Annals of Operations Research, 21 (1989) 59-84 59 SERIAL AND PARALLEL SIMULATED ANNEALING AND TABU SEARCH ALGORITHMS FOR THE TRAVELING SALESMAN PROBLEM Miroslaw MALEK, Mohan GURUSWAMY, Mihix PANDYA Department of Electrical and Computer Engineerin~ The University of Texas at Austin, Austin, Texas 78712, U.S.A. and Howard OWENS Microcomputer Division, Motorola lnc. Abstract This paper describes serial and parallel implementations of two different search techniques applied to the traveling salesman problem. A novel approach has been taken to parallelize simulated annealing and the results are compared with the traditional annealing algorithm. This approach uses abbreviated cooling schedule and achieves a superlinear speedup. Also a new search technique, called tabu search, has been adapted to execute in a parallel computing environment. Comparison between simulated annealing and tabu search indicate that tabu search consistently outperforms simulated annealing with respect to computation time while giving comparable solutions. F, xamples include 25, 33, 42, 50, 57, 75 and 100 city problems. 1. Introduction The Traveling Salesman Problem (TSP) is a classic problem in combinatorial optimization research. This is because it is easily defined, and improved al- gorithms to find optimized solutions to this problem can be adapted to an entire class of NP-complete problems. Our objective is to implement combinatorial optimization algorithms such that they may execute in parallel and exchange data periodically. The goal is to study the potential performance improvements as compared to a single processor implementation of the traveling salesman problem. In particular, we are interested in comparing the time efficiency and cost of simulated annealing [1] and tabu search [2] algorithms. Each of these algorithms have the ability to avoid or escape local minima in searching for the global optimal solution. However, the method of reaching the optimal solution is very different as will be described later. These tmiversal search algorithms are tested on a specific heuristic used for the TSP problem. The traveling salesman problem consists of finding the shortest Hamiltonian circuit in a complete graph where the nodes represent cities. The weights on the © J.C. Baltzer A.G. Scientific Publishing Company