Optimization of Scalarizing Functions Through Evolutionary Multiobjective Optimization

This paper proposes an idea of using evolutionary multiobjective optimization (EMO) to optimize scalarizing functions. We assume that a scalarizing function to be optimized has already been generated from an original multiobjective problem. Our task is to optimize the given scalarizing function. In order to efficiently search for its optimal solution without getting stuck in local optima, we generate a new multiobjective problem to which an EMO algorithm is applied. The point is to specify multiple objectives, which are similar to but different from the scalarizing function, so that the location of the optimal solution is near the center of the Pareto front of the generated multiobjective problem. The use of EMO algorithms helps escape from local optima. It also helps find a number of alternative solutions around the optimal solution. Difficulties of Pareto ranking-based EMO algorithms in the handling of many objectives are avoided by the use of similar objectives. In this paper, we first demonstrate that the performance of EMO algorithms as single-objective optimizers of scalarizing functions highly depends on the choice of multiple objectives. Based on this observation, we propose a specification method of multiple objectives for the optimization of a weighted sum fitness function. Experimental results show that our approach works very well in the search for not only a single optimal solution but also a number of good alternative solutions around the optimal solution. Next we evaluate the performance of our approach in comparison with a hybrid EMO algorithm where a single-objective fitness evaluation scheme is probabilistically used in an EMO algorithm. Then we show that our approach can be also used to optimize other scalarizing functions (e.g., those based on constraint conditions and reference solutions). Finally we show that our approach is applicable not only to scalarizing functions but also other single-objective optimization problems.