Abstract
Including designer preferences in every phase of the resolution of a multi-objective optimization problem is a fundamental issue to achieve a good quality in the final solution. To consider preferences, the proposal of this paper is based on the definition of what we call a preference basis that shows the preferred optimization directions in the objective space. Associated to this preference basis a new basis in the objective space—dominance basis—is computed. With this new basis the meaning of dominance is reinterpreted to include the designer’s preferences. In this paper, we show the effect of changing the geometric properties of the underlying structure of the Euclidean objective space by including preferences. This way of incorporating preferences is very simple and can be used in two ways: by redefining the optimization problem and/or in the decision-making phase. The approach can be used with any multi-objective optimization algorithm. An advantage of including preferences in the optimization process is that the solutions obtained are focused on the region of interest to the designer and the number of solutions is reduced, which facilitates the interpretation and analysis of the results. The article shows an example of the use of the preference basis and its associated dominance basis in the reformulation of the optimization problem, as well as in the decision-making phase.
Highlights
In a design problem posed as a multi-objective optimization, there is not a single solution
The designer—decision maker (DM in what follows)—must get, from the set of optimal solutions—Pareto set, a suitable solution adjusted to a given set of preferences
Using preference handling mechanisms in the optimization process has shown to be a valuable tool when facing multi-objective optimization problems [5]. These mechanisms facilitate the decision-making process at the selection step, because the DM will focus its attention to the pertinent region of the Pareto front [6]. This implies that it is necessary to have tools that allow to take into account the preferences in any of the phases of resolution of a design problem that is intended to be solved through multi-objective optimization
Summary
Xavier Blasco 1, * , Gilberto Reynoso-Meza 2 , Enrique A. Sánchez-Pérez 3 , Juan Vicente Sánchez-Pérez 4 and Natalia Jonard-Pérez 5. Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain. Programa de Pós-Graduação em Engenharia de Produção e Sistemas (PPGEPS), Pontificia Universidade
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