A polynomial-time deterministic approach to the travelling salesperson problem. Issue 4 (3rd July 2020)

• Record Type: Journal Article
• Authors: Jazayeri, Ali; Sayama, Hiroki
• Is Part Of: International journal of parallel, emergent and distributed systems. Volume 35:Issue 4(2020)
• Page Start: 454
• Page End: 460
• Publication Date: 2020-07-03
• Subjects: Travelling salesperson problem -- polynomial-time algorithm -- deterministic algorithm -- approximation; Parallel computers -- Periodicals; Electronic data processing -- Distributed processing -- Periodicals; Computer algorithms -- Periodicals; 004.35
• DOI: 10.1080/17445760.2020.1776867
• Languages: English
• ISSNs: 1744-5760

Abstract

ABSTRACT: We propose a new polynomial-time deterministic algorithm that produces an approximated solution for the travelling salesperson problem. The proposed algorithm ranks cities based on their priorities calculated using a power function of means and standard deviations of their distances from other cities and then connects the cities to their neighbours in the order of their priorities. When connecting a city, a neighbour is selected based on their neighbours' priorities calculated as another power function that additionally includes their distance from the focal city to be connected. This repeats until all the cities are connected into a single loop. The time complexity of the proposed algorithm is O ( n 2 ), where n is the number of cities. Numerical evaluation shows that, despite its simplicity, the proposed algorithm produces shorter tours with less time complexity than other conventional tour construction heuristics. The proposed algorithm can be used by itself or as an initial tour generator for other more complex heuristic optimisation algorithms.