Outperforming Several Heuristics for the Multidimensional Assignment Problem

The multidimensional assignment problem (MAP), also known as multi-index assignment problem, is a natural extension of the assignment problem. A MAP deals with the question of how to assign elements from s disjoint sets with n
₁
,...,n
_s
items on each. A MAP with s dimensions is called a sAP. Local search heuristics and Memetic algorithms have been proven to be the most effective techniques to solve MAP. In this work we use an exact technique that outperforms some local searches and Memetic algorithms on several instances of MAP. Then, we design a heuristic that uses repeatedly our exact technique in order to provide high quality solutions for harder types of instances of MAP. We perform an experimental evaluation of our exact technique and of our heuristic and we show its effectiveness against more complex local searches and some Memetic algorithms for MAP.