Evolutionary algorithms based on hypervolume have demonstrated good performance for solving many-objective optimization problems. However, hypervolume needs prohibitively expensive computational effort. This paper proposes a simplified hypervolume calculation method which can be used to roughly evaluate the convergence and diversity of solutions. The main idea is to use the nearest neighbors of a particular solution to calculate the volume as the solution’s hypervolume value. Moreover, this paper improves the selection operator and the update strategy of external population according to the simplified hypervolume. Then, the proposed algorithm (SHEA) is compared with some state-of-the-art algorithms on fifteen test functions of CEC2018 MaOP competition, and the experimental results prove the feasibility of the proposed algorithm.
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