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.
Highlights
M ULTIOBJECTIVE optimization problems (MOPs) arising in many real-world applications contain several conflicting objectives fi : S → R, with i = 1, . . . , k (k ≥ 2), that need to be optimized simultaneously over a feasible set in the decision space, S ⊂ Rn, formed by decision vectors x = (x1, . . . , xn)T
We focus on the use of preferences in Evolutionary Multiobjective Optimization (EMO) to reduce the search space to the region of interest (ROI) that best suits the desires of the decision maker (DM)
If we denote by Ra and Rr the ROIs defined by the aspiration and the reservation points, respectively, the subset R with the most interesting Pareto optimal solutions for the DM can be obtained as R = Rr ∩ Ra
Summary
Achieving convergence and diversity simultaneously is not always easy, especially when handling many-objective optimization problems (k > 3), since e.g. the percentage of non-dominated solutions increases with the number of objectives, or in problems with complicated PFs (such as e.g. non-convex, degenerated, or discontinuous) To cope with these issues, decompositionbased EMO algorithms transform the original MOP into a set of single-objective optimization sub-problems formulated using an aggregation function with one weight vector, and usually select the best individuals at each generation according to these sub-problems. If we denote by Ra and Rr the ROIs defined by the aspiration and the reservation points, respectively, the subset R with the most interesting Pareto optimal solutions for the DM can be obtained as R = Rr ∩ Ra. Figure 1 shows different situations for a bi-objective minimization problem, where R is the region of the PF in bold.
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