a hybrid genetic-simulated annealing-auction algorithm for a fully fuzzy multi-period multi-depot vehicle routing problem

In this paper, an integer linear programming formulation is developed for a novel fuzzy multi-period multi-depot vehicle routing problem. the novelty belongs to both the model and the solution methodology. in the proposed model, vehicles are not forced to return to their starting depots. the fuzzy problem is transformed into a mixed-integer programming problem by applying credibility measure whose optimal solution is an (α,β)-credibility optimal solution to the fuzzy problem. to solve the problem, a hybrid genetic-simulated annealing-auction algorithm (hgsa), empowered by a modern simulated annealing cooling schedule function, is developed. finally, the efficiency of the algorithm is illustrated by employing a variety of test problems and benchmark examples. the obtained results showed that the algorithm provides satisfactory results in terms of different performance criteria.