A polynomial-time deterministic approach to the travelling salesperson problem

Ali Jazayeri, Hiroki Sayama

Research output: Contribution to journalArticle

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 (Formula presented.), 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.

Original languageEnglish
Pages (from-to)454-460
Number of pages7
JournalInternational Journal of Parallel, Emergent and Distributed Systems
Volume35
Issue number4
DOIs
Publication statusPublished - 2020 Jul 3
Externally publishedYes

Keywords

  • approximation
  • deterministic algorithm
  • polynomial-time algorithm
  • Travelling salesperson problem

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications

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