Clustering-Based Subset Selection in Evolutionary Multiobjective Optimization

Subset selection is an important component in evolutionary multiobjective optimization (EMO) algorithms. Clustering, as a classic method to group similar data points together, has been used for subset selection in some EMO algorithms. However, clustering-based methods have not been evaluated in the context of subset selection from solution sets obtained by EMO algorithms. In this paper, we first review some classic clustering algorithms. We also point out that another popular subset selection method, i.e., IGD-based subset selection, can be viewed as clustering. Then, we perform a comprehensive experimental study to evaluate the performance of various clustering algorithms in different scenarios. Experimental results are analyzed in detail, and some suggestions about the use of clustering algorithms for subset selection are derived. Additionally, we demonstrate that decision maker’s preference can be introduced to clustering-based subset selection.

[1]  Christos Boutsidis,et al.  Clustered subset selection and its applications on it service metrics , 2008, CIKM '08.

[2]  Hisao Ishibuchi,et al.  Modified Distance-based Subset Selection for Evolutionary Multi-objective Optimization Algorithms , 2020, 2020 IEEE Congress on Evolutionary Computation (CEC).

[3]  Hans-Peter Kriegel,et al.  A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise , 1996, KDD.

[4]  Desire L. Massart,et al.  Representative subset selection , 2002 .

[5]  Eckart Zitzler,et al.  Pattern identification in pareto-set approximations , 2008, GECCO '08.

[6]  Hisao Ishibuchi,et al.  How to compare many-objective algorithms under different settings of population and archive sizes , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[7]  Aimin Zhou,et al.  A clustering based multiobjective evolutionary algorithm , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[8]  Robert R. Sokal,et al.  A statistical method for evaluating systematic relationships , 1958 .

[9]  Sergei Vassilvitskii,et al.  k-means++: the advantages of careful seeding , 2007, SODA '07.

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

[11]  Hisao Ishibuchi,et al.  Fast Greedy Subset Selection From Large Candidate Solution Sets in Evolutionary Multiobjective Optimization , 2021, IEEE Transactions on Evolutionary Computation.

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

[13]  Hisao Ishibuchi,et al.  A New Framework of Evolutionary Multi-Objective Algorithms with an Unbounded External Archive , 2020 .

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

[15]  Carl E. Rasmussen,et al.  The Infinite Gaussian Mixture Model , 1999, NIPS.

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

[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]  Ye Tian,et al.  Sampling Reference Points on the Pareto Fronts of Benchmark Multi-Objective Optimization Problems , 2018, 2018 IEEE Congress on Evolutionary Computation (CEC).

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

[20]  Hisao Ishibuchi,et al.  Solution Subset Selection for Final Decision Making in Evolutionary Multi-Objective Optimization , 2020, ArXiv.

[21]  J. H. Ward Hierarchical Grouping to Optimize an Objective Function , 1963 .

[22]  Kalyanmoy Deb,et al.  Finding Knees in Multi-objective Optimization , 2004, PPSN.

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

[24]  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.

[25]  S. C. Johnson Hierarchical clustering schemes , 1967, Psychometrika.

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

[27]  Xin Yao,et al.  A benchmark test suite for evolutionary many-objective optimization , 2017, Complex & Intelligent Systems.

[28]  Carlos M. Fonseca,et al.  Greedy Hypervolume Subset Selection in Low Dimensions , 2016, Evolutionary Computation.

[29]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[30]  Yingjie Tian,et al.  A Comprehensive Survey of Clustering Algorithms , 2015, Annals of Data Science.

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

[32]  Tapabrata Ray,et al.  Distance-Based Subset Selection for Benchmarking in Evolutionary Multi/Many-Objective Optimization , 2019, IEEE Transactions on Evolutionary Computation.

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

[34]  Hae-Sang Park,et al.  A simple and fast algorithm for K-medoids clustering , 2009, Expert Syst. Appl..

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

[36]  Yanbin Yuan,et al.  Multi-objective optimal power flow based on improved strength Pareto evolutionary algorithm , 2017 .

[37]  J. Bezdek,et al.  FCM: The fuzzy c-means clustering algorithm , 1984 .

[38]  Ka-Chun Wong,et al.  A Self-Guided Reference Vector Strategy for Many-Objective Optimization , 2020, IEEE Transactions on Cybernetics.

[39]  Jiong Yang,et al.  STING: A Statistical Information Grid Approach to Spatial Data Mining , 1997, VLDB.

[40]  Kuangrong Hao,et al.  A Clustering-Based Adaptive Evolutionary Algorithm for Multiobjective Optimization With Irregular Pareto Fronts , 2019, IEEE Transactions on Cybernetics.