Title: A parallel algorithm to solve the multiple travelling salesmen problem based on molecular computing model

Authors: Zhaocai Wang; Anjun Deng; Dangwei Wang; Tunhua Wu

Addresses: College of Information, Shanghai Ocean University, Shanghai 201306, China ' State Key Laboratory of Simulation and Regulation of River Basin Water Cycle, China Institute of Water Resources and Hydropower Research, Beijing 100044, China ' State Key Laboratory of Simulation and Regulation of River Basin Water Cycle, China Institute of Water Resources and Hydropower Research, Beijing 100044, China ' School of Information Engineering, Wenzhou Business College, Wenzhou 325035, China

Abstract: The multiple travelling salesmen problem (MTSP), which includes m salesmen starting and ending their tours at a same fixed node (m > 1), is an extension of travelling salesman problem (TSP) and has more applications and significance in the field of optimal control. As a classic NP-hard static combinatorial optimisation problem, its efficient solution has always been the direction of scholars' efforts. In this work, we propose biocomputing algorithms to solve the MTSP using Adleman-Lipton model. We make use of DNA chains to appropriately represent the nodes, edges and corresponding weights, and then efficiently generate all travelling salesmen tours combinations by biochemical reactions. Combining with the nature of the problem, we exclude the infeasible solution strands to get the optimal solutions, and reduce the algorithm computational complexity to O(n2) level. Meanwhile, the feasibility and practicability of DNA parallel algorithms are verified by theoretical proof and simulation experiments. The proposed algorithms are also helpful to better understand the nature of computing and can be further applied to the study of extended problems.

Keywords: DNA computing; multiple travelling salesmen problem; MTSP; Adleman-Lipton model; NP-hard problem; travelling salesman problem; TSP.

DOI: 10.1504/IJBIC.2022.127504

International Journal of Bio-Inspired Computation, 2022 Vol.20 No.3, pp.160 - 171

Received: 02 Apr 2020
Accepted: 03 May 2021

Published online: 07 Dec 2022 *

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