Combining Simulated Annealing with Local Search Heuristics

TLDR: A meta-heuristic to embed deterministic local search techniques into simulated annealing so that the chain explores only local optima makes large, global changes, even at low temperatures, thus overcoming large barriers in configuration space.

Abstract: We introduce a meta-heuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to significantly more powerful optimization methods that wither simulated annealing or local search. The main idea is to embed deterministic local search techniques into simulated annealing so that the chain explores only local optima. It makes large, global changes, even at low temperatures, thus overcoming large barriers in configuration space. We have tested this meta-heuristic for the traveling salesman and graph partitioning problems. Tests on instances from public libraries and random ensembles quantify the power of the method. Our algorithm is able to solve large instances to optimality, improving upon state of the art local search methods very significantly. For the traveling sales man problem with randomly distributed cities in a square, the procedure improves on 3-opt by 1.6% an d on Lin-Kernighan local search by 1.3%. For the partitioning of sparse random graphs of average degree equal to 5, the improvement over Kernighan-Lin local searches 8.9%. For both CO problems, we obtain new champion heuristics.