Iterative approach to indicator-based multiobjective optimization

An emerging trend in the design of evolutionary multiobjective optimization algorithms is to directly optimize a quality indicator of non-dominated solution sets such as the hypervolume measure. Some algorithms have been proposed to search for a set of a pre-specified number of non-dominated solutions that maximizes the given quality indicator. In this paper, we propose an iterative approach to indicator-based evolutionary multiobjective optimization. The main feature of our approach is that only a single solution is obtained by its single run. Thus multiple runs are needed to find a solution set. In each run, our approach searches for a solution with the maximum contribution to the hypervolume of the solution set obtained by its previous runs. We discuss several issues related to the implementation of such an iterative approach.