Mathematical Programming Computational for Solving NP-Hardness Problem

In this paper we will introduce a new approach for solving K-cluster problem which is one of the NP-hardness problem, in combinatorial optimization problems. In addition, P is NP-hardness if and only if the polynomial time of each NP problem is reduced to P. Actually, our study was focused on the tw...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 1818; no. 1; p. 12137
Main Authors Alridha, Ahmed, Al-Jilawi, Ahmed Sabah
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.03.2021
Subjects
Clusters
Combinatorial analysis
Hardness
Mathematical programming
Numerical methods
Optimization
Physics
Polynomials
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ISSN1742-6588
1742-6596
DOI10.1088/1742-6596/1818/1/012137

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Summary:In this paper we will introduce a new approach for solving K-cluster problem which is one of the NP-hardness problem, in combinatorial optimization problems. In addition, P is NP-hardness if and only if the polynomial time of each NP problem is reduced to P. Actually, our study was focused on the two methods which is Penalty and Augmented Lagrangian methods base on the numerical result. Moreover, we tested the K-cluster problem and found the Augmented Lagrangian Method faster than Penalty method. Finally, our research is not just focus on the numerical computational but also improving the theoretical converges properties.
Bibliography:ObjectType-Conference Proceeding-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1818/1/012137