A Simple Proposal for Including Designer Preferences in Multi-Objective Optimization Problems

Xavier Blasco, Gilberto Reynoso-Meza, Enrique A. Sánchez-Pérez, Juan Vicente Sánchez-Pérez and Natalia Jonard-Pérez
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Xavier Blasco: Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Gilberto Reynoso-Meza: Programa de Pós-Graduação em Engenharia de Produção e Sistemas (PPGEPS), Pontificia Universidade Católica do Paraná (PUCPR), Curitiba 80215-901, Brazil
Enrique A. Sánchez-Pérez: Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Juan Vicente Sánchez-Pérez: Centro de Tecnologías Físicas: Acústica, Materiales y Astrofísica (CTF:AMA), Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Natalia Jonard-Pérez: Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico

Mathematics, 2021, vol. 9, issue 9, 1-19

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.

Keywords: multi-objective decision-making; Pareto front; multi-objective optimization; preference in multi-objective optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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