A niching indicator-based multi-modal many-objective optimizer

Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. Some evolutionary algorithms for multi-modal multi-objective optimization have been proposed in the literature. However, there is no efficient method for multi-modal many-objective optimization, where the number of objectives is more than three. To address this issue, this paper proposes a niching indicator-based multi-modal multi- and many-objective optimization algorithm. In the proposed method, the fitness calculation is performed among a child and its closest individuals in the solution space to maintain the diversity. The performance of the proposed method is evaluated on multi-modal multi-objective test problems with up to 15 objectives. Results show that the proposed method can handle a large number of objectives and find a good approximation of multiple equivalent Pareto optimal solutions. The results also show that the proposed method performs significantly better than eight multi-objective evolutionary algorithms.

[1]  Hisao Ishibuchi,et al.  Performance comparison of NSGA-II and NSGA-III on various many-objective test problems , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[2]  Mike Preuss,et al.  Improved Topological Niching for Real-Valued Global Optimization , 2012, EvoApplications.

[3]  Michèle Sebag,et al.  A Multi-Objective Multi-Modal Optimization Approach for Mining Stable Spatio-Temporal Patterns , 2005, IJCAI.

[4]  Heike Trautmann,et al.  2 Indicator-Based Multiobjective Search , 2015, Evolutionary Computation.

[5]  Xiaodong Li,et al.  Seeking Multiple Solutions: An Updated Survey on Niching Methods and Their Applications , 2017, IEEE Transactions on Evolutionary Computation.

[6]  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.

[7]  Carlos A. Coello Coello,et al.  A new multi-objective evolutionary algorithm based on a performance assessment indicator , 2012, GECCO.

[8]  Aimin Zhou,et al.  A Multiobjective Evolutionary Algorithm Based on Decomposition and Preselection , 2015, BIC-TA.

[9]  Junichi Suzuki,et al.  R2-IBEA: R2 indicator based evolutionary algorithm for multiobjective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[10]  Jing J. Liang,et al.  A Self-organizing Multi-objective Particle Swarm Optimization Algorithm for Multimodal Multi-objective Problems , 2018, ICSI.

[11]  Marco Laumanns,et al.  Scalable test problems for evolutionary multi-objective optimization , 2001 .

[12]  Markus Wagner,et al.  Approximation-Guided Evolutionary Multi-Objective Optimization , 2011, IJCAI.

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

[14]  Ponnuthurai N. Suganthan,et al.  Real-parameter evolutionary multimodal optimization - A survey of the state-of-the-art , 2011, Swarm Evol. Comput..

[15]  Hisao Ishibuchi,et al.  A Review of Evolutionary Multi-modal Multi-objective Optimization , 2020, arXiv.org.

[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]  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.

[18]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[19]  Hisao Ishibuchi,et al.  A many-objective test problem for visually examining diversity maintenance behavior in a decision space , 2011, GECCO '11.

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

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

[22]  Markus Wagner,et al.  A modified indicator-based evolutionary algorithm (mIBEA) , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

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

[24]  Francisco Herrera,et al.  Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power , 2010, Inf. Sci..

[25]  Qingfu Zhang,et al.  Approximating the Set of Pareto-Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm , 2009, IEEE Transactions on Evolutionary Computation.

[26]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[27]  Günter Rudolph,et al.  Pareto Set and EMOA Behavior for Simple Multimodal Multiobjective Functions , 2006, PPSN.

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

[29]  Adriana Menchaca-Mendez,et al.  GD-MOEA: A New Multi-Objective Evolutionary Algorithm Based on the Generational Distance Indicator , 2015, EMO.

[30]  Tomoyuki Hiroyasu,et al.  Comparison study of SPEA2+, SPEA2, and NSGA-II in diesel engine emissions and fuel economy problem , 2005, 2005 IEEE Congress on Evolutionary Computation.

[31]  Günter Rudolph,et al.  Capabilities of EMOA to Detect and Preserve Equivalent Pareto Subsets , 2007, EMO.

[32]  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.

[33]  Xin Yao,et al.  of Birmingham Quality evaluation of solution sets in multiobjective optimisation , 2019 .

[34]  Jie Zhang,et al.  A Simple and Fast Hypervolume Indicator-Based Multiobjective Evolutionary Algorithm , 2015, IEEE Transactions on Cybernetics.

[35]  Saúl Zapotecas Martínez,et al.  LIBEA: A Lebesgue Indicator-Based Evolutionary Algorithm for multi-objective optimization , 2019, Swarm Evol. Comput..

[36]  Markus Wagner,et al.  A fast approximation-guided evolutionary multi-objective algorithm , 2013, GECCO '13.

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

[38]  Xiaodong Li,et al.  Adaptively choosing niching parameters in a PSO , 2006, GECCO.

[39]  Hisao Ishibuchi,et al.  A Decomposition-Based Evolutionary Algorithm for Multi-modal Multi-objective Optimization , 2018, PPSN.

[40]  Tomohiro Yoshikawa,et al.  A study on analysis of design variables in Pareto solutions for conceptual design optimization problem of hybrid rocket engine , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

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

[42]  Carlos A. Coello Coello,et al.  A Study of the Parallelization of a Coevolutionary Multi-objective Evolutionary Algorithm , 2004, MICAI.

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

[44]  Carlos A. Coello Coello,et al.  A multi-objective evolutionary hyper-heuristic based on multiple indicator-based density estimators , 2018, GECCO.

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

[46]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[47]  Kalyanmoy Deb,et al.  Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization , 2008, Eur. J. Oper. Res..

[48]  Eckart Zitzler,et al.  Integrating decision space diversity into hypervolume-based multiobjective search , 2010, GECCO '10.

[49]  Hisao Ishibuchi,et al.  Modified Distance Calculation in Generational Distance and Inverted Generational Distance , 2015, EMO.

[50]  Samir W. Mahfoud.  Crowding and Preselection Revisited , 1992, PPSN.

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

[52]  Xiaodong Li,et al.  Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology , 2010, IEEE Transactions on Evolutionary Computation.

[53]  Hisao Ishibuchi,et al.  Comparing solution sets of different size in evolutionary many-objective optimization , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

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

[55]  Gary G. Yen,et al.  A Multimodal Multiobjective Evolutionary Algorithm Using Two-Archive and Recombination Strategies , 2019, IEEE Transactions on Evolutionary Computation.

[56]  Hisao Ishibuchi,et al.  Benchmarking Multi- and Many-Objective Evolutionary Algorithms Under Two Optimization Scenarios , 2017, IEEE Access.

[57]  Carlos A. Coello Coello,et al.  IGD+-EMOA: A multi-objective evolutionary algorithm based on IGD+ , 2016, CEC.

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

[59]  Kalyanmoy Deb,et al.  Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations , 2017, Evolutionary Computation.

[60]  Nicola Beume,et al.  Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization , 2007, EMO.

[61]  Edmund K. Burke,et al.  Indicator-based multi-objective local search , 2007, 2007 IEEE Congress on Evolutionary Computation.

[62]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[63]  Thomas Bäck,et al.  Enhancing search space diversity in multi-objective evolutionary drug molecule design using niching , 2009, GECCO.

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

[65]  Hisao Ishibuchi,et al.  A Review of Evolutionary Multimodal Multiobjective Optimization , 2020, IEEE Transactions on Evolutionary Computation.

[66]  Wentong Cai,et al.  Evolving Optimal and Diversified Military Operational Plans for Computational Red Teaming , 2012, IEEE Systems Journal.

[67]  M. Hansen,et al.  Evaluating the quality of approximations to the non-dominated set , 1998 .

[68]  Hisao Ishibuchi,et al.  Effects of Removing Overlapping Solutions on the Performance of the NSGA-II Algorithm , 2005, EMO.

[69]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

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

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

[72]  Xiaodong Li,et al.  A dynamic archive niching differential evolution algorithm for multimodal optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[73]  Jing J. Liang,et al.  A Multiobjective Particle Swarm Optimizer Using Ring Topology for Solving Multimodal Multiobjective Problems , 2018, IEEE Transactions on Evolutionary Computation.

[74]  Tomoyuki Hiroyasu,et al.  SPEA2+: Improving the Performance of the Strength Pareto Evolutionary Algorithm 2 , 2004, PPSN.

[75]  Lino A. Costa,et al.  Many-objective optimization using differential evolution with variable-wise mutation restriction , 2013, GECCO '13.

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

[77]  Jing J. Liang,et al.  Multimodal multi-objective optimization: A preliminary study , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[78]  Ofer M. Shir,et al.  Enhancing Decision Space Diversity in Evolutionary Multiobjective Algorithms , 2009, EMO.

[79]  Carlos A. Coello Coello,et al.  Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.

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

[81]  Massimiliano Vasile,et al.  Computing the Set of Epsilon-Efficient Solutions in Multiobjective Space Mission Design , 2011, J. Aerosp. Comput. Inf. Commun..

[82]  Ofer M. Shir,et al.  Niching with derandomized evolution strategies in artificial and real-world landscapes , 2009, Natural Computing.

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

[84]  Xiaodong Yin,et al.  A Fast Genetic Algorithm with Sharing Scheme Using Cluster Analysis Methods in Multimodal Function Optimization , 1993 .