K. An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part ii: handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput. 2013;18(4):602–22. Jain H, Deb K. An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part ii: handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput. 2013;18(4):602–22.
77.
Zurück zum Zitat Jensen MT. Reducing the run-time complexity of multiobjective eas: the NSGA-II and other algorithms. IEEE Trans Evol Comput. 2003;7(5):503–15.CrossRef Jensen MT. Reducing the run-time complexity of multiobjective eas: the NSGA-II and other algorithms. IEEE Trans Evol Comput. 2003;7(5):503–15.CrossRef
78.
Zurück zum Zitat Jiao L, Gong M, Shang R, Du H, Lu B. Clonal selection with immune dominance and energy based multiobjective optimization. In: Proceedings of the 3rd international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 474–489. Jiao L, Gong M, Shang R, Du H, Lu B. Clonal selection with immune dominance and energy based multiobjective optimization. In: Proceedings of the 3rd international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 474–489.
79.
80.
Zurück zum Zitat Keerativuttitumrong N, Chaiyaratana N, Varavithya V. Multi-objective co-operative co-evolutionary genetic algorithm. In: Proceedings of the 7th international conference on parallel problem solving from nature (PPSN VII), Granada, Spain, Sept 2002. Berlin: Springer; 2002. p. 288–297. Keerativuttitumrong N, Chaiyaratana N, Varavithya V. Multi-objective co-operative co-evolutionary genetic algorithm. In: Proceedings of the 7th international conference on parallel problem solving from nature (PPSN VII), Granada, Spain, Sept 2002. Berlin: Springer; 2002. p. 288–297.
81.
Zurück zum Zitat Khan N. Bayesian optimization algorithms for multi-objective and hierarchically difficult problem. IlliGAL Report No. 2003021, Department of General Engineering, University of Illinois at Urbana-Champainge, Urbana, IL, USA. 2003. Khan N. Bayesian optimization algorithms for multi-objective and hierarchically difficult problem. IlliGAL Report No. 2003021, Department of General Engineering, University of Illinois at Urbana-Champainge, Urbana, IL, USA. 2003.
82.
Zurück zum Zitat Khare V, Yao X, Deb K. Performance scaling of multiobjective evolutionary algorithms. In: Proceedings of the 2nd international conference on evolutionry multi-criterion optimization (EMO), Faro, Portugal, April 2003. p. 376–390. Khare V, Yao X, Deb K. Performance scaling of multiobjective evolutionary algorithms. In: Proceedings of the 2nd international conference on evolutionry multi-criterion optimization (EMO), Faro, Portugal, April 2003. p. 376–390.
83.
Zurück zum Zitat Knowles J. ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans Evol Comput. 2006;10(1):50–66.CrossRef Knowles J. ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans Evol Comput. 2006;10(1):50–66.CrossRef
84.
Zurück zum Zitat Knowles JD, Corne DW. Approximating the nondominated front using the Pareto archived evolution strategy. Evol Comput. 2000;8(2):149–72.CrossRef Knowles JD, Corne DW. Approximating the nondominated front using the Pareto archived evolution strategy. Evol Comput. 2000;8(2):149–72.CrossRef
85.
Zurück zum Zitat Knowles JD, Corne DW. M-PAES: a memetic algorithm for multiobjective optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), La Jolla, CA, USA, July 2000. p. 325–332. Knowles JD, Corne DW. M-PAES: a memetic algorithm for multiobjective optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), La Jolla, CA, USA, July 2000. p. 325–332.
86.
Zurück zum Zitat Knowles JD, Corne DW. Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In: Proceedings of the 4th international conference on evolutionary multi-criterion optimization (EMO), Matsushima, Japan, March 2007. p. 757–771. Knowles JD, Corne DW. Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In: Proceedings of the 4th international conference on evolutionary multi-criterion optimization (EMO), Matsushima, Japan, March 2007. p. 757–771.
87.
Zurück zum Zitat Koppen M, Yoshida K. Substitute distance assignments in NSGAII for handling many-objective optimization problems. In: Proceedings of the 4th international conference on evolutionary multi-criterion optimization (EMO), Matsushima, Japan, March 2007. p. 727–741. Koppen M, Yoshida K. Substitute distance assignments in NSGAII for handling many-objective optimization problems. In: Proceedings of the 4th international conference on evolutionary multi-criterion optimization (EMO), Matsushima, Japan, March 2007. p. 727–741.
88.
Zurück zum Zitat Kukkonen S, Lampinen J. GDE3: the third evolution step of generalized differential evolution. In: Proceedings of IEEE congress on evolutionary computation (CEC), Edinburgh, UK, Sept 2005. p. 443–450. Kukkonen S, Lampinen J. GDE3: the third evolution step of generalized differential evolution. In: Proceedings of IEEE congress on evolutionary computation (CEC), Edinburgh, UK, Sept 2005. p. 443–450.
89.
Zurück zum Zitat Kumar V, Chhabra JK, Kumar D. Differential search algorithm for multiobjective problems. Procedia Comput Sci. 2015;48:22–8.CrossRef Kumar V, Chhabra JK, Kumar D. Differential search algorithm for multiobjective problems. Procedia Comput Sci. 2015;48:22–8.CrossRef
90.
Zurück zum Zitat Kundu D, Suresh K, Ghosh S, Das S, Panigrahi BK, Das S. Multi-objective optimization with artificial weed colonies. Inf Sci. 2011;181(12):2441–54.MathSciNetCrossRef Kundu D, Suresh K, Ghosh S, Das S, Panigrahi BK, Das S. Multi-objective optimization with artificial weed colonies. Inf Sci. 2011;181(12):2441–54.MathSciNetCrossRef
91.
Zurück zum Zitat Lara A, Sanchez G, Coello CAC, Schutze O. HCS: a new local search strategy for memetic multiobjective evolutionary algorithms. IEEE Trans Evol Comput. 2010;14(1):112–32.CrossRef Lara A, Sanchez G, Coello CAC, Schutze O. HCS: a new local search strategy for memetic multiobjective evolutionary algorithms. IEEE Trans Evol Comput. 2010;14(1):112–32.CrossRef
92.
Zurück zum Zitat Laumanns M, Ocenasek J. Bayesian optimization algorithms for multi-objective optimization. In: Proceedings of the 7th international conference on parallel problem solving from nature (PPSN-VII), Granada, Spain, Sept 2002. Berlin: Springer; 2002. p. 298–307. Laumanns M, Ocenasek J. Bayesian optimization algorithms for multi-objective optimization. In: Proceedings of the 7th international conference on parallel problem solving from nature (PPSN-VII), Granada, Spain, Sept 2002. Berlin: Springer; 2002. p. 298–307.
93.
Zurück zum Zitat Laumanns M, Rudolph G, Schwefel H-P. A spatial predator-prey approach to multiobjective optimization: a preliminary study. In: Proceedings of the 5th international conference on parallel problem solving from nature (PPSN-V), Amsterdam, The Netherlands, Sept 1998. Berlin: Springer; 1998. p. 241–249. Laumanns M, Rudolph G, Schwefel H-P. A spatial predator-prey approach to multiobjective optimization: a preliminary study. In: Proceedings of the 5th international conference on parallel problem solving from nature (PPSN-V), Amsterdam, The Netherlands, Sept 1998. Berlin: Springer; 1998. p. 241–249.
94.
Zurück zum Zitat Laumanns M, Thiele L, Deb K, Zitzler E. Combining convergence and diversity in evolutionary multi-objective optimization. Evol Comput. 2002;10(3):263–82.CrossRef Laumanns M, Thiele L, Deb K, Zitzler E. Combining convergence and diversity in evolutionary multi-objective optimization. Evol Comput. 2002;10(3):263–82.CrossRef
95.
Zurück zum Zitat Li H, Zhang Q. Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput. 2009;13(2):284–302.CrossRef Li H, Zhang Q. Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput. 2009;13(2):284–302.CrossRef
96.
Zurück zum Zitat Li JQ, Pan QK, Gao KZ. Pareto-based discrete artificial bee colony algorithm for multi-objective flexible job shop scheduling problems. Int J Adv Manuf Technol. 2011;55:1159–69.CrossRef Li JQ, Pan QK, Gao KZ. Pareto-based discrete artificial bee colony algorithm for multi-objective flexible job shop scheduling problems. Int J Adv Manuf Technol. 2011;55:1159–69.CrossRef
97.
Zurück zum Zitat Li K, Zhang Q, Kwong S, Li M, Wang R. Stable matching-based selection in evolutionary multiobjective optimization. IEEE Trans Evol Comput. 2014;18(6):909–23.CrossRef Li K, Zhang Q, Kwong S, Li M, Wang R. Stable matching-based selection in evolutionary multiobjective optimization. IEEE Trans Evol Comput. 2014;18(6):909–23.CrossRef
98.
Zurück zum Zitat Li M, Yang S, Liu X. Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput. 2014;18(3):348–65.CrossRef Li M, Yang S, Liu X. Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput. 2014;18(3):348–65.CrossRef
100.
Zurück zum Zitat Li X. A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Proceedings of genetic and evolutionary computation conference (GECCO), Chicago, IL, USA, July 2003. p. 37–48. Li X. A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Proceedings of genetic and evolutionary computation conference (GECCO), Chicago, IL, USA, July 2003. p. 37–48.
101.
Zurück zum Zitat Li X. Better spread and convergence: particle swarm multiobjective optimization using the maximin fitness function. In: Proceedings of genetic and evolutionary computation conference (GECCO), Seattle, WA, USA, June 2004. p. 117–128. Li X. Better spread and convergence: particle swarm multiobjective optimization using the maximin fitness function. In: Proceedings of genetic and evolutionary computation conference (GECCO), Seattle, WA, USA, June 2004. p. 117–128.
102.
Zurück zum Zitat Li Z, Nguyen TT, Chen SM, Truong TK. A hybrid algorithm based on particle swarm and chemical reaction optimization for multi-object problems. Appl Soft Comput. 2015;35:525–40.CrossRef Li Z, Nguyen TT, Chen SM, Truong TK. A hybrid algorithm based on particle swarm and chemical reaction optimization for multi-object problems. Appl Soft Comput. 2015;35:525–40.CrossRef
103.
Zurück zum Zitat Liang Z, Song R, Lin Q, Du Z, Chen J, Ming Z, Yu J. A double-module immune algorithm for multi-objective optimization problems. Appl Soft Comput. 2015;35:161–74.CrossRef Liang Z, Song R, Lin Q, Du Z, Chen J, Ming Z, Yu J. A double-module immune algorithm for multi-objective optimization problems. Appl Soft Comput. 2015;35:161–74.CrossRef
104.
Zurück zum Zitat Liu D, Tan KC, Goh CK, Ho WK. A multiobjective memetic algorithm based on particle swarm optimization. IEEE Trans Syst Man Cybern Part B. 2007;37(1):42–50.CrossRef Liu D, Tan KC, Goh CK, Ho WK. A multiobjective memetic algorithm based on particle swarm optimization. IEEE Trans Syst Man Cybern Part B. 2007;37(1):42–50.CrossRef
105.
Zurück zum Zitat Lohn JD, Kraus WF, Haith GL. Comparing a coevolutionary genetic algorithm for multiobjective optimization. In: Proceedings of the world on congress on computational intelligence, Honolulu, HI, USA, May 2002. p. 1157–1162. Lohn JD, Kraus WF, Haith GL. Comparing a coevolutionary genetic algorithm for multiobjective optimization. In: Proceedings of the world on congress on computational intelligence, Honolulu, HI, USA, May 2002. p. 1157–1162.
106.
Zurück zum Zitat Lu H, Yen G. Rank-density-based multiobjective genetic algorithm and benchmark test function study. IEEE Trans Evol Comput. 2003;7(4):325–43.CrossRef Lu H, Yen G. Rank-density-based multiobjective genetic algorithm and benchmark test function study. IEEE Trans Evol Comput. 2003;7(4):325–43.CrossRef
107.
Zurück zum Zitat Leong W-F, Yen GG. PSO-based multiobjective optimization with dynamic population size and adaptive local archives. IEEE Trans Syst Man Cybern Part B. 2008;38(5):1270–93.CrossRef Leong W-F, Yen GG. PSO-based multiobjective optimization with dynamic population size and adaptive local archives. IEEE Trans Syst Man Cybern Part B. 2008;38(5):1270–93.CrossRef
108.
Zurück zum Zitat Lopez-Jaimes A, Coello Coello CA. Including preferences into a multiobjective evolutionary algorithm to deal with many-objective engineering optimization problems. Inf Sci. 2014;277:1–20.MathSciNetCrossRef Lopez-Jaimes A, Coello Coello CA. Including preferences into a multiobjective evolutionary algorithm to deal with many-objective engineering optimization problems. Inf Sci. 2014;277:1–20.MathSciNetCrossRef
109.
Zurück zum Zitat Lu Z, Zhao H, Xiao H, Wang H, Wang H. An improved multi-objective bacteria colony chemotaxis algorithm and convergence analysis. Appl Soft Comput. 2015;31:274–92.CrossRef Lu Z, Zhao H, Xiao H, Wang H, Wang H. An improved multi-objective bacteria colony chemotaxis algorithm and convergence analysis. Appl Soft Comput. 2015;31:274–92.CrossRef
110.
Zurück zum Zitat Ma X, Qi Y, Li L, Liu F, Jiao L, Wu J. MOEA/D with uniform decomposition measurement for many-objective problems. Soft Comput. 2014;18:2541–64.CrossRef Ma X, Qi Y, Li L, Liu F, Jiao L, Wu J. MOEA/D with uniform decomposition measurement for many-objective problems. Soft Comput. 2014;18:2541–64.CrossRef
111.
Zurück zum Zitat Madavan NK. Multiobjective optimization using a Pareto differential evolution approach. In: Proceedings of IEEE congress on evolutionary computation (CEC), Honolulu, HI, USA, May 2002. p. 1145–1150. Madavan NK. Multiobjective optimization using a Pareto differential evolution approach. In: Proceedings of IEEE congress on evolutionary computation (CEC), Honolulu, HI, USA, May 2002. p. 1145–1150.
112.
Zurück zum Zitat Marti L, Garcia J, Berlanga A, Molina JM. Solving complex high-dimensional problems with the multi-objective neural estimation of distribution algorithm. In: Proceedings of the 11th genetic and evolutionary computation conference (GECCO), Montreal, Canada, July 2009. p. 619–626. Marti L, Garcia J, Berlanga A, Molina JM. Solving complex high-dimensional problems with the multi-objective neural estimation of distribution algorithm. In: Proceedings of the 11th genetic and evolutionary computation conference (GECCO), Montreal, Canada, July 2009. p. 619–626.
113.
Zurück zum Zitat Menczer F, Degeratu M, Steet WN. Efficient and scalable Pareto optimization by evolutionary local selection algorithms. Evol Comput. 2000;8(2):223–47.CrossRef Menczer F, Degeratu M, Steet WN. Efficient and scalable Pareto optimization by evolutionary local selection algorithms. Evol Comput. 2000;8(2):223–47.CrossRef
114.
Zurück zum Zitat Miettinen K. Nonlinear multiobjective optimization. Boston: Kluwer; 1999.MATH Miettinen K. Nonlinear multiobjective optimization. Boston: Kluwer; 1999.MATH
115.
Zurück zum Zitat Mo H, Xu Z, Xu L, Wu Z, Ma H. Constrained multiobjective biogeography optimization algorithm. Sci World J. 2014;2014, Article ID 232714:12p. Mo H, Xu Z, Xu L, Wu Z, Ma H. Constrained multiobjective biogeography optimization algorithm. Sci World J. 2014;2014, Article ID 232714:12p.
116.
Zurück zum Zitat Modiri-Delshad M, Rahim NA. Multi-objective backtracking search algorithm for economic emission dispatch problem. Appl Soft Comput. 2016;40:479–94.CrossRef Modiri-Delshad M, Rahim NA. Multi-objective backtracking search algorithm for economic emission dispatch problem. Appl Soft Comput. 2016;40:479–94.CrossRef
117.
Zurück zum Zitat Molina J, Laguna M, Marti R, Caballero R. SSPMO: a scatter tabu search procedure for non-linear multiobjective optimization. INFORMS J Comput. 2007;19(1):91–100.MathSciNetMATHCrossRef Molina J, Laguna M, Marti R, Caballero R. SSPMO: a scatter tabu search procedure for non-linear multiobjective optimization. INFORMS J Comput. 2007;19(1):91–100.MathSciNetMATHCrossRef
118.
Zurück zum Zitat Mora AM, Garcia-Sanchez P, Merelo JJ, Castillo PA. Pareto-based multi-colony multi-objective ant colony optimization algorithms: an island model proposal. Soft Comput. 2013;17:1175–207.CrossRef Mora AM, Garcia-Sanchez P, Merelo JJ, Castillo PA. Pareto-based multi-colony multi-objective ant colony optimization algorithms: an island model proposal. Soft Comput. 2013;17:1175–207.CrossRef
119.
Zurück zum Zitat Murata T, Ishibuchi H, Gen M. Specification of genetic search direction in cellular multi-objective genetic algorithm. In: Proceedings of the 1st international conference on evolutionary multicriterion optimization (EMO), Zurich, Switzerland, March 2001. Berlin: Springer; 2001. p. 82–95. Murata T, Ishibuchi H, Gen M. Specification of genetic search direction in cellular multi-objective genetic algorithm. In: Proceedings of the 1st international conference on evolutionary multicriterion optimization (EMO), Zurich, Switzerland, March 2001. Berlin: Springer; 2001. p. 82–95.
120.
Zurück zum Zitat Nam DK, Park CH. Multiobjective simulated annealing: a comparative study to evolutionary algorithms. Int J Fuzzy Syst. 2000;2(2):87–97. Nam DK, Park CH. Multiobjective simulated annealing: a comparative study to evolutionary algorithms. Int J Fuzzy Syst. 2000;2(2):87–97.
121.
Zurück zum Zitat Nebro AJ, Durillo JJ, Luna F, Dorronsoro B, Alba E. MOCell: a cellular genetic algorithm for multiobjective optimization. Int J Intell Syst. 2009;24:726–46.MATHCrossRef Nebro AJ, Durillo JJ, Luna F, Dorronsoro B, Alba E. MOCell: a cellular genetic algorithm for multiobjective optimization. Int J Intell Syst. 2009;24:726–46.MATHCrossRef
122.
Zurück zum Zitat Nebro AJ, Luna F, Alba E. New ideas in applying scatter search to multiobjective optimization. In: Proceedings of the 3rd international conference on evolutionary multicriterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 443–458. Nebro AJ, Luna F, Alba E. New ideas in applying scatter search to multiobjective optimization. In: Proceedings of the 3rd international conference on evolutionary multicriterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 443–458.
123.
Zurück zum Zitat Nebro AJ, Luna F, Alba E, Dorronsoro B, Durillo JJ, Beham A. AbYSS: adapting scatter search to multiobjective optimization. IEEE Trans Evol Comput. 2008;12(4):439–57.CrossRef Nebro AJ, Luna F, Alba E, Dorronsoro B, Durillo JJ, Beham A. AbYSS: adapting scatter search to multiobjective optimization. IEEE Trans Evol Comput. 2008;12(4):439–57.CrossRef
124.
Zurück zum Zitat Nguyen L, Bui LT, Abbass HA. DMEA-II: the direction-based multi-objective evolutionary algorithm-II. Soft Comput. 2014;18:2119–34.CrossRef Nguyen L, Bui LT, Abbass HA. DMEA-II: the direction-based multi-objective evolutionary algorithm-II. Soft Comput. 2014;18:2119–34.CrossRef
125.
Zurück zum Zitat Okabe T, Jin Y, Sendhoff B, Olhofer M. Voronoi-based estimation of distribution algorithm for multi-objective optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), Portland, OR, USA, June 2004. p. 1594–1601. Okabe T, Jin Y, Sendhoff B, Olhofer M. Voronoi-based estimation of distribution algorithm for multi-objective optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), Portland, OR, USA, June 2004. p. 1594–1601.
126.
Zurück zum Zitat Parsopoulos KE, Tasoulis DK, Pavlidis NG, Plagianakos VP, Vrahatis MN. Vector evaluated differential evolution for multiobjective optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), Portland, Oregon, USA, June 2004. p. 204–211. Parsopoulos KE, Tasoulis DK, Pavlidis NG, Plagianakos VP, Vrahatis MN. Vector evaluated differential evolution for multiobjective optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), Portland, Oregon, USA, June 2004. p. 204–211.
127.
Zurück zum Zitat Parsopoulos KE, Tasoulis DK, Vrahatis MN. Multiobjective optimization using parallel vector evaluated particle swarm optimization. In: Proceedings of the IASTED international conference on artificial intelligence and applications, Innsbruck, Austria, Feb 2004. p. 823–828. Parsopoulos KE, Tasoulis DK, Vrahatis MN. Multiobjective optimization using parallel vector evaluated particle swarm optimization. In: Proceedings of the IASTED international conference on artificial intelligence and applications, Innsbruck, Austria, Feb 2004. p. 823–828.
128.
Zurück zum Zitat Pelikan M, Sastry K, Goldberg DE. Multiobjective HBOA, clustering, and scalability. In: Proceedings of international conference on genetic and evolutionary computation; 2005. p. 663–670. Pelikan M, Sastry K, Goldberg DE. Multiobjective HBOA, clustering, and scalability. In: Proceedings of international conference on genetic and evolutionary computation; 2005. p. 663–670.
129.
Zurück zum Zitat Pulido GT, Coello CAC. Using clustering techniques to improve the performance of a particle swarm optimizer. In: Proceedings of genetic and evolutionary computation conference (GECCO), Seattle, WA, USA, June 2004. p. 225–237. Pulido GT, Coello CAC. Using clustering techniques to improve the performance of a particle swarm optimizer. In: Proceedings of genetic and evolutionary computation conference (GECCO), Seattle, WA, USA, June 2004. p. 225–237.
130.
Zurück zum Zitat Purshouse RC, Fleming PJ. On the evolutionary optimization of many conflicting objectives. IEEE Trans Evol Comput. 2007;11(6):770–84.CrossRef Purshouse RC, Fleming PJ. On the evolutionary optimization of many conflicting objectives. IEEE Trans Evol Comput. 2007;11(6):770–84.CrossRef
131.
Zurück zum Zitat Rahimi-Vahed A, Mirzaei AH. A hybrid multi-objective shuffled frog-leaping algorithm for a mixed-model assembly line sequencing problem. Comput Ind Eng. 2007;53(4):642–66.CrossRef Rahimi-Vahed A, Mirzaei AH. A hybrid multi-objective shuffled frog-leaping algorithm for a mixed-model assembly line sequencing problem. Comput Ind Eng. 2007;53(4):642–66.CrossRef
132.
Zurück zum Zitat Rao RV, Patel V. Multi-objective optimization of two stage thermoelectric cooler using a modified teaching-learning-based optimization algorithm. Eng Appl Artif Intell. 2013;26:430–45.CrossRef Rao RV, Patel V. Multi-objective optimization of two stage thermoelectric cooler using a modified teaching-learning-based optimization algorithm. Eng Appl Artif Intell. 2013;26:430–45.CrossRef
133.
Zurück zum Zitat Ray T, Liew KM. A swarm metaphor for multiobjective design optimization. Eng Optim. 2002;34(2):141–53.CrossRef Ray T, Liew KM. A swarm metaphor for multiobjective design optimization. Eng Optim. 2002;34(2):141–53.CrossRef
134.
Zurück zum Zitat Reddy MJ, Kumar DN. An efficient multi-objective optimization algorithm based on swarm intelligence for engineering design. Eng Optim. 2007;39(1):49–68.MathSciNetCrossRef Reddy MJ, Kumar DN. An efficient multi-objective optimization algorithm based on swarm intelligence for engineering design. Eng Optim. 2007;39(1):49–68.MathSciNetCrossRef
135.
Zurück zum Zitat Reynoso-Meza G, Sanchis J, Blasco X, Martinez M. Design of continuous controllers using a multiobjective differential evolution algorithm with spherical pruning. In: Applications of evolutionary computation. Lecture notes in computer science, vol. 6024. Berlin: Springer; 2010. p. 532–541. Reynoso-Meza G, Sanchis J, Blasco X, Martinez M. Design of continuous controllers using a multiobjective differential evolution algorithm with spherical pruning. In: Applications of evolutionary computation. Lecture notes in computer science, vol. 6024. Berlin: Springer; 2010. p. 532–541.
136.
Zurück zum Zitat Robic T, Filipic B. DEMO: differential evolution for multiobjective optimization. In: Proceedings of the 3rd international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 520–533. Robic T, Filipic B. DEMO: differential evolution for multiobjective optimization. In: Proceedings of the 3rd international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 520–533.
137.
Zurück zum Zitat Sadollah A, Eskandar H, Kim JH. Water cycle algorithm for solving constrained multi-objectiveoptimization problems. Appl Soft Comput. 2015;27:279–98.CrossRef Sadollah A, Eskandar H, Kim JH. Water cycle algorithm for solving constrained multi-objectiveoptimization problems. Appl Soft Comput. 2015;27:279–98.CrossRef
138.
Zurück zum Zitat Sastry K, Goldberg DE, Pelikan M. Limits of scalability of multi-objective estimation of distribution algorithms. In: Proceedings of IEEE congress on evolutionary computation (CEC), Edinburgh, UK, Sept 2005. p. 2217–2224. Sastry K, Goldberg DE, Pelikan M. Limits of scalability of multi-objective estimation of distribution algorithms. In: Proceedings of IEEE congress on evolutionary computation (CEC), Edinburgh, UK, Sept 2005. p. 2217–2224.
139.
Zurück zum Zitat Sato H, Aguirre H, Tanaka K. Controlling dominance area of solutions and its impact on the performance of MOEAs. In: Proceedings of the 4th international conference on evolutionary multi-criterion optimization (EMO), Matsushima, Japan, March 2007. p. 5–20. Sato H, Aguirre H, Tanaka K. Controlling dominance area of solutions and its impact on the performance of MOEAs. In: Proceedings of the 4th international conference on evolutionary multi-criterion optimization (EMO), Matsushima, Japan, March 2007. p. 5–20.
140.
Zurück zum Zitat Schaffer JD. Multiple objective optimization with vector evaluated genetic algorithms. In: Grefenstette JJ, editor. Proceedings of the 1st international conference on genetic algorithms, Pittsburgh, PA, USA, July 1985. Hillsdale, NJ, USA: Lawrence Erlbaum; 1985. p. 93–100. Schaffer JD. Multiple objective optimization with vector evaluated genetic algorithms. In: Grefenstette JJ, editor. Proceedings of the 1st international conference on genetic algorithms, Pittsburgh, PA, USA, July 1985. Hillsdale, NJ, USA: Lawrence Erlbaum; 1985. p. 93–100.
141.
Zurück zum Zitat Schott JR. Fault tolerant design using single and multicriteria genetic algorithm optimization. Master’s Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA; 1995. Schott JR. Fault tolerant design using single and multicriteria genetic algorithm optimization. Master’s Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA; 1995.
142.
Zurück zum Zitat Shim VA, Tan KC, Cheong CY. An energy-based sampling technique for multi-objective restricted Boltzmann machine. IEEE Trans Evol Comput. 2013;17(6):767–85.CrossRef Shim VA, Tan KC, Cheong CY. An energy-based sampling technique for multi-objective restricted Boltzmann machine. IEEE Trans Evol Comput. 2013;17(6):767–85.CrossRef
143.
Zurück zum Zitat Shim VA, Tan KC, Chia JY, Al Mamun A. Multi-objective optimization with estimation of distribution algorithm in a noisy environment. Evol Comput. 2013;21(1):149–77.CrossRef Shim VA, Tan KC, Chia JY, Al Mamun A. Multi-objective optimization with estimation of distribution algorithm in a noisy environment. Evol Comput. 2013;21(1):149–77.CrossRef
144.
Zurück zum Zitat Sierra MR, Coello CAC. Improving PSO-based multiobjective optimization using crowding, mutation and \(\epsilon \)-dominance. In: Proceedings of the 3rd international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 505–519. Sierra MR, Coello CAC. Improving PSO-based multiobjective optimization using crowding, mutation and \(\epsilon \)-dominance. In: Proceedings of the 3rd international conference on evolutionary multi-criterion optimization (EMO), Guanajuato, Mexico, March 2005. p. 505–519.
145.
Zurück zum Zitat Singh HK, Isaacs A, Ray T. A Pareto corner search evolutionary algorithm and dimensionality reduction in many-objective optimization problems. IEEE Trans Evol Comput. 2011;15(4):539–56.CrossRef Singh HK, Isaacs A, Ray T. A Pareto corner search evolutionary algorithm and dimensionality reduction in many-objective optimization problems. IEEE Trans Evol Comput. 2011;15(4):539–56.CrossRef
146.
Zurück zum Zitat Smith KI, Everson RM, Fieldsend JE, Murphy C, Misra R. Dominance-based multiobjective simulated annealing. IEEE Trans Evol Comput. 2008;12(3):323–42.CrossRef Smith KI, Everson RM, Fieldsend JE, Murphy C, Misra R. Dominance-based multiobjective simulated annealing. IEEE Trans Evol Comput. 2008;12(3):323–42.CrossRef
147.
Zurück zum Zitat Soh H, Kirley M. moPGA: toward a new generation of multiobjective genetic algorithms. In: Proceedings of IEEE congress on evolutionary computation, Vancouver, BC, Canada, July 2006. p. 1702–1709. Soh H, Kirley M. moPGA: toward a new generation of multiobjective genetic algorithms. In: Proceedings of IEEE congress on evolutionary computation, Vancouver, BC, Canada, July 2006. p. 1702–1709.
148.
Zurück zum Zitat Soylu B, Köksalan M. A favorable weight-based evolutionary algorithm for multiple criteria problems. IEEE Trans Evol Comput. 2010;14(2):191–205. Soylu B, Köksalan M. A favorable weight-based evolutionary algorithm for multiple criteria problems. IEEE Trans Evol Comput. 2010;14(2):191–205.
149.
Zurück zum Zitat Srinivas N, Deb K. Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput. 1994;2(3):221–48.CrossRef Srinivas N, Deb K. Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput. 1994;2(3):221–48.CrossRef
150.
Zurück zum Zitat Srinivas M, Patnaik LM. Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Trans Syst Man Cybern. 1994;24(4):656–67.CrossRef Srinivas M, Patnaik LM. Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Trans Syst Man Cybern. 1994;24(4):656–67.CrossRef
151.
Zurück zum Zitat Tan KC, Lee TH, Khor EF. Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization. IEEE Trans Evol Comput. 2001;5(6):565–88.CrossRef Tan KC, Lee TH, Khor EF. Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization. IEEE Trans Evol Comput. 2001;5(6):565–88.CrossRef
152.
Zurück zum Zitat Tan KC, Yang YJ, Goh CK. A distributed cooperative coevolutionary algorithm for multiobjective optimization. IEEE Trans Evol Comput. 2006;10(5):527–49.CrossRef Tan KC, Yang YJ, Goh CK. A distributed cooperative coevolutionary algorithm for multiobjective optimization. IEEE Trans Evol Comput. 2006;10(5):527–49.CrossRef
153.
Zurück zum Zitat Tang HJ, Shim VA, Tan KC, Chia JY. Restricted Boltzmann machine based algorithm for multi-objective optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), Barcelona, Spain, July 2010. p. 3958–3965. Tang HJ, Shim VA, Tan KC, Chia JY. Restricted Boltzmann machine based algorithm for multi-objective optimization. In: Proceedings of IEEE congress on evolutionary computation (CEC), Barcelona, Spain, July 2010. p. 3958–3965.
154.
Zurück zum Zitat Teo J. Exploring dynamic self-adaptive populations in differential evolution. Soft Comput. 2006;10(8):673–86.CrossRef Teo J. Exploring dynamic self-adaptive populations in differential evolution. Soft Comput. 2006;10(8):673–86.CrossRef
155.
Zurück zum Zitat Toffolo A, Benini E. Genetic diversity as an objective in multi-objective evolutionary algorithms. Evol Comput. 2003;11(2):151–67.CrossRef Toffolo A, Benini E. Genetic diversity as an objective in multi-objective evolutionary algorithms. Evol Comput. 2003;11(2):151–67.CrossRef
156.
Zurück zum Zitat Vasconcelos JA, Maciel JHRD, Parreiras RO. Scatter search techniques applied to electromagnetic problems. IEEE Trans Magn. 2005;4:1804–7.CrossRef Vasconcelos JA, Maciel JHRD, Parreiras RO. Scatter search techniques applied to electromagnetic problems. IEEE Trans Magn. 2005;4:1804–7.CrossRef
157.
Zurück zum Zitat Veldhuizen DAV, Lamont GB. Multiobjective evolutionary algorithm research: a history and analysis. Technical Report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH, USA; 1998. Veldhuizen DAV, Lamont GB. Multiobjective evolutionary algorithm research: a history and analysis. Technical Report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH, USA; 1998.
158.
Zurück zum Zitat Vrugt JA, Robinson BA, Hyman JM. Self-adaptive multimethod search for global optimization in real-parameter spaces. IEEE Trans Evol Comput. 2009;13(2):243–59.CrossRef Vrugt JA, Robinson BA, Hyman JM. Self-adaptive multimethod search for global optimization in real-parameter spaces. IEEE Trans Evol Comput. 2009;13(2):243–59.CrossRef
159.
Zurück zum Zitat Wagner T, Beume N, Naujoks B. Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Proceedings of the 4th international conference on evolutionary multi-criterion optimization (EMO), Matsushima, Japan, March 2007. p. 742–756. Wagner T, Beume N, Naujoks B. Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Proceedings of the 4th international conference on evolutionary multi-criterion optimization (EMO), Matsushima, Japan, March 2007. p. 742–756.
160.
Zurück zum Zitat Wang R, Purshouse RC, Fleming PJ. Preference-inspired coevolutionary algorithms for many-objective optimization. IEEE Trans Evol Comput. 2013;17(4):474–94.CrossRef Wang R, Purshouse RC, Fleming PJ. Preference-inspired coevolutionary algorithms for many-objective optimization. IEEE Trans Evol Comput. 2013;17(4):474–94.CrossRef
161.
Zurück zum Zitat Wanner EF, Guimaraes FG, Takahashi RHC, Fleming PJ. Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria. Evol Comput. 2008;16(2):185–224.CrossRef Wanner EF, Guimaraes FG, Takahashi RHC, Fleming PJ. Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria. Evol Comput. 2008;16(2):185–224.CrossRef
162.
Zurück zum Zitat Wu Y, Jin Y, Liu X. A directed search strategy for evolutionary dynamic multiobjective optimization. Soft Comput. 2015;19:3221–35.CrossRef Wu Y, Jin Y, Liu X. A directed search strategy for evolutionary dynamic multiobjective optimization. Soft Comput. 2015;19:3221–35.CrossRef
163.
Zurück zum Zitat Xiang Y, Zhou Y. A dynamic multi-colony artificial bee colony algorithm for multi-objective optimization. Appl Soft Comput. 2015;35:766–85.CrossRef Xiang Y, Zhou Y. A dynamic multi-colony artificial bee colony algorithm for multi-objective optimization. Appl Soft Comput. 2015;35:766–85.CrossRef
164.
Zurück zum Zitat Xue J, Wu Y, Shi Y, Cheng S. Brain storm optimization algorithm for multi-objective optimization problems. In: Proceedings of the 3rd international conference on advances in swarm intelligence, Shenzhen, China, June 2012. Berlin: Springer; 2012. p. 513–519. Xue J, Wu Y, Shi Y, Cheng S. Brain storm optimization algorithm for multi-objective optimization problems. In: Proceedings of the 3rd international conference on advances in swarm intelligence, Shenzhen, China, June 2012. Berlin: Springer; 2012. p. 513–519.
165.
Zurück zum Zitat Yang S, Li M, Liu X, Zheng J. A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput. 2013;17(5):721–36.CrossRef Yang S, Li M, Liu X, Zheng J. A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput. 2013;17(5):721–36.CrossRef
166.
Zurück zum Zitat Yang X-S. Bat algorithm for multi-objective optimization. Int J Bio-Inspired Comput. 2011;3(5):267–74.CrossRef Yang X-S. Bat algorithm for multi-objective optimization. Int J Bio-Inspired Comput. 2011;3(5):267–74.CrossRef
167.
Zurück zum Zitat Yen GG, Leong WF. Dynamic multiple swarms in multiobjective particle swarm optimization. IEEE Trans Syst Man Cybern Part A. 2009;39(4):890–911.CrossRef Yen GG, Leong WF. Dynamic multiple swarms in multiobjective particle swarm optimization. IEEE Trans Syst Man Cybern Part A. 2009;39(4):890–911.CrossRef
168.
Zurück zum Zitat Yen GG, Lu H. Dynamic multiobjective evolutionary algorithm: adaptive cell-based rank and density estimation. IEEE Trans Evol Comput. 2003;7(3):253–74.CrossRef Yen GG, Lu H. Dynamic multiobjective evolutionary algorithm: adaptive cell-based rank and density estimation. IEEE Trans Evol Comput. 2003;7(3):253–74.CrossRef
169.
Zurück zum Zitat Zhan Z-H, Li J, Cao J, Zhang J, Chung HS-H, Shi Y-H. Multiple populations for multiple objectives: a coevolutionary technique for solving multiobjective optimization problems. IEEE Trans Cybern. 2013;43(2):445–63. Zhan Z-H, Li J, Cao J, Zhang J, Chung HS-H, Shi Y-H. Multiple populations for multiple objectives: a coevolutionary technique for solving multiobjective optimization problems. IEEE Trans Cybern. 2013;43(2):445–63.
170.
Zurück zum Zitat Zhang Q, Li H. MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput. 2007;11(6):712–31.CrossRef Zhang Q, Li H. MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput. 2007;11(6):712–31.CrossRef
171.
Zurück zum Zitat Zhang Q, Liu W, Li H. The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In: Proceedings of the IEEE conference on evolutionary computation (CEC), Trondheim, Norway, May 2009. p. 203–208. Zhang Q, Liu W, Li H. The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In: Proceedings of the IEEE conference on evolutionary computation (CEC), Trondheim, Norway, May 2009. p. 203–208.
172.
Zurück zum Zitat Zhang Q, Zhou A, Jin Y. Global multiobjective optimization via estimation of distribution algorithm with biased initialization and crossover. In: Proceedings of the genetic and evolutionary computation conference (GECCO), London, UK, July 2007. p. 617–622. Zhang Q, Zhou A, Jin Y. Global multiobjective optimization via estimation of distribution algorithm with biased initialization and crossover. In: Proceedings of the genetic and evolutionary computation conference (GECCO), London, UK, July 2007. p. 617–622.
173.
Zurück zum Zitat Zhang Q, Zhou A, Jin Y. RM-MEDA: a regularity model-based multi-objective estimation of distribution algorithm. IEEE Trans Evol Comput. 2008;12(1):41–63.CrossRef Zhang Q, Zhou A, Jin Y. RM-MEDA: a regularity model-based multi-objective estimation of distribution algorithm. IEEE Trans Evol Comput. 2008;12(1):41–63.CrossRef
174.
Zurück zum Zitat Zhang X, Tian Y, Cheng R, Jin Y. An efficient approach to non-dominated sorting for evolutionary multi-objective optimization. IEEE Trans Evol Comput. 2015;19(2):201–15.CrossRef Zhang X, Tian Y, Cheng R, Jin Y. An efficient approach to non-dominated sorting for evolutionary multi-objective optimization. IEEE Trans Evol Comput. 2015;19(2):201–15.CrossRef
175.
Zurück zum Zitat Zhong X, Li W. A decision-tree-based multi-objective estimation of distribution algorithm. In: Proceedings of international conference on computational intelligence and security, Harbin, China, Dec 2007. p. 114–118. Zhong X, Li W. A decision-tree-based multi-objective estimation of distribution algorithm. In: Proceedings of international conference on computational intelligence and security, Harbin, China, Dec 2007. p. 114–118.
176.
Zurück zum Zitat Zhou A, Zhang Q, Jin Y. Approximating the set of pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm. Trans Evol Comput. 2009;13(5):1167–89.CrossRef Zhou A, Zhang Q, Jin Y. Approximating the set of pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm. Trans Evol Comput. 2009;13(5):1167–89.CrossRef
177.
Zurück zum Zitat Zitzler E, Deb K, Thiele L. Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput. 2000;8(2):173–95.CrossRef Zitzler E, Deb K, Thiele L. Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput. 2000;8(2):173–95.CrossRef
178.
Zurück zum Zitat Zitzler E, Kunzli S. Indicator-based selection in multiobjective search. In: Proceedings of the 8th international conference on parallel problem solving from nature (PPSN VIII), Birmingham, UK, Sept 2004. Berlin: Springer; 1998. p. 832–842. Zitzler E, Kunzli S. Indicator-based selection in multiobjective search. In: Proceedings of the 8th international conference on parallel problem solving from nature (PPSN VIII), Birmingham, UK, Sept 2004. Berlin: Springer; 1998. p. 832–842.
179.
Zurück zum Zitat Zitzler E, Laumanns M, Thiele L. SPEA2: improving the strength Pareto evolutionary algorithm. TIK-Report 103, Departmentt of Electrical Engineering, Swiss Federal Institute of Technology, Switzerland. 2001. Zitzler E, Laumanns M, Thiele L. SPEA2: improving the strength Pareto evolutionary algorithm. TIK-Report 103, Departmentt of Electrical Engineering, Swiss Federal Institute of Technology, Switzerland. 2001.
180.
Zurück zum Zitat Zitzler E, Laumanns M, Thiele L. SPEA2: improving the strength pareto evolutionary algorithm. In: Proceedings of evolutionary methods for design, optimisation and control. CIMNE, Barcelona, Spain; 2002. p. 95–100. Zitzler E, Laumanns M, Thiele L. SPEA2: improving the strength pareto evolutionary algorithm. In: Proceedings of evolutionary methods for design, optimisation and control. CIMNE, Barcelona, Spain; 2002. p. 95–100.
181.
Zurück zum Zitat Zitzler E, Thiele L. Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput. 1999;3(4):257–71.CrossRef Zitzler E, Thiele L. Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput. 1999;3(4):257–71.CrossRef
182.
Zurück zum Zitat Zitzler E, Thiele L, Laumanns M, Fonseca CM, da Fonseca VG. Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput. 2003;7:117–32.CrossRef Zitzler E, Thiele L, Laumanns M, Fonseca CM, da Fonseca VG. Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput. 2003;7:117–32.CrossRef
Metadaten
Titel
Multiobjective Optimization
verfasst von
Ke-Lin Du
M. N. S. Swamy
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-41192-7_23

Premium Partner