Bilinear Assignment Problem: Large Neighborhoods and Experimental Analysis of Algorithms

TL;DR

This paper introduces new neighborhood structures and heuristic algorithms for the bilinear assignment problem, providing the first comprehensive experimental analysis and benchmark instances to evaluate algorithm performance.

Contribution

It presents novel neighborhood structures, heuristic algorithms, and benchmark instances, along with a thorough experimental analysis of their effectiveness on BAP.

Findings

Algorithms are effective in solving BAP

Fast construction heuristics perform well

BAP exhibits properties different from similar models

Abstract

The bilinear assignment problem (BAP) is a generalization of the well-known quadratic assignment problem (QAP). In this paper, we study the problem from the computational analysis point of view. Several classes of neigborhood structures are introduced for the problem along with some theoretical analysis. These neighborhoods are then explored within a local search and a variable neighborhood search frameworks with multistart to generate robust heuristic algorithms. Results of systematic experimental analysis have been presented which divulge the effectiveness of our algorithms. In addition, we present several very fast construction heuristics. Our experimental results disclosed some interesting properties of the BAP model, different from those of comparable models. This is the first thorough experimental analysis of algorithms on BAP. We have also introduced benchmark test instances that can be used for future experiments on exact and heuristic algorithms for the problem.