An adaptive clustering-based evolutionary algorithm for many-objective optimization problems

This paper proposes an adaptive clustering-based evolutionary algorithm for many-objective optimization problems (MaOPs), called MaOEA/AC. In this algorithm, an adaptive clustering strategy (ACS) is first introduced to divide the population into multiple clusters, which can properly fit various Pareto fronts (PFs) of the target MaOPs. Then, the environmental selection of MaOEA/AC is designed based on these clusters to collect the solutions with balanceable convergence and diversity. To be more detail, the similarity between solutions in ACS is appropriately measured by computing the Euclidean distance between their projections on an adaptive unit hyper-surface, whose curving rate is controlled by a parameter p. A simple yet effective estimation method is proposed to get a suitable value of p based on the distribution of the current non-dominated solution set, so that the estimated unit hyper-surface can roughly reflect the characteristics of PFs in the target MaOPs. The effectiveness of MaOEA/AC is validated by numerous experimental studies on solving test MaOPs with various PFs, which have the characteristics with convex, concave, inverted, disconnected, degenerated, and other mixed or irregular PFs. The experiments also show that MaOEA/AC has the superior performance over several recent many-objective evolutionary algorithms, when solving most of these test MaOPs.