A Parallel Multi-Phase Implementation of Simulated Annealing for the Traveling Salesman Problem

Abstract

This paper describes and unulyses a new parallel algorithm using simulated annealing forfinding a good solution to the Traveling Salesman Problem. This algorithm combines the strong points of three recent implementations [ I ,251 with some new features. An initial tour is generated and partitioned among a ring of processors. Each processor receives two disconnected parts (tiers) of the tour. The algorithm is subdivided into three phases. In phase one, 2-opting is performed separately within each of the two tiers of the tour. During the secondphase remoteswapping is performed between cities from the two diflerent tiers of the tour. During phase three, synchronization of the cities is accomplished by each processor shifting a quarter of its cities in a clock-wise direction to its neighboring node. This is called a quarter-spin. Results show this algorithm is superior over recent implementations. For the datasets tested, this algorithm yielded improvements ranging from 32% to 56% compared to three recent implementations. The signiBcance of this algorithm is the manner in which cities from different parts of the tour are combined to form new tours. The multiple phases within the algorithm allows for a better mixture of cities compared to previous algorithms.