A Memetic Algorithm for the Multidimensional Assignment Problem

TL;DR

This paper introduces a memetic algorithm for the multidimensional assignment problem that dynamically adjusts its generation size, achieving high-quality solutions efficiently across various instance sizes.

Contribution

It presents a novel memetic algorithm with a dynamically adjusted generation size, enhancing flexibility and performance for MAP across different problem scales.

Findings

Outperforms existing 3-AP memetic algorithms

Produces high-quality solutions in reasonable time

Effective for small and large problem instances

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.