uma nova abordagem na resolução do problema do caixeiro viajante

ABSTRACT
In this work two Recurrent Neural Networks are presented to solve the Linear Assignment
problem. In the initial phase of the problem, where the Assignment problem’s costs’ must be
determined, uses Kohonen Maps, also known as Self-Organizing Maps, and in the
Assignment’s problem resolution properly said, the used technique is the Wang’s Recurrent
Neural Network, with the application of a called “Winner Takes All” principle, proposal in
this work. The phase of definition of the costs in the resolution of the Assignment problem is
of great importance, therefore if the costs will not be determined of adjusted form, the final
solution will not be the ideal. The calculation of costs for Assignment problems with the use
of Artificial Neural Networks is a subject little explored, that depends on the type of intended
application. When the Assignment problem’s cost’s matrix is such that admits multiple global
optimal solutions, or very next local optimal solutions, the Wang’s Neural Network does not
converge, and the proposal presented in this work shows the use of the principle “Winner
Takes All” fo r this network, getting global optimal solutions in the majority of the tested
matrices, using approximately 1% of the necessary number of iterations of the original
Wang’s Network. In this work the results of the application of this technique (Wang’s
Recurrent Neural Network with the principle “Winner Takes All”) are presented for 73
matrices with random costs to the Assignment problem, beyond some criteria for adjustments
of parameters of the Wang’s Neural Network, between them some traditional, and others that
use measured of dispersion enter the problem’s costs. The methodology proposal in this work
is applied in a case study: the Problem of Allocation of Classrooms for disciplines of
graduation and post-graduation of the UFPR, where maps with many dimensions for the
determination of the problem’s costs are tested. The results found with the application of this
methodology in the case study are considered satisfactory, with average error in the solution
of the Assignment problem less than 3% for the best-founded maps. Another application of
the Wang’s Neural Network with the principle “Winner Takes All” is the resolution of the
classic Traveling Salesman problem, with global optimal solutions in some problems of the
data base TSPLIB, and with local optimal solutions with errors less than 16%. To apply the
methodology proposal in this work for the Traveling Salesman problem an adaptation of
“Winner Takes All” principle is made, getting always feasible routes for this problem. The
same technique is used for symmetrical and asymmetrical Traveling Salesman problems, and
the technique 2-opt is used to improve the founded solutions.