Local Search Heuristics For The Multidimensional Assignment Problem

TL;DR

This paper explores local search heuristics for the Multidimensional Assignment Problem, generalizing neighborhoods, proposing new ones, and demonstrating that combining neighborhoods can produce superior heuristics through theoretical and experimental evaluation.

Contribution

It introduces generalized and new neighborhood structures for MAP and shows that combining neighborhoods can improve heuristic performance.

Findings

Certain neighborhood combinations outperform individual heuristics

Theoretical analysis supports the effectiveness of proposed neighborhoods

Experimental results validate the superiority of combined heuristics

Abstract

The Multidimensional Assignment Problem (MAP) (abbreviated 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 also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate a combination of two neighborhoods may yield a heuristics which is superior to both of its components.