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.1302/04/15143154Angéniol, B., Vaubois, C., Le Texier, J.Y., Self-organizing feature maps and the travelling salesman problem (1998) Neural Networks, 1, pp. 289-293Caprara, A., Fischetti, M., Branch-and-cut algorithms (1997) Annotated Bibliographies in Combinatorial Optimization, pp. 45-64. , M. Dell'Amico, F. Maffioli AND S. Martello, eds, WileyChristofides, N., Eilon, S., An algorithm for the vehicle dispatching problem (1969) Operational Research Quartely, 20, pp. 309-318Dantzig, G.B., Ramser, R.H., The truck dispatching problem (1959) Management Science, 6, pp. 80-91De Castro, L.N., Timmis, J., (2002) Artificial Immune Systems: A New Computational Intelligence Approach, , Springer-VerlagDorigo, M., Di Caro, G., Ant algorithms for discrete optimization (1999) Artificial Life, 2 (5), pp. 137-172Fogel, D.B., (1995) Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, , IEEE PressGarey, M.R., Johnson, D., (1979) Computers and Intractability: A Guide to the Theory of NP-completeness, , FreemanGhaziri, H., Solving routing problems by a self-organizing map (1991) Artificial Neural Networks, pp. 829-834. , T. Kohonen, K. Makisara, O. Simula and J. Kangas, edsGlover, F., Laguna, M., (1997) Tabu Search, , Kluwer Academic PublishersGlover, F., Kochenberger, G.A., (2002) Handbook of Metaheuristics, , Kluwer Academic PublishersGomes, L.C.T., Von Zuben, F.J., A heuristic method based on unsupervised learning and fuzzy inference for the vehicle routing problem (2002) Proc. of VII Brazilian Symposium on Neural Networks, pp. 130-135Gong, D., Gen, M., Yamazaki, G., Xu, W., Neural network approach for general assignment problem (1995) Proc. of International Conference on Neural Networks, 4, pp. 1861-1866Kennedy, J., Eberhart, R.C., Shi, Y., (2001) Swarm Intelligence, , Morgan Kaufmann PublishersKirkpatrick, S., Gelatt, C.D., Vecchi, M.P., Optimization by simulated annealing (1983) Science, 4598 (220), pp. 671-680Kohonen, T., (1997) Self-organizing Maps, (2nd Ed.), , Springer VerlagMatsuyama, Y., Harmonic competition: A self-organizing multiple criteria optimization (1996) IEEE Transactions on Neural Networks, 7 (3), pp. 652-668Modares, A., Somhom, S., Enkawa, T., A self-organizing neural network approach for multiple traveling salesman and vehicle routing problems (1999) Int. Transactions in Operational Research, 6, pp. 591-606Nemhauser, G.L., Wolsey, L.A., (1988) Integer and Combinatorial Optimization, , John Wiley and SonsSmith, K.A., Neural networks for combinatorial optimization: A review of more than a decade of research (1999) INFORMS Journal on Computing, 11 (1), pp. 15-34Toth, P., Vigo, D., (2002) The Vehicle Routing Problem, , Society for Industrial and Applied Mathematics (SIAM)Vakhutinsky, A.I., Golden, B.L., Solving vehicle routing problems using elastic nets (1994) Proc. of IEEE Int. Conf. on Neural Networks, 7, pp. 4535-4540Zadeh, L.A., Fuzzy sets (1965) Inform. Control, 8, pp. 338-35