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2016 | OriginalPaper | Chapter

23. Multiobjective Optimization

Authors : Ke-Lin Du, M. N. S. Swamy

Published in: Search and Optimization by Metaheuristics

Publisher: Springer International Publishing

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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.

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previous chapter Dynamic, Multimodal, and Constrained Optimizations
Literature
1.
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.
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.
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.
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.
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.
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.
Bader J, Zitzler E. HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput. 2011;19(1):45–76.CrossRef
8.
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.
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.
Bastos-Filho CJA, Guimaraes ACS. Multi-objective fish school search. Int J Swarm Intell Res. 2015;6(1):18p.
11.
Beausoleil RP. Moss: multiobjective scatter search applied to nonlinear multiple criteria optimization. Eur J Oper Res. 2006;169(2):426–49.MathSciNetMATHCrossRef
12.
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.
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.
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.
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.
Brockhoff D, Zitzler E. Objective reduction in evolutionary multiobjective optimization: theory and applications. Evol Comput. 2009;17(2):135–66.CrossRef
17.
18.
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.
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.
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.
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.
Chen Q, Guan S-U. Incremental multiple objective genetic algorithms. IEEE Trans Syst Man Cybern Part B. 2004;34(3):1325–34.MathSciNetCrossRef
23.
Clymont KM, Keedwell E. Deductive sort and climbing sort: new methods for non-dominated sorting. Evol Comput. 2012;20(1):1–26.CrossRef
24.
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.
Coello CAC, Cortes NC. Solving multiobjective optimization problems using an artificial immune system. Genet Program Evolvable Mach. 2005;6:163–90.CrossRef
26.
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.
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.
Coello CAC, Pulido GT, Lechuga MS. Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput. 2004;8(3):256–79.CrossRef
29.
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.
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.
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.
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.
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.
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.
Deb K. Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol Comput. 1999;7(3):205–30.CrossRef
36.
Deb K. Multi-objective optimization using evolutionary algorithms. Chichester: Wiley; 2001.MATH
37.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Giagkiozis I, Purshouse RC, Fleming PJ. Generalized decomposition and cross entropy methods for many-objective optimization. Inf Sci. 2014;282:363–87.MathSciNetCrossRef
56.
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.
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.
Goldberg DE. Genetic algorithms in search, optimization, and machine learning. Reading, MA, USA: Addison-Wesley; 1989.MATH
59.
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.
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.
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.
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.
Hadka D, Reed P. Borg: an auto-adaptive many-objective evolutionary computing framework. Evol Comput. 2013;21:231–59.CrossRef
64.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Knowles JD, Corne DW. Approximating the nondominated front using the Pareto archived evolution strategy. Evol Comput. 2000;8(2):149–72.CrossRef
85.
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.
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.
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.
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.
Kumar V, Chhabra JK, Kumar D. Differential search algorithm for multiobjective problems. Procedia Comput Sci. 2015;48:22–8.CrossRef
90.
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.
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.
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.
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.
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.
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.
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.
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.
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
99.
100.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Miettinen K. Nonlinear multiobjective optimization. Boston: Kluwer; 1999.MATH
115.
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.
Modiri-Delshad M, Rahim NA. Multi-objective backtracking search algorithm for economic emission dispatch problem. Appl Soft Comput. 2016;40:479–94.CrossRef
117.
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.
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.
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.
Nam DK, Park CH. Multiobjective simulated annealing: a comparative study to evolutionary algorithms. Int J Fuzzy Syst. 2000;2(2):87–97.
121.
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.
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.
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.
Nguyen L, Bui LT, Abbass HA. DMEA-II: the direction-based multi-objective evolutionary algorithm-II. Soft Comput. 2014;18:2119–34.CrossRef
125.
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.
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.
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.
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.
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.
Purshouse RC, Fleming PJ. On the evolutionary optimization of many conflicting objectives. IEEE Trans Evol Comput. 2007;11(6):770–84.CrossRef
131.
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.
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.
Ray T, Liew KM. A swarm metaphor for multiobjective design optimization. Eng Optim. 2002;34(2):141–53.CrossRef
134.
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.
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.
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.
Sadollah A, Eskandar H, Kim JH. Water cycle algorithm for solving constrained multi-objectiveoptimization problems. Appl Soft Comput. 2015;27:279–98.CrossRef
138.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Soylu B, Köksalan M. A favorable weight-based evolutionary algorithm for multiple criteria problems. IEEE Trans Evol Comput. 2010;14(2):191–205.
149.
Srinivas N, Deb K. Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput. 1994;2(3):221–48.CrossRef
150.
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.
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.
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.
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.
Teo J. Exploring dynamic self-adaptive populations in differential evolution. Soft Comput. 2006;10(8):673–86.CrossRef
155.
Toffolo A, Benini E. Genetic diversity as an objective in multi-objective evolutionary algorithms. Evol Comput. 2003;11(2):151–67.CrossRef
156.
Vasconcelos JA, Maciel JHRD, Parreiras RO. Scatter search techniques applied to electromagnetic problems. IEEE Trans Magn. 2005;4:1804–7.CrossRef
157.
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.
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.
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.
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.
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.
Wu Y, Jin Y, Liu X. A directed search strategy for evolutionary dynamic multiobjective optimization. Soft Comput. 2015;19:3221–35.CrossRef
163.
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.
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.
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.
Yang X-S. Bat algorithm for multi-objective optimization. Int J Bio-Inspired Comput. 2011;3(5):267–74.CrossRef
167.
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.
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.
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.
Zhang Q, Li H. MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput. 2007;11(6):712–31.CrossRef
171.
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.
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.
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.
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.
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.
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.
Zitzler E, Deb K, Thiele L. Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput. 2000;8(2):173–95.CrossRef
178.
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.
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.
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.
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.
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
Metadata
Title
Multiobjective Optimization
Authors
Ke-Lin Du
M. N. S. Swamy
Copyright Year
2016
Book
Search and Optimization by Metaheuristics

Print ISBN: 978-3-319-41191-0

Electronic ISBN: 978-3-319-41192-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-41192-7_23

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