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Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front
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Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front
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Journal Article
Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front
2021
Overview
With many efficient solutions for a multi-objective optimization problem, this paper aims to cluster the Pareto Front in a given number of clusters K and to detect isolated points. K-center problems and variants are investigated with a unified formulation considering the discrete and continuous versions, partial K-center problems, and their min-sum-K-radii variants. In dimension three (or upper), this induces NP-hard complexities. In the planar case, common optimality property is proven: non-nested optimal solutions exist. This induces a common dynamic programming algorithm running in polynomial time. Specific improvements hold for some variants, such as K-center problems and min-sum K-radii on a line. When applied to N points and allowing to uncover M
Publisher
MDPI AG,MDPI
Subject
[INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC]
/ [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]
/ [INFO.INFO-RO] Computer Science [cs]/Operations Research [math.OC]
/ [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO]
/ [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
/ K-center
/ P-center
/ QA1-939
