A Polar-Metric-Based Evolutionary Algorithm

Over the past two decades, numerous multi- and many-objective evolutionary algorithms (MOEAs and MaOEAs) have been proposed to solve the multi- and many-objective optimization problems (MOPs and MaOPs), respectively. It is known that the difficulty of maintaining the convergence and diversity performances rapidly grows as the number of objectives increases. This phenomenon is especially evident for the Pareto-dominance-based EAs, because the nondominated sorting often fails to provide enough convergent pressure toward the Pareto front (PF). Therefore, many researchers came up with some non-Pareto-dominance-based EAs, which are based on indicator, decomposition, and so on. In this article, we propose a polar-metric ( p-metric)-based EA (PMEA) for tackling both MOPs and MaOPs. p-metric is a recently proposed performance indicator which adopts a set of uniformly distributed direction vectors. In PMEA, we use a two-phase selection which combines both nondominated sorting and p-metric. Moreover, a modification is proposed to adjust the direction vectors of p-metric dynamically. In the experiments, PMEA is compared with six state-of-the-art EAs in total and is measured by three performance metrics, including p-metric. According to the empirical results, PMEA shows promising performances on most of the test problems, involving both MOPs and MaOPs.