Finding top-K solutions for the decision-maker in multiobjective optimization

Multiobjective optimization problems (MOPs) are the optimization problem with multiple conflicting objectives. Generally, an optimization algorithm can find a large number of optimal solutions for MOPs, which easily overwhelm decision makers (DMs) and make it difficult for decision-making. Preference-based evolutionary multiobjective optimization (EMO) aims to find the partial optima in the regions preferred by the DM. Although it narrows the scope of the optimal solutions, it usually still returns a population of optimal solutions (typically 100 or larger in EMO) with a small distance between adjacent optima. Top-K, which is a well-established research subject in many fields to find the best K solutions, may be a direction to reduce the number of optimal solutions. In this paper, first, we introduce the top-K notion into preference-based EMO and propose the top-K model to obtain the best K individuals of multiobjective optimization problems (MOPs). Then, with the top-K model, we propose NSGA-II-TopK and SPEA2-TopK to search for the top-K preferred solutions for preference-based continuous and combinatorial MOPs, respectively. Finally, the proposed algorithms with several representative preference-based EMO algorithms are compared in different preference situations for MOPs. Experimental results show the proposed algorithms have strong performances against the compared algorithms.