A hybrid genetic–GRASP algorithm using Langrangean relaxation for the traveling salesman problem

Hybridization techniques are very effective for the solution of combinatorial optimization problems. This paper presents a genetic algorithm based on Expanding Neighborhood Search technique for the solution of the traveling salesman problem: The initial population of the algorithm is created not entirely at random but rather using a modified version of the Greedy Randomized Adaptive Search Procedure. Furthermore, a stopping criterion based on Lagrangean Relaxation is proposed. The combination of these difference techniques produces high quality solutions. The proposed algorithm was tested on numerous benchmark problems from TSPLIB with very satisfactory results. Comparisons with the algorithms of the DIMACS Implementation Challenge are also presented.