Towards a More Balanced Reference Set Adaptation Method: First Results

Abstract

Reference sets are widely used by many multi-objective evolutionary algorithms (MOEAs) to decompose the objective space, define search directions, or calculate quality indicators (QIs) embedded into the selection mechanisms. Well-known MOEAs adopt the generation of uniformly distributed points on a unit simplex to construct such reference sets. Although these mechanisms are useful for approximating Pareto fronts with regular shapes, i.e., simplex-like shapes, they have difficulties representing Pareto fronts with irregular geometries. To overcome this drawback, many reference set adaptation methods have been proposed so far. However, some adaptation methods present a degraded performance on regular Pareto front shapes, while others promote a balanced performance. Nevertheless, an extensive assessment has not been made. In this paper, a MOEA based on the inverted generational distance plus indicator, using an adaptive reference set, is used to study the performance of well-known adaptation methods. Although an adaptation method promotes a balanced performance on both regular and irregular Pareto front shapes, results show some difficulties related to the distribution of solutions in complex Pareto front shapes. The results of this study allow detecting the main drawbacks of adaptation methods, which can be addressed by using diversity-oriented selection mechanisms in the generation of reference sets. Hence, these could impact the generation of reference set-based MOEAs achieving good coverage, convergence, and diversity regardless of the Pareto front shape.