An ensemble approach with external archive for multi- and many-objective optimization with adaptive mating mechanism and two-level environmental selection

Abstract Based on mating and environmental selections employed, multi-objective evolutionary algorithms (MOEAs) are classified as Pareto-based, decomposition-based and indicator-based approaches that are associated with their own advantages and disadvantages. To benefit from the advantages of different MOEAs, we propose an ensemble framework (ENMOEA) in which mating and environmental selections of diverse MOEAs are combined. ENMOEA is a single-population competitive ensemble, where resource allocation to individual mating operators is done adaptively. In addition, ENMOEA employs a two-level environmental selection where constituent environmental selection operators are first applied to label solutions as “selected” and “non-selected”. Solutions “selected” by most operators are preferred for future evolution. An external archive is employed to facilitate effective usage of function evaluations and achieve a better comprise between convergence and diversity. To demonstrate generality of ENMOEA, we developed two variants: 1) specific case (ENMOEAS - combines different Pareto-based MOEAs) and 2) general case (ENMOEAG - combines Pareto-based, indicator-based and decomposition-based MOEAs). From simulation results on various test suites (DTLZ, WFG and 16 real-world problems), it is evident that ENMOEA is robust to the parameters of the constituent algorithms. In addition, it evident that the effectiveness of ensemble improves with the diversity of the constituent algorithms.

[1]  Qingfu Zhang,et al.  Adaptive Operator Selection With Bandits for a Multiobjective Evolutionary Algorithm Based on Decomposition , 2014, IEEE Transactions on Evolutionary Computation.

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

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

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

[5]  Qingfu Zhang,et al.  Hybridization of Decomposition and Local Search for Multiobjective Optimization , 2014, IEEE Transactions on Cybernetics.

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

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

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

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

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

[11]  Kay Chen Tan,et al.  Adaptive Memetic Computing for Evolutionary Multiobjective Optimization , 2015, IEEE Transactions on Cybernetics.

[12]  Qiuzhen Lin,et al.  Adaptive composite operator selection and parameter control for multiobjective evolutionary algorithm , 2016, Inf. Sci..

[13]  Peter J. Fleming,et al.  Preference-inspired co-evolutionary algorithms using weight vectors , 2015, Eur. J. Oper. Res..

[14]  Qingfu Zhang,et al.  An Effective Ensemble Framework for Multiobjective Optimization , 2019, IEEE Transactions on Evolutionary Computation.

[15]  Tao Li,et al.  A novel two-archive strategy for evolutionary many-objective optimization algorithm based on reference points , 2019, Appl. Soft Comput..

[16]  Carlos A. Coello Coello,et al.  Indicator-based Multi-objective Evolutionary Algorithms , 2020, ACM Comput. Surv..

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

[18]  Xin Yao,et al.  A New Multi-objective Evolutionary Optimisation Algorithm: The Two-Archive Algorithm , 2006, 2006 International Conference on Computational Intelligence and Security.

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

[20]  Xin Yao,et al.  Two_Arch2: An Improved Two-Archive Algorithm for Many-Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[21]  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).

[22]  Qingfu Zhang,et al.  An External Archive Guided Multiobjective Evolutionary Algorithm Based on Decomposition for Combinatorial Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[23]  Qingfu Zhang,et al.  Decomposition-Based Multiobjective Evolutionary Algorithm With an Ensemble of Neighborhood Sizes , 2012, IEEE Transactions on Evolutionary Computation.

[24]  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.

[25]  Xin Yao,et al.  Stochastic Ranking Algorithm for Many-Objective Optimization Based on Multiple Indicators , 2016, IEEE Transactions on Evolutionary Computation.

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

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

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

[29]  Hisao Ishibuchi,et al.  An easy-to-use real-world multi-objective optimization problem suite , 2020, Appl. Soft Comput..

[30]  P. N. Suganthan,et al.  Ensemble of Constraint Handling Techniques , 2010, IEEE Transactions on Evolutionary Computation.

[31]  Aurora Trinidad Ramirez Pozo,et al.  A New Adaptive Operator Selection for NSGA-III Applied to CEC 2018 Many-Objective Benchmark , 2018, 2018 7th Brazilian Conference on Intelligent Systems (BRACIS).

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

[33]  Edmund K. Burke,et al.  A methodology for determining an effective subset of heuristics in selection hyper-heuristics , 2017, Eur. J. Oper. Res..

[34]  Lei Cai,et al.  Two-archive method for aggregation-based many-objective optimization , 2018, Inf. Sci..

[35]  Yalan Zhou,et al.  Ensemble of many-objective evolutionary algorithms for many-objective problems , 2017, Soft Comput..

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

[37]  Aurora Trinidad Ramirez Pozo,et al.  Adaptive Operator Selection in NSGA-III , 2016, 2016 5th Brazilian Conference on Intelligent Systems (BRACIS).

[38]  John A. W. McCall,et al.  D2MOPSO: MOPSO Based on Decomposition and Dominance with Archiving Using Crowding Distance in Objective and Solution Spaces , 2014, Evolutionary Computation.

[39]  Rammohan Mallipeddi,et al.  Pareto Dominance-Based Algorithms With Ranking Methods for Many-Objective Optimization , 2017, IEEE Access.

[40]  Yaonan Wang,et al.  Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure , 2010, Soft Comput..

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

[42]  Ponnuthurai Nagaratnam Suganthan,et al.  $I_{\rm SDE}$ +—An Indicator for Multi and Many-Objective Optimization , 2019, IEEE Transactions on Evolutionary Computation.

[43]  Zexuan Zhu,et al.  A novel adaptive hybrid crossover operator for multiobjective evolutionary algorithm , 2016, Inf. Sci..

[44]  Jianbin Huang,et al.  An immune multi-objective optimization algorithm with differential evolution inspired recombination , 2015, Appl. Soft Comput..

[45]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[46]  Zexuan Zhu,et al.  A Survey of Weight Vector Adjustment Methods for Decomposition-Based Multiobjective Evolutionary Algorithms , 2020, IEEE Transactions on Evolutionary Computation.

[47]  Yilong Yin,et al.  A Hybrid Evolutionary Immune Algorithm for Multiobjective Optimization Problems , 2016, IEEE Transactions on Evolutionary Computation.

[48]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[49]  Xin Yao,et al.  Many-Objective Evolutionary Algorithms , 2015, ACM Comput. Surv..

[50]  Kay Chen Tan,et al.  Online Diversity Assessment in Evolutionary Multiobjective Optimization: A Geometrical Perspective , 2015, IEEE Transactions on Evolutionary Computation.