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<p>This paper presents a methodology for optimizing multiobjective non-convex problems using a preference-guided approach through the establishment of a hyperellipsoid-shaped Region of Interest (<i>ROI</i>). By incorporating this layer into an optimization algorithm, the primary goal is to support the Decision Maker (<i>DM</i>) in filtering the optimal solutions within a specific region of the Pareto Front. This approach establishes a hyperellipsoid through its general equation, employing geometric transformations to rotate and translate the solutions, thereby adapting them to the shape of the hyperellipsoid. The evaluation of the results relied on metrics such as Generational Distance (GD), Inverted Generational Distance (IGD), the modified Inverted Generational Distance (IGD+), Hypervolume (HV), and the minimum distance from the reference point <i>p</i> to the identified solutions. The proposed approach exhibited satisfactory performance in comparison to the original algorithms.</p>

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Definition of Region of Interest in multiobjective problems using hyperellipsoids

  • 期刊论文

  • 发表日期：

    2025年12月27日

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  • Patrick Ferreira,
  • Luciana Cosme,
  • Allysson Lacerda

摘要

This paper presents a methodology for optimizing multiobjective non-convex problems using a preference-guided approach through the establishment of a hyperellipsoid-shaped Region of Interest (ROI). By incorporating this layer into an optimization algorithm, the primary goal is to support the Decision Maker (DM) in filtering the optimal solutions within a specific region of the Pareto Front. This approach establishes a hyperellipsoid through its general equation, employing geometric transformations to rotate and translate the solutions, thereby adapting them to the shape of the hyperellipsoid. The evaluation of the results relied on metrics such as Generational Distance (GD), Inverted Generational Distance (IGD), the modified Inverted Generational Distance (IGD+), Hypervolume (HV), and the minimum distance from the reference point p to the identified solutions. The proposed approach exhibited satisfactory performance in comparison to the original algorithms.