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

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.