Plane Separation: A method to solve dynamic multi-objective optimization problems with incorporated preferences

Abstract

Dynamic optimization multi-objective problems (DMOPs) are characterized by the environmental changes they experiment . For these problems, optimization algorithms have limited time to find accurate results before every change. A common scenario in optimization is the presence of a decision maker (DM), which establishes preferences on the problem being solved. Nowadays, there are few works focused on applying preference incorporation techniques in DMOPs. This work proposes the Plane Separation (PS) method, a novel technique that allows incorporating preferences in the optimization process by splitting the population into multiple planes based on the proximity of solutions to the region of interest (ROI). PS uses those planes to focus the search towards the ROI while maintaining diversity in the solutions set to avoid stagnation in local optima. PS is incorporated into two versions of DNSGA-II, and in a novel dynamic version of GDE3 we propose. These algorithms are also used as low-level heuristics of a hyper-heuristic. All PS-incorporated algorithms were compared against DRNSGA-II, a dynamic version proposal of a single-reference-point technique for solving MOPs under different preferential setups. The results favor the performance of the proposed PS-based algorithms, confirming its feasibility and effectiveness as a technique for incorporating preferences within a dynamic environment.