A Method for Solving the Monge–Kantorovich Problem Using an Automaton and Wavelet Analysis

This article introduces an automaton designed to improve feasible solutions to the Monge–Kantorovich (MK) problem, particularly effective when the cost function is continuous. To enhance its performance, a good initial solution is obtained using the discrete wavelet transform. Specifically, a transportation problem is solved where the cost matrix is composed of the approximation coefficients of the transform, reducing the number of variables to one quarter of the original discrete problem. The solution to this reduced problem is extended using the detail coefficients, yielding a feasible solution to the original problem. This solution serves as the initial state of the tuning automaton, whose final states provide approximations to the optimal solution of the transportation problem.