Extremal Optimization Applied to the Minimum Order Frequency Assignment Problem

Abstract

Extremal Optimization (EO) is a metaheuristic used to solve complex combinatorial optimization problems. However, the behavior of this algorithm has not been studied for various interesting problems. Such as, it is the case of the Minimum Order Frequency Assignment Problem (MO-FAP). Specifically, this problem seeks to minimize the number of frequencies assigned to a group of transceiver, without violating any of the problems constraints. In particular, the aim of this study was to use EO to solve the MO-FAP. Furthermore, it was found that EO was able to find the best reported value for most instances of the dataset used for experimentation. Additionally, it was possible to identify how the EO Tau hyperparameter reported better results for much higher values than those reported in the literature. Finally, the difficulty of defining and configuring a fitness function for each element of the solution was evidenced. Therefore, this can affect the effectiveness of the algorithm according to the particular characteristics of the dataset to be solved. Consequently, this opens an opportunity to develop improvements in the form of defining the contribution of each element of the solution to the objective function.