A Memetic Algorithm for the Multidimensional Assignment Problem

Abstract: The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of applications. In this paper we propose a memetic algorithm for MAP that is a combination of a genetic algorithm with a local search procedure. The main contribution of the paper is an idea of dynamically adjusted generation size, that yields an outstanding flexibility of the algorithm to perform well for both small and large fixed running times. The results of computational experiments for several instance families show that the proposed algorithm produces solutions of very high quality in a reasonable time and outperforms the state-of-the art 3-AP memetic algorithm.