Preference Incorporation into Moea/D Using an Outranking Approach with Imprecise Model Parameters

Abstract

Multi-objective Optimization Evolutionary Algorithms (MOEAs) face numerous challenges when solving Many-objective Optimization problems (MaOPs); for example, they might suffer from an underdeveloped population derived from a weakened selective pressure towards the Pareto front due to an increment in the number of dominant resistance solutions. Decomposition-based strategies, such as MOEA/D, divide the MaOP into multiple single-optimization subproblems, achieving better diversity and approximation of the Pareto Frontier, and dealing with some of the MaOPs challenges. However, these approaches still require solving a multi-criteria selection problem that will allow a Decision-Maker (DM) to choose the final solution. Incorporating preferences may bring closer results to the Region of Interest of a DM. However, most of the proposals to integrate preferences in decomposition-based MOEAs prefer the progressive articulation over “a priori” incorporation of preferences. Progressive articulation methods can hardly work without comparable and transitive preferences, and can significantly increment the required cognitive effort of a DM. On the other hand, the “a priori” strategies might be simpler for a DM and can handle non-transitivity, but they require a direct parameter elicitation that usually is subject to imprecision. This paper explores how to incorporate DM preferences into MOEA/D using “a priori” incorporation of preferences based on interval outranking relations to handle imprecision. An experimental design analyzes the proposal’s performance in benchmark problems and compares the results against the classic MOEA/D without preference incorporation. The results demonstrate improvement, increasing with the number of objectives, in the quality of the solutions related to DMs.

Keywords: MOEA/D, Many-objective optimization, DTLZ benchmark problems, Interval numbers, outranking relations

JEL Classification: D70, D81