Incorporation of Hypervolume Approximation with Scalarizing Functions into Indicator-Based Evolutionary Multiobjective Optimization Algorithms
Noritaka Tsukamoto, Yuji Sakane, Yusuke Nojima, Hisao Ishibuchi
The handling of many-objective problems is a hot issue in the evolutionary multiobjective optimization (EMO) community. Whereas Pareto-based EMO algorithms usually work very well on two-objective problems, they do not work well on many-objective problems. A promising approach to the search for the non-dominated solutions of many-objective problems is a class of indicator-based EMO algorithms. The goal of indicator-based EMO algorithms is to maximize an indicator function which evaluates the quality of a set of solutions. The hypervolume has been frequently used as an indicator function. The main difficulty of the use of hypervolume is that the computation load for its calculation increases exponentially with the number of objectives. Thus the application of indicator-based EMO algorithms to many-objective problems is time-consuming. In our former study, we proposed an idea of approximating the hypervolume using a number of achievement functions with uniformly distributed weight vectors. In this paper, we incorporate our hypervolume approximation into indicator-based EMO algorithms. Experimental results show that the computation time of indicator-based EMO algorithms for many-objective problems is drastically decreased by the use of our hypervolume approximation method with no severe deterioration in its search ability.