Using a Family of Curves to Approximate the Pareto Front of a Multi-Objective Optimization Problem

The design of selection mechanisms based on quality assessment indicators has become one of the main research topics in the development of Multi-Objective Evolutionary Algorithms (MOEAs). Currently, most indicator-based MOEAs have employed the hypervolume indicator as their selection mechanism in the search process. However, hypervolume-based MOEAs become inefficient (and eventually, unaffordable) as the number of objectives increases. In this paper, we study the construction of a reference set from a family of curves. Such reference set is used together with a performance indicator (namely Delta(p)) to assess the quality of solutions in the evolutionary process of an MOEA. We show that our proposed approach is able to deal (in an efficient way) with problems having many objectives (up to ten objective functions). Our preliminary results indicate that our proposed approach is highly competitive with respect to two state-of-the-art MOEAs over the set of test problems that were adopted in our comparative study.