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Evolutionary many-objective optimization has been gaining increasingattention from the evolutionary computation research community. Much effort hasbeen devoted to addressing this issue by improving the scalability ofmultiobjective evolutionary algorithms, such as Pareto-based,decomposition-based, and indicator-based approaches. Different from currentwork, we propose a novel algorithm in this paper called AnD, which consists ofan angle-based selection strategy and a shift-based density estimationstrategy. These two strategies are employed in the environmental selection todelete the poor individuals one by one. Specifically, the former is devised tofind a pair of individuals with the minimum vector angle, which means thatthese two individuals share the most similar search direction. The latter,which takes both the diversity and convergence into account, is adopted tocompare these two individuals and to delete the worse one. AnD has a simplestructure, few parameters, and no complicated operators. The performance of AnDis compared with that of seven state-of-the-art many-objective evolutionaryalgorithms on a variety of benchmark test problems with up to 15 objectives.The experimental results suggest that AnD can achieve highly competitiveperformance. In addition, we also verify that AnD can be readily extended tosolve constrained many-objective optimization problems.

A Many-Objective Evolutionary Algorithm with Angle-Based Selection and Shift-Based Density Estimation