An enhanced diversity indicator-based many-objective evolutionary algorithm with shape-conforming convergence metric

Abstract

As the number of objectives increases, many-objective optimization problems(MaOPs) become increasingly complex. Traditional indicator-based many-objective evolutionary algorithms can often ensure the convergence of the population but tend to struggle with maintaining its diversity. In this paper, an enhanced diversity indicator-based many-objective evolutionary algorithm with shape-conforming convergence metric, namely, MaOEA-DISC, is presented to relieve this weakness. In MaOEA-DISC, firstly, we focus on the inter-individual spacing relationships within the population based on Iϵ+ Indicator, proposing a novel enhanced diversity Iϵ+ Indicator to ensure the enhancement of population diversity while converging. Secondly, we propose a new metrics of individual convergence, which calculates the convergence of individuals based on the shape of Pareto front, reducing the errors caused by the shape of the Pareto front when measuring individual convergence, thereby assessing individual convergence more accurately. Finally, to further improve the convergence speed of the population, different mating strategies are employed for mating in the parental generation. MaOEA-DISC is compared with other algorithms on various benchmark MaOPs ranging from 3 to 10 objectives, as well as a real-world MaOPs. Experimental results demonstrate that when dealing with MaOPs, MaOEA-DISC not only achieves excellent population convergence and diversity but also effectively maintains a balance between them, showing promising practical value.