Multiobjective evolutionary algorithm based on mixture Gaussian models

Ruan Jian Xue Bao/Journal of Software

Volumn 25, Issue 5, 2014, Pages 913-928

  Zhou, Ai Min ^a   Zhang, Qing Fu ^b   Zhang, Gui Xu ^a  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF ESSEX   (United Kingdom)

Author keywords

Evolutionary algorithm; Mixture Gaussian probability model; MOEA D; Multiobjective optimization

Indexed keywords

EVOLUTIONARY ALGORITHMS; GAUSSIAN DISTRIBUTION; MIXTURES;

GAUSSIAN PROBABILITY; MIXTURE GAUSSIAN MODEL; MOEA/D; MULTI OBJECTIVE EVOLUTIONARY ALGORITHMS; MULTIOBJECTIVE OPTIMIZATION PROBLEMS (MOPS); RECOMBINATION OPERATORS; REPRODUCTION OPERATOR; SINGLE OBJECTIVE OPTIMIZATION;

MULTIOBJECTIVE OPTIMIZATION;

EID: 84901377430     PISSN: 10009825     EISSN: None     Source Type: Journal    
DOI: 10.13328/j.cnki.jos.004514     Document Type: Article

References (44)

1. Miettinen K. Nonlinear Multiobjective Optimization. Boston: Kluwer Academic Publishers, 1999.
2. Schaffer J D. Multiple objective optimization with vector valuated genetic algorithms. In: Proc. of the 1st Int'l Conf. on Genetic Algorithms. Hillsdale: L. Erlbaum Associates Inc., 1985. 93-100.
3. Deb K. Multi-Objective Optimization Using Evolutionary Algorithms. New York: John Wiley & Sons LTD, 2001.
4. Coello Coello C A. An updated survey of GA-based multiobjective optimization techniques. ACM Computing Surveys, 2000, 32(2): 109-143. [doi: 10.1145/358923.358929]
5. Zhou A, Qu B Y, Li H, Zhao S Z, Suganthan P N, Zhang Q. Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm and Evolutionary Computation, 2011, 1(1):32-49. [doi: 10.1016/j.swevo.2011.03.001]
6. Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation, 2002, 6(2):182-197. [doi: 10.1109/4235.996017]
7. Zitzler E, Laumanns M, Thiele L. SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Proc. of the Evolutionary Methods for Design, Optimisation and Control. Athens: International Center for Numerical Methods in Engineering, 2002. 95-100.
8. Knowles J D, Corne D W. Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation, 200, 8(2):149-172. [doi: 10.1162/106365600568167]
9. Zitzler E, Kunzli S. Indicator-Based selection in multiobjective search. In: Proc. of the Parallel Problem Solving from Nature (PPSN VIII). LNCS 3242, Berlin, Heidelberg: Springer-Verlag, 2004. 832-842. [doi: 10.1007/978-3-540-30217-9_84]
10. Bader J, Zitzler E. HypE: An algorithm for fast hypervolume-based many-objective optimization. Evolutionary Computation, 2011, 19(1):45-76. [doi: 10.1162/EVCO_a_00009]
11. Zhang Q F, Li H. MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. on Evolutionary Computation, 2007, 11(6):712-731. [doi: 10.1109/TEVC.2007.892759]
12. Zheng J H. Multiobjective Optimization Algorithms and Their Applications. Beijing: Science Press, 2007 (in Chinese).
13. Lei D M, Yan X P. Multiobjective Intelligent Optimization Algorithms and their Applications. Beijing: Science Press, 2009 (in Chinese).
14. Jiao L C, Shang R H, Ma W P. Multiobjective Immune Algorithms, Theory and Applications. Beijing: Science Press, 2010 (in Chinese).
15. Leung Y, Wang Y. Multi-Objective programming using uniform design and genetic algorithm. IEEE Trans. on Systems, Man, and Cybernetics, Part C, 2000, 30(3):293-304. [doi: 10.1109/5326.885111]
16. Zeng S Y, Kang L S, Ding L X. An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints. Evolutionary Computation, 2004, 12(1):77-98. [doi: 10.1162/evco.2004.12.1.77]
17. Wang Y N, Wu L H, Yuan X F. Multi-Objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure. Soft Computing, 2010, 14(3):193-209. [doi: 10.1007/s00500-008-0394-9]
18. Gong W Y, Cai Z H. An improved multiobjective differential evolution based on Pareto-adaptive epsilon-dominance and orthogonal design. European Journal of Operational Research, 2009, 198(2):576-601. [doi: 10.1016/j.ejor.2008.09.022]
19. Gong D W, Zhang Y, Zhang J H. Multi-Objective particle swarm optimization based on minimal particle angle. In: Proc. of the Int'l Conf. on Intelligent Computing. Berlin, Heidelberg: Springer-Verlag, 2005. 571-580. [doi: 10.1007/11538059_60]
20. Zhan Z H, Zhang J. A parallel particle swarm optimization approach for multiobjective optimization problems. In: Proc. of the Genetic and Evolutionary Computation Conf. New York: ACM, 2010. 81-82. [doi: 10.1145/1830483.1830497]
21. Gong M G, Jiao L C, Du H F, Bo L F. Multiobjective immune algorithm with nondominated neighbor-based selection. Evolutionary Computation, 2008, 16(2):225-255. [doi: 10.1162/evco.2008.16.2.225]
22. Chen J Y, Lin Q Z, Ji Z. A hybrid immune multiobjective optimization algorithm. European Journal of Operational Research, 2010, 204(2):294-302. [doi: 10.1016/j.ejor.2009.10.010]
23. Li B B, Wang L. A hybrid quantum-inspired genetic algorithm for multiobjective flow shop scheduling. IEEE Trans. on Systems, Man, and Cybernetics, Part B, 2007, 37(3):576-591. [doi: 10.1109/TSMCB.2006.887946]
24. Wang Y, Zeng J C, Tan Y. An artificial physics optimization algorithm for multi-objective problems based on virtual force sorting. In: Proc. of the 1st Int'l Conf. on Swarm, Evolutionary, and Memetic Computing. Berlin, Heidelberg: Springer-Verlag, 2010. 615-622. [doi: 10.1007/978-3-642-17563-3_72]
25. Zhang D M, Gong X S, Dai G M. Multi-Objective evolutionary algorithm for principal curve model based on multifractal. Journal of Computer Research and Development, 2011, 48(9):1729-1739 (in Chinese with English abstract).
26. Yang D D, Ma J J, Jiao L C, Gong M G, Si X Y. Improved ε dominance by ISOmap. Ruan Jian Xue Bao/Journal of Software, 2011, 22 (10):2291-2304 (in Chinese with English abstract). http://www.jos.org.cn/1000-9825/3933.htm [doi: 10.3724/SP.J.1001.2011.039 33]
27. Wang Y, Cai Z X, Guo G Q, Zhou Y R. Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems. IEEE Trans. on Systems, Man, and Cybernetics, Part B, 2007, 37(3):560-575. [doi: 10.1109/TSMCB.2006. 886164]
28. Zou X F, Chen Y, Liu M Z, Kang L H. A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans. on Systems, Man, and Cybernetics, Part B, 2008, 38(5):1402-1412. [doi: 10.1109/TSMCB.2008.926329]
29. Wei W, Ouyang D T, Lü S, Feng Y X. Multiobjective path planning under dynamic uncertain environment. Chinese Journal of Computers, 2011, 34(5):836-846 (in Chinese with English abstract). [doi: 10.3724/SP.J.1016.2011.00836]
30. Huo W G, Shao X L. A fuzzy associative classification method based on multi-objective evolutionary algorithm. Journal of Computer Research and Development, 2011, 48(4):567-575 (in Chinese with English abstract).
31. Wang Z, Tang K, Yao X. Multi-Objective approaches to optimal testing resource allocation in modular software systems. IEEE Trans. on Reliability, 2010, 59(3):563-575. [doi: 10.1109/TR.2010.2057310]
32. Wang Y, Li B, Chen Y B. Digital IIR filter design using multi-objective optimization evolutionary algorithm. Applied Soft Computing, 2011, 11(2):1851-1857. [doi: 10.1016/j.asoc.2010.05.034]
33. Li Q, Hao Q F, Xiao L M, Li Z J. Adaptive management and multi-objective optimization for virtual machine placement in cloud computing. Chinese Journal of Computers, 2011, 34(12):2253-2264 (in Chinese with English abstract). [doi: 10.3724/SP.J.1016. 2011.02253]
34. Lu H C, Li Y J, Zhu Y H. Simultaneous deployment and scheduling for real-time event capture in sensor networks. Ruan Jian Xue Bao/Journal of Software, 2011, 22:182-190 (in Chinese with English abstract). http://www.jos.org.cn/1000-9825/11020.htm
35. Shi C, Yan Z Y, Shi Z Z, Zhang L. A fast multi-objective evolutionary algorithm based on a tree structure. Applied Soft Computing, 2010, 10(2):468-480. [doi: 10.1016/j.asoc.2009.08.018]
36. Li M Q, Zheng J H. An indicator for assessing the spread of solutions in multi-objective evolutionary algorithms. Chinese Journal of Computers, 2011, 34(4):647-664 (in Chinese with English abstract). [doi: 10.3724/SP.J.1016.2011.00647]
37. Iorio A W, Li X. Rotated problems and rotationally invariant crossover in evolutionary multi-objective optimization. Int'l Journal of Computational Intelligence and Applications, 2008, 7(2):149-186. [doi: 10.1142/S1469026808002223]
38. Zhang Q F, Zhou A M, Jin Y C. RM-MEDA: A regularity model-based multiobjective estimation of distribution algorithm. IEEE Trans. on Evolutionary Computation, 2008, 12(1):41-63. [doi: 10.1109/TEVC.2007.894202]
39. Weinert K, Zabel A, Kersting P, Michelitsch T, Wagner T. On the use of problem-specific candidate generators for the hybrid optimization of multi-objective production engineering problems. Evolutionary Computation, 2009, 17(4):527-544. [doi: 10.1162/evco.2009.17.4.17405]
40. Hillermeier C. Nonlinear Multiobjective Optimization-A Generalized Homotopy Approach. Basel: Birkhauser Verlag AG, 2001.
41. Zhou A M, Zhang Q F, Jin Y C. Approximating the set of Pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm. IEEE Trans. on Evolutionary Computation, 2009, 13(5):1167-1189. [doi: 10.1109/TEVC.2009. 2021467]
42. Zhou A M, Zhang Q F, Zhang G X. A multiobjective evolutionary algorithm based on decomposition and probability model. In: Proc. of the IEEE Congress of Evolutionary Computation (CEC 2012). Brisbane: IEEE Press, 2012. 1-8. [doi: 10.1109/CEC.2012.62529 54]
43. Li H, Zhang Q F. Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans. on Evolutionary Computation, 2009, 13(2):284-302. [doi: 10.1109/TEVC.2008.925798]
44. Larrañaga P, Lozano J. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Boston: Kluwer Academic Publishers, 2002.