A new non-redundant objective set generation algorithm in many-objective optimization problems

Among the many-objective optimization problems, there exists a kind of problem with redundant objectives, it is possible to design effective algorithms by removing the redundant objectives and keeping the non-redundant objectives so that the original problem becomes the one with much fewer objectives. In this paper, a new non-redundant objective set generation algorithm is proposed. To do so, first, a multi-objective evolutionary algorithm based decomposition is adopted to generate a small number of representative non-dominated solutions widely distributed on the Pareto front. Then, the conflicting objective pairs are identified through these non-dominated solutions, and the non-redundant objective set is determined by these pairs. Finally, the experiments are conducted on a set of benchmark test problems and the results indicate the effectiveness and efficiency of the proposed algorithm.

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

[2]  Eckart Zitzler,et al.  Are All Objectives Necessary? On Dimensionality Reduction in Evolutionary Multiobjective Optimization , 2006, PPSN.

[3]  Mario Köppen,et al.  Substitute Distance Assignments in NSGA-II for Handling Many-objective Optimization Problems , 2007, EMO.

[4]  Thomas Bäck,et al.  Combining Aggregation with Pareto Optimization: A Case Study in Evolutionary Molecular Design , 2009, EMO.

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

[6]  Eckart Zitzler,et al.  Objective Reduction in Evolutionary Multiobjective Optimization: Theory and Applications , 2009, Evolutionary Computation.

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

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

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

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

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

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

[13]  Lothar Thiele,et al.  The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration , 2007, EMO.

[14]  Soon-Thiam Khu,et al.  An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[15]  Tapabrata Ray,et al.  A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems , 2011, IEEE Transactions on Evolutionary Computation.

[16]  Qingfu Zhang,et al.  Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms , 2013, IEEE Transactions on Evolutionary Computation.

[17]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

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

[19]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[20]  Peter J. Fleming,et al.  Evolutionary many-objective optimisation: an exploratory analysis , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

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

[22]  R. Lyndon While,et al.  A Scalable Multi-objective Test Problem Toolkit , 2005, EMO.

[23]  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).

[24]  M. Farina,et al.  On the optimal solution definition for many-criteria optimization problems , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[25]  Peter J. Fleming,et al.  Conflict, Harmony, and Independence: Relationships in Evolutionary Multi-criterion Optimisation , 2003, EMO.