Preference-Based Evolutionary Multiobjective Optimization Through the Use of Reservation and Aspiration Points

Abstract

Preference-based Evolutionary Multiobjective Optimization (EMO) algorithms approximate the region of interest (ROI) of the Pareto optimal front defined by the preferences of a decision maker (DM). Here, we propose a preference-based EMO algorithm, in which the preferences are given by means of aspiration and reservation points. The aspiration point is formed by objective values which the DM wants to achieve, while the reservation point is constituted by values for the objectives not to be worsened. Internally, the first generations are performed in order to generate an initial approximation set according to the reservation point. Next, in the remaining generations, the algorithm adapts the search for new non-dominated solutions depending on the dominance relation between the solutions obtained so far and both the reservation and aspiration points. This allows knowing if the given points are achievable or not; this type of information cannot be known before the solution process starts. On this basis, the algorithm proceeds according to three different scenarios with the aim of re-orienting the search directions towards the ROI formed by the Pareto optimal solutions with objective values within the given aspiration and reservation values. Computational results show the potential of our proposal in 2, 3 and 5-objective test problems, in comparison to other state- of-the-art algorithms.