ESOEA: Ensemble of single objective evolutionary algorithms for many-objective optimization

Abstract Inspired by the success of decomposition based evolutionary algorithms and the necessary search for a versatile many-objective optimization algorithm which is adaptive to several kinds of characteristics of the search space, the proposed work presents an adaptive framework which addresses many-objective optimization problems by using an ensemble of single objective evolutionary algorithms (ESOEA). It adopts a reference-direction based approach to decompose the population, followed by scalarization to transform the many-objective problem into several single objective sub-problems which further enhances the selection pressure. Additionally, with a feedback strategy, ESOEA explores the directions along difficult regions and thus, improving the search capabilities along those directions. For experimental validation, ESOEA is integrated with an adaptive Differential Evolution and experimented on several benchmark problems from the DTLZ, WFG, IMB and CEC 2009 competition test suites. To assess the efficacy of ESOEA, the performance is noted in terms of convergence metric, inverted generational distance, and hypervolume indicator, and is compared with numerous other multi- and/or many-objective evolutionary algorithms. For a few test cases, the resulting Pareto-fronts are also visualized which help in the further analysis of the results and in establishing the robustness of ESOEA.

[1]  Hussein A. Abbass,et al.  Adaptive Cross-Generation Differential Evolution Operators for Multiobjective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

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

[3]  Qingfu Zhang,et al.  Decomposition of a Multiobjective Optimization Problem Into a Number of Simple Multiobjective Subproblems , 2014, IEEE Transactions on Evolutionary Computation.

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

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

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

[7]  Antonio López Jaimes,et al.  An investigation into many-objective optimization on combinatorial problems: Analyzing the pickup and delivery problem , 2018, Swarm Evol. Comput..

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

[9]  Sanghamitra Bandyopadhyay,et al.  DECOR: Differential Evolution using Clustering based Objective Reduction for many-objective optimization , 2018, Inf. Sci..

[10]  Qingfu Zhang,et al.  Comparison between MOEA/D and NSGA-III on a set of novel many and multi-objective benchmark problems with challenging difficulties , 2019, Swarm Evol. Comput..

[11]  Kalyanmoy Deb,et al.  Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multiobjective Algorithms , 2017, IEEE Transactions on Evolutionary Computation.

[12]  Sanghamitra Bandyopadhyay,et al.  Clustering based online automatic objective reduction to aid many-objective optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

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

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

[15]  Jiang Siwei,et al.  Multiobjective optimization by decomposition with Pareto-adaptive weight vectors , 2011, 2011 Seventh International Conference on Natural Computation.

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

[17]  Xin Yao,et al.  Diversity creation methods: a survey and categorisation , 2004, Inf. Fusion.

[18]  Carlos Cotta,et al.  Memetic algorithms and memetic computing optimization: A literature review , 2012, Swarm Evol. Comput..

[19]  Xin Yao,et al.  Decomposition-Based Memetic Algorithm for Multiobjective Capacitated Arc Routing Problem , 2011, IEEE Transactions on Evolutionary Computation.

[20]  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.

[21]  Kalyanmoy Deb,et al.  Evaluating the -Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions , 2005, Evolutionary Computation.

[22]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[23]  Qingfu Zhang,et al.  MOEA/D-DRA with two crossover operators , 2010, 2010 UK Workshop on Computational Intelligence (UKCI).

[24]  Carlos M. Fonseca,et al.  Hypervolume Sharpe-Ratio Indicator: Formalization and First Theoretical Results , 2016, PPSN.

[25]  Carlos A. Coello Coello,et al.  Objective reduction using a feature selection technique , 2008, GECCO '08.

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

[27]  Bara'a Ali Attea,et al.  Improving the performance of evolutionary multi-objective co-clustering models for community detection in complex social networks , 2016, Swarm Evol. Comput..

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

[29]  A. Kai Qin,et al.  Self-adaptive differential evolution algorithm for numerical optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[30]  Carlos A. Coello Coello,et al.  Online Objective Reduction to Deal with Many-Objective Problems , 2009, EMO.

[31]  Xin Yao,et al.  Self-adaptive differential evolution with neighborhood search , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

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

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

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

[35]  Rolf Drechsler,et al.  Multi-objective Optimisation Based on Relation Favour , 2001, EMO.

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

[37]  Chris Lacor,et al.  CFD modeling and multi-objective optimization of cyclone geometry using desirability function, artificial neural networks and genetic algorithms , 2013 .

[38]  Evan J. Hughes,et al.  MSOPS-II: A general-purpose Many-Objective optimiser , 2007, 2007 IEEE Congress on Evolutionary Computation.

[39]  Carlos A. Coello Coello,et al.  Recent Results and Open Problems in Evolutionary Multiobjective Optimization , 2017, TPNC.

[40]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

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

[42]  Andrzej Jaszkiewicz,et al.  Genetic local search for multi-objective combinatorial optimization , 2022 .

[43]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

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

[45]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[46]  Bernhard Sendhoff,et al.  Adapting Weighted Aggregation for Multiobjective Evolution Strategies , 2001, EMO.

[47]  Gary G. Yen,et al.  An improved visualization approach in many-objective optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[48]  James Demmel,et al.  IEEE Standard for Floating-Point Arithmetic , 2008 .

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

[50]  Ajith Abraham,et al.  On stability and convergence of the population-dynamics in differential evolution , 2009, AI Commun..

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

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

[53]  Günter Rudolph,et al.  Convergence properties of some multi-objective evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[54]  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.

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

[56]  Patrick M. Reed,et al.  Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework , 2013, Evolutionary Computation.

[57]  Peter J. Fleming,et al.  On the Evolutionary Optimization of Many Conflicting Objectives , 2007, IEEE Transactions on Evolutionary Computation.

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

[59]  Guohua Wu,et al.  Ensemble strategies for population-based optimization algorithms - A survey , 2019, Swarm Evol. Comput..

[60]  Sanghamitra Bandyopadhyay,et al.  Many-objective feature selection for motor imagery EEG signals using differential evolution and support vector machine , 2016, 2016 International Conference on Microelectronics, Computing and Communications (MicroCom).

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

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

[63]  Sanghamitra Bandyopadhyay,et al.  Reliability of convergence metric and hypervolume indicator for many-objective optimization , 2016, 2016 2nd International Conference on Control, Instrumentation, Energy & Communication (CIEC).

[64]  Xiao Zhi Gao,et al.  Self-organizing multiobjective optimization based on decomposition with neighborhood ensemble , 2016, Neurocomputing.

[65]  Sanghamitra Bandyopadhyay,et al.  An Algorithm for Many-Objective Optimization With Reduced Objective Computations: A Study in Differential Evolution , 2015, IEEE Transactions on Evolutionary Computation.

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