Dynamic Specification of a Reference Point for Hypervolume Calculation in SMS-EMOA

Abstract

The hypervolume has been frequently used as an indicator to compare the performance of evolutionary multi-objective optimization (EMO) algorithms. It has also been used in indicator-based algorithms (e.g., SMS-EMOA and HypE). In such an EMO algorithm, a multi-objective problem is handled as a single-objective problem to maximize the hypervolume of a pre-specified number of solutions. Whereas a reference point is needed for hypervolume calculation, its specification has not been discussed in detail in many studies. This may be because the reference point specification has almost no effect on experimental results when hypervolume-based EMO algorithms are applied to frequently-used scalable test problems such as DTLZ and WFG with triangular Pareto fronts. However, when the Pareto front of a test problem is not triangular (e.g., minus-DTLZ and minus-WFG), the reference point specification has a dominant effect on solution sets obtained by hypervolume-based EMO algorithms. In this paper, first we explain the importance of an appropriate reference point specification in SMS-EMOA. Then we examine the use of a dynamically changing specification of the reference point in SMS-EMOA.