In EDS ansehen

Approximation Algorithm for Travelling Salesman Problem

Gespeichert in:
Bibliographische Detailangaben
Titel: Approximation Algorithm for Travelling Salesman Problem
Autoren: Oladele, R. O, Mobolaji, D. M.
Quelle: University of Ibadan Journal of Science and Logics in ICT Research; Vol. 14 No. 1 (2025): Journal of Science and Logics in ICT Research
Verlagsinformationen: University of Ibadan Journal of Science and Logics in ICT Research
Publikationsjahr: 2025
Bestand: University of Ibadan Journal System
Schlagwörter: Hamiltonian ath, Linear Programming, Relaxation, Semi-Definite Programming
Beschreibung: Designing approximation algorithms often involves, among other things, relaxing the integrality constraint and obtaining a convex relaxation of the problem. The most well-known relaxation schemes are the Linear Programming (LP) relaxation and Semi-Definite Programing (SDP) relaxation. While LP relaxation has been widely used for solving TSP, SDP has been rarely employed. The primary goal of this paper therefore is to employ SDP and develop approximation algorithm for metric TSP. The SDP relaxation of the TSP is first obtained, and the approximation algorithm is thereafter developed. When compared to optimal results of some standard TSP instances, implementation result showed a relatively fair performance.
Publikationsart: article in journal/newspaper
Dateibeschreibung: application/pdf
Sprache: English
Relation: https://journals.ui.edu.ng/index.php/uijslictr/article/view/2022/1584; https://journals.ui.edu.ng/index.php/uijslictr/article/view/2022
Verfügbarkeit: https://journals.ui.edu.ng/index.php/uijslictr/article/view/2022
Rights: Copyright (c) 2025 University of Ibadan Journal of Science and Logics in ICT Research
Dokumentencode: edsbas.5F62B7D0
Datenbank: BASE
Beschreibung
Abstract:Designing approximation algorithms often involves, among other things, relaxing the integrality constraint and obtaining a convex relaxation of the problem. The most well-known relaxation schemes are the Linear Programming (LP) relaxation and Semi-Definite Programing (SDP) relaxation. While LP relaxation has been widely used for solving TSP, SDP has been rarely employed. The primary goal of this paper therefore is to employ SDP and develop approximation algorithm for metric TSP. The SDP relaxation of the TSP is first obtained, and the approximation algorithm is thereafter developed. When compared to optimal results of some standard TSP instances, implementation result showed a relatively fair performance.