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Article

A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification

by
Alejandro Castellanos-Alvarez
1,
Laura Cruz-Reyes
1,
Eduardo Fernandez
2,
Nelson Rangel-Valdez
3,
Claudia Gómez-Santillán
1,*,
Hector Fraire
1 and
José Alfredo Brambila-Hernández
1
1
Graduate Program Division, Tecnológico Nacional de México, Instituto Tecnológico de Ciudad Madero, Cd. Madero 89440, Mexico
2
Research and Postgraduate Directorate, Universidad Autonoma de Coahuila, Saltillo 26200, Mexico
3
CONACyT Research Fellow at Graduate Program Division, Tecnológico Nacional de México, Instituto Tecnológico de Ciudad Madero, Cd. Madero 89440, Mexico
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2021, 26(2), 27; https://doi.org/10.3390/mca26020027
Submission received: 3 March 2021 / Revised: 25 March 2021 / Accepted: 26 March 2021 / Published: 30 March 2021
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Abstract

Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to unsatisfactory solutions. The imperfect knowledge can be present either in objective functions, restrictions, or decision-maker’s preferences. These optimization problems have been solved using various techniques such as multi-objective evolutionary algorithms (MOEAs). This paper proposes a new MOEA called NSGA-III-P (non-nominated sorting genetic algorithm III with preferences). The main characteristic of NSGA-III-P is an ordinal multi-criteria classification method for preference integration to guide the algorithm to the region of interest given by the decision-maker’s preferences. Besides, the use of interval analysis allows the expression of preferences with imprecision. The experiments contrasted several versions of the proposed method with the original NSGA-III to analyze different selective pressure induced by the DM’s preferences. In these experiments, the algorithms solved three-objectives instances of the DTLZ problem. The obtained results showed a better approximation to the region of interest for a DM when its preferences are considered.
Keywords: incorporation of preferences; multi-criteria classification; decision-making process; multi-objective evolutionary optimization; outranking relationships incorporation of preferences; multi-criteria classification; decision-making process; multi-objective evolutionary optimization; outranking relationships

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MDPI and ACS Style

Castellanos-Alvarez, A.; Cruz-Reyes, L.; Fernandez, E.; Rangel-Valdez, N.; Gómez-Santillán, C.; Fraire, H.; Brambila-Hernández, J.A. A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification. Math. Comput. Appl. 2021, 26, 27. https://doi.org/10.3390/mca26020027

AMA Style

Castellanos-Alvarez A, Cruz-Reyes L, Fernandez E, Rangel-Valdez N, Gómez-Santillán C, Fraire H, Brambila-Hernández JA. A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification. Mathematical and Computational Applications. 2021; 26(2):27. https://doi.org/10.3390/mca26020027

Chicago/Turabian Style

Castellanos-Alvarez, Alejandro, Laura Cruz-Reyes, Eduardo Fernandez, Nelson Rangel-Valdez, Claudia Gómez-Santillán, Hector Fraire, and José Alfredo Brambila-Hernández. 2021. "A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification" Mathematical and Computational Applications 26, no. 2: 27. https://doi.org/10.3390/mca26020027

APA Style

Castellanos-Alvarez, A., Cruz-Reyes, L., Fernandez, E., Rangel-Valdez, N., Gómez-Santillán, C., Fraire, H., & Brambila-Hernández, J. A. (2021). A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification. Mathematical and Computational Applications, 26(2), 27. https://doi.org/10.3390/mca26020027

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