A New Local Search Heuristic for the Multidimensional Assignment Problem

The Multidimensional Assignment Problem (MAP) is a natural extension of the well-known assignment problem. The most studied case of the MAP is the 3-dimensional Assignment Problem (3AP), though in recent years some local search heuristics and a memetic algorithm were proposed for the general case. Until now, a memetic algorithm has been proven to be the best-known option to solve MAP instances and it uses some procedures called dimensionwise variation heuristics as part of the improvement of individuals. We propose a new local search heuristic, based on ideas from dimensionwise variation heuristics, which consider a bigger space of neighborhoods, providing higher quality solutions for the MAP. Our main contribution is a generalization of several local search heuristics known from the literature, the conceptualization of a new one, and the application of exact techniques to find local optimum solutions at its neighborhoods. The results of computational evaluation show how our heuristic outperforms the previous local search heuristics and its competitiveness against a state-of-the-art memetic algorithm.