Comparative study between a neural network, approach metaheuristic and exact method for solving Traveling salesman Problem

optimization problems currently occupy an important place in the scientific community. Intuitively, an optimization problem can be seen as a search problem that consists in exploring a space containing the set of all feasible solutions, in order to find the optimal solution. The traveling salesman problem (TSP), considered as a classical example of combinatorial optimization problem, is considered as an NP-complete problem. In this work we will divide the solution of combinatorial optimization problems into three classes: continuous Hopfield network (CHN), ant colony optimization (ACO) and exact methods programmed in Cplex. The solution of a CHN optimization problem is based on a certain energy or Lyapunov function, which decreases as the system evolves until it reaches a local minimum value. Ant colony optimization to solve the traveling salesman problem (TSP) is inspired by the foraging behavior of ants. As a special case, and in order to test these methods, some computational experiments solving the TSP are also included.