Large-Step Markov Chains for the Traveling Salesman Problem

We int rodu ce a new class of Markov chain Monte Carlo search pr ocedures tha t lead to mor e powerful optimization met hods than simulated annealing . The main idea is to embed det erminist ic local search techniques into stochas tic algorithms. The Mont e Carlo explores only local optima, and it is ab le to make large, global changes even at low temperatur es, t hus overcoming large barr iers in configuration space. We test these pr ocedures in the case of the Tr aveling Salesman Problem. The embedded local searches we use are 3-opt and Lin-Kernighan . T he large change or ste p consist s of a sp ecial kind of 4-change followed by local-opt minimization. We test this algorit hm on a number of instan ces. T he power of the method is illustra ted by solving to opt imality some large problems such as the LIN318, th e AT &T532, and the RAT783 problems. For even larger instances with randomly distributed cit ies, the Markov chain proce dure improves 3opt by over 1.6%, and Lin-Kernighan by 1.3%, leading to a new best