An Improved MOEA/D with Optimal DE Schemes for Many-Objective Optimization Problems

MOEA/D is a promising multi-objective evolutionary algorithm based on decomposition, and it has been used to solve many multi-objective optimization problems very well. However, there is a class of multi-objective problems, called many-objective optimization problems, but the original MOEA/D cannot solve them well. In this paper, an improved MOEA/D with optimal differential evolution (oDE) schemes is proposed, called MOEA/D-oDE, aiming to solve many-objective optimization problems. Compared with MOEA/D, MOEA/D-oDE has two distinguishing points. On the one hand, MOEA/D-oDE adopts a newly-introduced decomposition approach to decompose the many-objective optimization problems, which combines the advantages of the weighted sum approach and the Tchebycheff approach. On the other hand, a kind of combination mechanism for DE operators is designed for finding the best child solution so as to do the a posteriori computing. In our experimental study, six continuous test instances with 4–6 objectives comparing NSGA-II (nondominated sorting genetic algorithm II) and MOEA/D as accompanying experiments are applied. Additionally, the final results indicate that MOEA/D-oDE outperforms NSGA-II and MOEA/D in almost all cases, particularly in those problems that have complicated Pareto shapes and higher dimensional objectives, where its advantages are more obvious.

[1]  Y. Jiao,et al.  MOEA/D-SQA: a multi-objective memetic algorithm based on decomposition , 2012 .

[2]  Cheng Liang,et al.  A Discriminative Feature Extraction Approach for Tumor Classification Using Gene Expression Data , 2016 .

[3]  Kiyoshi Tanaka,et al.  Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs , 2007, EMO.

[4]  Yong-Chang Jiao,et al.  MOEA/D with Uniform Design for Solving Multiobjective Knapsack Problems , 2013, J. Comput..

[5]  Qingfu Zhang,et al.  Constrained Subproblems in a Decomposition-Based Multiobjective Evolutionary Algorithm , 2016, IEEE Transactions on Evolutionary Computation.

[6]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[7]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[8]  Qingfu Zhang,et al.  An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition , 2015, IEEE Transactions on Evolutionary Computation.

[9]  Hong Liu,et al.  Multi-objective artificial bee algorithm based on decomposition by PBI method , 2016, Applied Intelligence.

[10]  Joseph R. Kasprzyk,et al.  Optimal Design of Water Distribution Systems Using Many-Objective Visual Analytics , 2013 .

[11]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[12]  DebK.,et al.  A fast and elitist multiobjective genetic algorithm , 2002 .

[13]  Qingfu Zhang,et al.  MOEA/D-ACO: A Multiobjective Evolutionary Algorithm Using Decomposition and AntColony , 2013, IEEE Transactions on Cybernetics.

[14]  Fang Liu,et al.  MOEA/D with Adaptive Weight Adjustment , 2014, Evolutionary Computation.

[15]  Hong Li,et al.  A modification to MOEA/D-DE for multiobjective optimization problems with complicated Pareto sets , 2012, Inf. Sci..

[16]  Kalyanmoy Deb,et al.  Approximating a multi-dimensional Pareto front for a land use management problem: A modified MOEA with an epigenetic silencing metaphor , 2012, 2012 IEEE Congress on Evolutionary Computation.

[17]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[18]  Ye Tian,et al.  PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] , 2017, IEEE Computational Intelligence Magazine.

[19]  Xiaonan Fang,et al.  MOEA/D with Adaptive IWO for Synthesizing Phase-Only Reconfigurable Linear Arrays , 2015 .

[20]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithm test suites , 1999, SAC '99.

[21]  Wei Li,et al.  Multiobjective Cloud Particle Optimization Algorithm Based on Decomposition , 2015, Algorithms.

[22]  Hong Liu,et al.  A novel approach to task assignment in a cooperative multi-agent design system , 2015, Applied Intelligence.

[23]  Peter J. Fleming,et al.  Methods for multi-objective optimization: An analysis , 2015, Inf. Sci..

[24]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[25]  Lakhmi C. Jain,et al.  Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[26]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[27]  Hui Li,et al.  Evolutionary Multi-objective Simulated Annealing with adaptive and competitive search direction , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[28]  Peter J. Fleming,et al.  A Real-World Application of a Many-Objective Optimisation Complexity Reduction Process , 2013, EMO.

[29]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[30]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[31]  Qingfu Zhang,et al.  The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances , 2009, 2009 IEEE Congress on Evolutionary Computation.

[32]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[33]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[34]  Hong Liu,et al.  A cooperative coevolutionary biogeography-based optimizer , 2015, Applied Intelligence.

[35]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[36]  Qingfu Zhang,et al.  Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters , 2011, IEEE Transactions on Evolutionary Computation.

[37]  Hong Li,et al.  MOEA/D + uniform design: A new version of MOEA/D for optimization problems with many objectives , 2013, Comput. Oper. Res..

[38]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..