AnD: A many-objective evolutionary algorithm with angle-based selection and shift-based density estimation

Evolutionary many-objective optimization has been gaining increasing attention from the evolutionary computation research community. Much effort has been devoted to addressing this issue by improving the scalability of multiobjective evolutionary algorithms , such as Pareto-based, decomposition-based, and indicator-based approaches. Different from current work, we propose an alternative algorithm in this paper called AnD, which consists of an angle-based selection strategy and a shift-based density estimation strategy. These two strategies are employed in the environmental selection to delete poor individuals one by one. Specifically, the former is devised to find a pair of individuals with the minimum vector angle, which means that these two individuals have the most similar search directions. The latter, which takes both diversity and convergence into account, is adopted to compare these two individuals and to delete the worse one. AnD has a simple structure, few parameters, and no complicated operators. The performance of AnD is compared with that of seven state-of-the-art many-objective evolutionary algorithms on a variety of benchmark test problems with up to 15 objectives. The results suggest that AnD can achieve highly competitive performance. In addition, we also verify that AnD can be readily extended to solve constrained many-objective optimization problems.