TY - JOUR

T1 - A polynomial-time deterministic approach to the travelling salesperson problem

AU - Jazayeri, Ali

AU - Sayama, Hiroki

PY - 2020/7/3

Y1 - 2020/7/3

N2 - 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.

AB - 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.

KW - Travelling salesperson problem

KW - approximation

KW - deterministic algorithm

KW - polynomial-time algorithm

UR - http://www.scopus.com/inward/record.url?scp=85087424084&partnerID=8YFLogxK

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U2 - 10.1080/17445760.2020.1776867

DO - 10.1080/17445760.2020.1776867

M3 - Article

AN - SCOPUS:85087424084

VL - 35

SP - 454

EP - 460

JO - Parallel Algorithms and Applications

JF - Parallel Algorithms and Applications

SN - 1744-5760

IS - 4

ER -