A Clustering-Based Evolutionary Algorithm for Many-Objective Optimization Problems

• Published in: IEEE transactions on evolutionary computation Vol. 23; no. 3; pp. 391 - 405
• Main Authors: Lin, Qiuzhen, Liu, Songbai, Wong, Ka-Chun, Gong, Maoguo, Coello Coello, Carlos A., Chen, Jianyong, Zhang, Jun
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-06-2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Classification; Cluster analysis; Clustering; Clustering algorithms; Clustering methods; Convergence; Evolutionary algorithm (EA); Evolutionary algorithms; Evolutionary computation; Genetic algorithms; hierarchical clustering; many-objective optimization; Multiple objective analysis; Optimization; partitional clustering; Phase change materials; Population; Sociology; Statistics
• ISSN: 1089-778X; 1941-0026
• DOI: 10.1109/TEVC.2018.2866927

This paper suggests a novel clustering-based evolutionary algorithm for many-objective optimization problems. Its main idea is to classify the population into a number of clusters, which is expected to solve the difficulty of balancing convergence and diversity in high-dimensional objective space. The individuals showing high similarities on the vector angles are gathered into the same cluster, such that the population's distribution can be well portrayed by the clusters. To efficiently find these clusters, partitional clustering is first used to classify the union population into <inline-formula> <tex-math notation="LaTeX">{m} </tex-math></inline-formula> main clusters based on the <inline-formula> <tex-math notation="LaTeX">{m} </tex-math></inline-formula> axis vectors (<inline-formula> <tex-math notation="LaTeX">{m} </tex-math></inline-formula> is the number of objectives), and then hierarchical clustering is further run on these <inline-formula> <tex-math notation="LaTeX">{m} </tex-math></inline-formula> main clusters to get <inline-formula> <tex-math notation="LaTeX">{N} </tex-math></inline-formula> final clusters (<inline-formula> <tex-math notation="LaTeX">{N} </tex-math></inline-formula> is the population size and <inline-formula> <tex-math notation="LaTeX">{N>m} </tex-math></inline-formula>). At last, in environmental selection, one individual from each of <inline-formula> <tex-math notation="LaTeX">{N} </tex-math></inline-formula> clusters closest to the axis vectors is selected to maintain diversity, while one individual from each of the other clusters is preferred by a simple convergence indicator to ensure convergence. When tackling some well-known test problems with 5-15 objectives, extensive experiments validate the superiority of our algorithm over six competitive many-objective EAs, especially on problems with incomplete and irregular Pareto-optimal fronts.