A hybrid heuristic approach for the multi‐commodity one‐to‐one pickup‐and‐delivery traveling salesman problem

This paper addresses an extension of the Traveling Salesman Problem where a vehicle with a limited capacity must transport commodities. Each commodity has a weight, and exactly one origin and one destination. The objective is to find a minimum length Hamiltonian tour satisfying all the transportation requests without ever violating the capacity constraint. We propose for this problem a hybrid heuristic approach that combines the GRASP and VND metaheuristic techniques. Two variants of the method are presented, one of them using a mathematical programming based local search. We conduct computational experiments to compare the developed algorithms. The experiments show that they improve the best known solutions for a set of instances from the literature, and are able to cope with instances with up to 300 customers and 600 commodities in a reasonable amount of computation time.