Indicator-based evolutionary algorithm with hypervolume approximation by achievement scalarizing functions

Abstract

Pareto dominance-based algorithms have been the main stream in the field of evolutionary multiobjective optimization (EMO) for the last two decades. It is, however, well-known that Pareto-dominance-based algorithms do not always work well on many-objective problems with more than three objectives. Currently alternative frameworks are studied in the EMO community very actively. One promising framework is the use of an indicator function to find a good solution set of a multiobjective problem. EMO algorithms with this framework are called indicator-based evolutionary algorithms (IBEAs) where the hypervolume measure is frequently used as an indicator. IBEAs with the hypervolume measure have strong theoretical support and high search ability. One practical difficult of such an IBEA is that the hypervolume calculation needs long computation time especially when we have many objectives. In this paper, we propose an idea of using a scalarizing function-based hypervolume approximation method in IBEAs. We explain how the proposed idea can be implemented in IBEAs. We also demonstrate through computational experiments that the proposed idea can drastically decrease the computation time of IBEAs without severe performance deterioration.