Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front

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 vers...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematics Jg. 9; H. 4; S. 453
Hauptverfasser: Dupin, Nicolas, Nielsen, Frank, Talbi, El-Ghazali
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 23.02.2021
MDPI
Schlagworte:
[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]
[INFO]Computer Science [cs]
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Algorithms
bi-objective optimization
Clustering
Complexity
Computational Complexity
Computational Geometry
Computer Science
Discrete optimization
Dynamic programming
Food science
K-center
Linear programming
Mathematics
Multiple objective analysis
Objectives
Operational research
Operations Research
Optimization
Optimization and Control
P-center
Parallel programming
Pareto Front
Pareto optimization
Polynomials
QA1-939
Sum-diameter clustering
sum-radii clustering
Operational research
Clustering
Pareto Front
Complexity
Sum-diameter clustering
Computational geometry
Bi-objective optimization
Parallel programming
Algorithms
K-center
Discrete optimization
Sum-radii clustering
P-center
Dynamic programming
ISSN:2227-7390, 2227-7390
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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<N points, K-center and min-sum-K-radii variants are, respectively, solvable in O(K(M+1)NlogN) and O(K(M+1)N2) time. Such complexity of results allows an efficient straightforward implementation. Parallel implementations can also be designed for a practical speed-up. Their application inside multi-objective heuristics is discussed to archive partial Pareto fronts, with a special interest in partial clustering variants.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math9040453