A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization

Both convergence and diversity are crucial to evolutionary many-objective optimization, whereas most existing dominance relations show poor performance in balancing them, thus easily leading to a set of solutions concentrating on a small region of the Pareto fronts. In this paper, a novel dominance relation is proposed to better balance convergence and diversity for evolutionary many-objective optimization. In the proposed dominance relation, an adaptive niching technique is developed based on the angles between the candidate solutions, where only the best converged candidate solution is identified to be nondominated in each niche. Experimental results demonstrate that the proposed dominance relation outperforms existing dominance relations in balancing convergence and diversity. A modified NSGA-II is suggested based on the proposed dominance relation, which shows competitiveness against the state-of-the-art algorithms in solving many-objective optimization problems. The effectiveness of the proposed dominance relation is also verified on several other existing multi- and many-objective evolutionary algorithms.

[1]  Qingfu Zhang,et al.  Combining Model-based and Genetics-based Offspring Generation for Multi-objective Optimization Using a Convergence Criterion , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[2]  Markus Olhofer,et al.  Evolutionary Many-Objective Optimization of Hybrid Electric Vehicle Control: From General Optimization to Preference Articulation , 2017, IEEE Transactions on Emerging Topics in Computational Intelligence.

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

[4]  Marco Farina,et al.  A fuzzy definition of "optimality" for many-criteria optimization problems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[5]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

[6]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[7]  Shengxiang Yang,et al.  A Grid-Based Evolutionary Algorithm for Many-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

[8]  Frederico G. Guimarães,et al.  Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms , 2011, EMO.

[9]  H. Kita,et al.  Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[10]  K. Deb,et al.  On Finding Pareto-Optimal Solutions Through Dimensionality Reduction for Certain Large-Dimensional Multi-Objective Optimization Problems , 2022 .

[11]  Bernhard Sendhoff,et al.  A Multiobjective Evolutionary Algorithm Using Gaussian Process-Based Inverse Modeling , 2015, IEEE Transactions on Evolutionary Computation.

[12]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[13]  Yaochu Jin,et al.  A Many-Objective Evolutionary Algorithm Using A One-by-One Selection Strategy , 2017, IEEE Transactions on Cybernetics.

[14]  Bernhard Sendhoff,et al.  A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[15]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[16]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach , 2014, IEEE Transactions on Evolutionary Computation.

[17]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[18]  Xin Yao,et al.  A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[19]  Shengxiang Yang,et al.  Bi-goal evolution for many-objective optimization problems , 2015, Artif. Intell..

[20]  Erik D. Goodman,et al.  Generalization of Pareto-Optimality for Many-Objective Evolutionary Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[21]  Shengxiang Yang,et al.  Diversity Comparison of Pareto Front Approximations in Many-Objective Optimization , 2014, IEEE Transactions on Cybernetics.

[22]  Carlos A. Coello Coello,et al.  Pareto-adaptive -dominance , 2007, Evolutionary Computation.

[23]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[24]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[25]  Ye Tian,et al.  A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

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

[27]  Yuren Zhou,et al.  A Vector Angle-Based Evolutionary Algorithm for Unconstrained Many-Objective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[28]  Ye Tian,et al.  Effectiveness and efficiency of non-dominated sorting for evolutionary multi- and many-objective optimization , 2017, Complex & Intelligent Systems.

[29]  Xin Yao,et al.  How to Read Many-Objective Solution Sets in Parallel Coordinates [Educational Forum] , 2017, IEEE Computational Intelligence Magazine.

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

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

[32]  Ye Tian,et al.  A Decision Variable Clustering-Based Evolutionary Algorithm for Large-Scale Many-Objective Optimization , 2018, IEEE Transactions on Evolutionary Computation.

[33]  Shengxiang Yang,et al.  Pareto or Non-Pareto: Bi-Criterion Evolution in Multiobjective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[34]  Kiyoshi Tanaka,et al.  Self-Controlling Dominance Area of Solutions in Evolutionary Many-Objective Optimization , 2010, SEAL.

[35]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[36]  Fang Liu,et al.  A Multiobjective Evolutionary Algorithm Based on Decision Variable Analyses for Multiobjective Optimization Problems With Large-Scale Variables , 2016, IEEE Transactions on Evolutionary Computation.

[37]  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.

[38]  Hisao Ishibuchi,et al.  Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes , 2017, IEEE Transactions on Evolutionary Computation.

[39]  Carlos A. Coello Coello,et al.  Improved Metaheuristic Based on the R2 Indicator for Many-Objective Optimization , 2015, GECCO.

[40]  Ye Tian,et al.  An Efficient Approach to Nondominated Sorting for Evolutionary Multiobjective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

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

[42]  Shengxiang Yang,et al.  Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[43]  Ye Tian,et al.  An Efficient Approach to Non-dominated Sorting for Evolutionary Multi-objective Optimization , 2014 .

[44]  Slim Bechikh,et al.  A New Decomposition-Based NSGA-II for Many-Objective Optimization , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[45]  R. Lyndon While,et al.  A faster algorithm for calculating hypervolume , 2006, IEEE Transactions on Evolutionary Computation.

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

[47]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization , 2008, 2008 3rd International Workshop on Genetic and Evolving Systems.

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

[49]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[50]  Shengxiang Yang,et al.  The Supplement of the Paper “ Multi-Line Distance Minimization : A Visualized Many-Objective Test Problem Suite ” , 2017 .

[51]  Ye Tian,et al.  An Indicator-Based Multiobjective Evolutionary Algorithm With Reference Point Adaptation for Better Versatility , 2018, IEEE Transactions on Evolutionary Computation.

[52]  Richard Curran,et al.  Optimization of noise abatement aircraft terminal routes using a multi-objective evolutionary algorithm based on decomposition , 2018 .

[53]  Gaoping Wang,et al.  Fuzzy-Dominance and Its Application in Evolutionary Many Objective Optimization , 2007, 2007 International Conference on Computational Intelligence and Security Workshops (CISW 2007).

[54]  Jun Zhang,et al.  Fuzzy-Based Pareto Optimality for Many-Objective Evolutionary Algorithms , 2014, IEEE Transactions on Evolutionary Computation.

[55]  Lishan Kang,et al.  A New Evolutionary Algorithm for Solving Many-Objective Optimization Problems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[56]  Kent McClymont,et al.  Deductive Sort and Climbing Sort: New Methods for Non-Dominated Sorting , 2012, Evolutionary Computation.

[57]  Xin Yao,et al.  Diversity Assessment in Many-Objective Optimization , 2017, IEEE Transactions on Cybernetics.