Multiple criteria optimization based on unsupervised learning and fuzzy inference applied to the vehicle routing problem

This paper presents a neuro-fuzzy system based on competitive learning to solve multiple criteria optimization problems. The proposed method promotes the simultaneous self-organization of several networks, employing unsupervised learning guided by a fuzzy rule base. The algorithm implements a policy of penalties and rewards, a strategy of neuron inhibition, insertion and pruning, and also takes into account certain statistical characteristics of the input space. A fuzzy inference system is designed to implement the decision making process under a multiobjective scenario, leading to an adaptive process of constraint relaxation. The effectiveness of the proposed method is attested by means of a series of computational simulations performed on standard data. In our simulations, we address two variants of the vehicle routing problem: the capacitated vehicle routing problem (CVRP) and the multiple traveling salesman problem (MTSP). There are a few works treating the vehicle routing problem by means of competitive learning. These approaches are briefly reviewed in this paper. We also present some improvements in the results of an implementation of tabu search by providing the solutions obtained by the neuro-fuzzy system as initial condition, showing that the proposed method can effectively produce satisfactory results when used in association with more dedicated approaches.

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