A Modification of MOEA/D for Solving Multi-Objective Optimization Problems
Wei Zheng*,**, Yanyan Tan*,**,†, Meng Gao*,**, Wenzhen Jia*,**, and Qiang Wang*,**
*School of Information Science and Engineering, Shandong Normal University
No. 1, University Road, Changqing District, Jinan 250358, China
**Institute of Data Science and Technology, Shandong Normal University
Jinan, Shandong 250358, China
In this paper, a novel modified algorithm based on MOEA/D, abbreviated as mMOEA/D, is proposed for well solving the multi-objective optimization problems. Our proposed mMOEA/D inherits from MOEA/D. In mMOEA/D, a novel elastic weight vectors design method is introduced and adopted to make those weight vectors spread more widely. On the other hand, a flexible and efficient trail DE operator is designed and used in mMOEA/D for further enhancing the performance of MOEA/D. Three groups of experimental studies are carried out. Proposed mMOEA/D is compared with the four state-the-art multi-objective optimization evolutionary algorithms on solving the multi-objective optimization problems with many objectives, and the other is that mMOEA/D is compared with MOEA/D-DE, an improved version of MOEA/D, on solving the multi-objective optimization problems with complicated PS shapes. The versions of mMOEA/D with the improvement of weight vector and DE operator are compared with MOEA/D-DE to solve multi-objective optimization problems at last. The experimental results show that mMOEA/D performs the best on almost all test instances. In other words, our proposed modification of MOEA/D is effective.
-  K. Deb and D. Kalyanmoy, “Multi-Objective Optimization Using Evolutionary Algorithms,” John Wiley & Sons, Inc, 2001.
-  K. Miettinen, “Nonlinear multiobjective optimization,” Springer Science & Business Media, 2012.
-  G. Capi, “Effect of Genetic Encoding on Evolution of Efficient Neural Controllers,” J. Adv. Comput. Intell. Intell. Inform., Vol.12, No.4, pp. 377-381, 2008.
-  A. Abraham and L. Jain, “Evolutionary multiobjective optimization,” Evolutionary Multiobjective Optimization, Springer London, pp. 1-6, 2005.
-  E. Zitzler, “Evolutionary multiobjective optimization,” Handbook of Natural Computing, Springer Berlin Heidelberg, pp. 871-904, 2012.
-  Y. Y. Tan, S. Li, and X. Fang, “MOEA/D with Adaptive IWO for Synthesizing Phase-Only Reconfigurable Linear Arrays,” Open Chemical Engineering J., Vol.9, No.1, pp. 125-133, 2015.
-  Y. Y. Tan and Y. Jiao, “MOEA/D with Uniform Design for Solving Multiobjective Knapsack Problems,” J. of Computers, Vol.8, No.2, pp. 302-307, 2013.
-  K. Deb, A. Pratap, S. Agarwal et al., “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. on Evolutionary Computation, Vol.6, No.2, pp. 182-197, 2002.
-  Q. Zhang and H. Li, “MOEA/D: A multiobjective evolutionary algorithm based on decomposition,” IEEE Trans. on Evolutionary Computation, Vol.11, No.6, pp. 712-731, 2007.
-  Q. Zhang, W. Liu, and H. Li, “The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances,” IEEE Congress on Evolutionary Computation, Vol.1, pp. 203-208, 2009.
-  H. Li and Q. Zhang, “Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II,” IEEE Trans. on Evolutionary Computation, Vol.13, No.2, pp. 284-302, 2009.
-  R. Storn and K. Price, “Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces,” J. of Global Optimization, Vol.11, No.4, pp. 341-359, 1997.
-  R. Storn and K. Price, “Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces,” Int. Comput. Sci. Inst., Berkeley, CA, Tech. Rep. TR-95-012, 1995.
-  A. K. Qin, V. L. Huang, and P. N. Suganthan, “Differential evolution algorithm with strategy adaptation for global numerical optimization,” IEEE Trans. on Evolutionary Computation, Vol.13, No.2, pp. 398-41, 2009.
-  J. Brest, S. Greiner, B. Boskovic et al., “Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems,” IEEE Trans. on Evolutionary Computation, Vol.10, No.6, pp. 646-657, 2006.
-  R. Mallipeddi, P. N. Suganthan, Q. K. Pan et al., “Differential evolution algorithm with ensemble of parameters and mutation strategies,” Applied Soft Computing, Vol.11, No.2, pp. 1679-1696, 2011.
-  J. Zhang and A. C. Sanderson, “JADE: adaptive differential evolution with optional external archive,” IEEE Trans. on Evolutionary Computation, Vol13, No.5, pp. 945-958, 2009.
-  Y. Wang, Z. Cai, and Q. Zhang, “Differential evolution with composite trial vector generation strategies and control parameters,” IEEE Trans. on Evolutionary Computation, Vol.15, No.1, pp. 55-66, 2011.
-  Y. Y. Tan, Y. C. Jiao, Li H, and X. K. Wang, “A modification to MOEA/D-DE for multiobjective optimization problems with complicated Pareto sets,” Information Sciences, Vol.213, pp. 14-38, 2012.
-  Y. Y. Tan, Y. C. Jiao, H. Li, and X. K. Wang, “MOEA/D+ uniform design: A new version of MOEA/D for optimization problems with many objectives,”. Computers & Operations Research, Vol.40, No.6, pp. 1648-1660, 2013.
-  K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, “Scalable test problems for evolutionary multiobjective optimization,” Springer Science, London, pp. 105-145, 2005.
-  E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. G. Da Fonseca, “Performance assessment of multiobjective optimizers: an analysis and review,” IEEE Trans. on Evolutionary Computation, Vol.7, No.2, pp. 117-132, 2003.