An Improved Simulated Annealing Algorithm for Traveling Salesman Problem

Abstract

AbstractTraveling salesman problem (TSP) is one of the well-known NP-Complete problems. The simulated annealing algorithm is improved with the four vertices and three lines inequality to search the optimal Hamiltonian circuit or near optimal Hamiltonian circuit. The four vertices and three lines inequality is considered as the heuristic information to change the local Hamiltonian paths into the local optimal Hamiltonian paths. The local optimal Hamiltonian circuits are generated with the basic simulated algorithm firstly, and the local Hamiltonian paths in them are changed into the local optimal Hamiltonian paths with the four vertices and three lines inequality, and then the shorter local optimal Hamiltonian circuits are obtained. The algorithm of the improved simulated annealing is designed and tested with several TSP instances. The experimental results show that the shorter local optimal Hamiltonian circuits are found than those searched with the basic simulated annealing algorithm under the same preconditions.KeywordsTraveling salesman problemSimulated annealingFour vertices and three lines inequalityAlgorithm