From the Magic Square to the Optimization of Networks of AGVs and from MIP to an Improved Hybrid Tabu-Genetic Optimization Algorithm

Abstract:- In a previous work we presented an algorithm inspired in the Strong Artificial Intelligence and in the minimax optimization that imitates the human being in the solution of the magic square and we showed that in most cases its performance was better than the human’s performance and even better than the performance of the best genetic algorithms to solve the magic square, in terms of number of changes. In this paper we adapt and transform this algorithm to solve the optimization of an AGVs network problem, using as a first test case 9 workstations in fixed positions and 9 operations to be executed, and the optimization problem is translated in the search of which of the 9! possible manners to distribute 9 operations by the 9 workstations that minimizes the total production time for a given plan of production. As a final validation test, using random search, in 1000 runs it never reached the optimal solution at the end of 100000 iterations. Finally we considered the more general case where the number of workstations is greater than the number of operations, and so there are some workstations that make the same operation, and we will have a layout with repetitions and multiple trajectories that implement the same product. This turns the problem more complex since when a product has operations that are executed by various workstations we must search all the possible combinations and find the average distance over all possible trajectories associated to a product. Furthermore th