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The Improvement Direction Mapping Method

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Advances in Soft Computing (MICAI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12468))

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Abstract

The Improvement Direction Mapping (IDM) is a novel multi-objective local-search method, that independently steers a solution set towards promising regions by computing improvement directions in the objective space and transform them, into the variable space, as search directions. The IDM algorithm consists of two main sub-tasks 1) the computation of the improvement directions in the objective space 2) the transformation of directions from the objective space to the variable space. The transformation from the objective to the variable space is carried out via a pseudo-inverse of the Jacobian matrix. The goal of this paper is two fold: it introduces the main IDM algorithm and three approaches to determine improvement directions, and then it explores the trade-off of either approach by performing statistical analysis on the experimental results. The approaches are based on: 1) Pareto dominance, 2) aggregation functions, and 3) indicator functions. A set of well-known benchmark problems are used to compare the three proposed improvement directions and the Directed Search method. This paper is devoted to introduce the IDM algorithm for multi-objective optimization, nonetheless, the application of IDM for hybridizing stochastic-global-search algorithms is straight forward.

S. I. Valdez is supported by the Consejo Nacional de Ciencia y Tecnología, CONACYT México, Cátedra 7795.

A. Hernández-Aguirre—We acknowledge support from Proyecto FORDECyT No. 296737 “Consorcio en Inteligencia Artificial”.

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Authors and Affiliations

  1. Centro de Investigación en Matemáticas, A.C., Jalisco S/N, Col. Valenciana CP: 36023, Guanajuato, Gto, Mexico

    Salvador Botello-Aceves & Arturo Hernández-Aguirre

  2. Centro de Investigación en Ciencias de Información Geoespacial, Contoy 137 Esq. Chemax, Col. Lomas de Padierna, Querétaro, Qro, Mexico

    S. Ivvan Valdez

Authors
  1. Salvador Botello-Aceves
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  2. S. Ivvan Valdez
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  3. Arturo Hernández-Aguirre
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Corresponding author

Correspondence to Salvador Botello-Aceves .

Editor information

Editors and Affiliations

  1. Facultad de Ingeniería, Universidad Panamericana, Mexico City, Mexico

    Lourdes Martínez-Villaseñor

  2. Universidad Autónoma Metropolitana, Mexico City, Mexico

    Oscar Herrera-Alcántara

  3. Facultad de Ingeniería, Universidad Panamericana, Mexico City, Mexico

    Hiram Ponce

  4. Universidad Autónoma del Estado de Hidalgo, Hidalgo, Mexico

    Félix A. Castro-Espinoza

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Botello-Aceves, S., Valdez, S.I., Hernández-Aguirre, A. (2020). The Improvement Direction Mapping Method. In: Martínez-Villaseñor, L., Herrera-Alcántara, O., Ponce, H., Castro-Espinoza, F.A. (eds) Advances in Soft Computing. MICAI 2020. Lecture Notes in Computer Science(), vol 12468. Springer, Cham. https://doi.org/10.1007/978-3-030-60884-2_20

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  • DOI: https://doi.org/10.1007/978-3-030-60884-2_20

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