Multiobjective Distinct Candidates Optimization (MODCO): A Cluster-Forming Differential Evolution Algorithm

Abstract

Traditionally, Multiobjective Evolutionary Algorithms (MOEAs) aim at approximating the entire true pareto-front of their input problems. However, the actual number of solutions with different trade-offs between objectives in a resulting pareto-front is often too large to be applicable in practice. The new field Multiobjective Distinct Candidates Optimization (MODCO) research is concerned with the optimization of a low and user-defined number of clearly distinct candidates. This dramatically decreases the amount of post-processing needed in the decision making process of which solution to actually implement, as described in our related technical repport “Multiobjective Distinct Candidates Optimization (MODCO): A new Branch of Multiobjective Optimization Research” [9].

In this paper, we introduce the first algorithm designed for the challenges of MODCO; providing a given number of distinct solutions as close as possible to the true pareto-front. The algorithm is using subpopulations to enforce clusters of solutions, in such a way that the number of clusters formed can be set directly. The algorithm is based on the Differential Evolution for Multiobjective Optimization (DEMO) algorithm versions, but is exchanging the crowding/density measure with two alternating secondary fitness measures. Applying these measures ensures that subpopulations are attracted towards knee regions while also making them repel each other if they get too close to one another. This way subpopulations traverse different parts of the objective space while forming clusters each returning a single distinct solution.