Mathematical Programming Computational for Solving NP-Hardness Problem

Abstract 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...

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Bibliographic Details
Published in:Journal of physics. Conference series 2021-03, Vol.1818 (1), p.12137
Main Authors: Alridha, Ahmed, Al-Jilawi, Ahmed Sabah
Format: Article
Language:English
Subjects:
Clusters
Combinatorial analysis
Hardness
Mathematical programming
Numerical methods
Optimization
Physics
Polynomials
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Summary:Abstract 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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1818/1/012137