Approximate Muscle Guided Beam Search for Three-Index Assignment Problem

TL;DR

This paper introduces Approximate Muscle guided Beam Search (AMBS), a heuristic for the NP-hard Three-Index Assignment Problem that balances solution quality and computational efficiency, especially for large instances.

Contribution

The paper proposes a novel heuristic combining approximate muscle with beam search, significantly reducing search space and time while maintaining competitive solution quality.

Findings

Achieves high-quality solutions efficiently on large-scale instances.

Reduces search time compared to existing heuristics.

Provides a new approach to improve beam search efficiency.

Abstract

As a well-known NP-hard problem, the Three-Index Assignment Problem (AP3) has attracted lots of research efforts for developing heuristics. However, existing heuristics either obtain less competitive solutions or consume too much time. In this paper, a new heuristic named Approximate Muscle guided Beam Search (AMBS) is developed to achieve a good trade-off between solution quality and running time. By combining the approximate muscle with beam search, the solution space size can be significantly decreased, thus the time for searching the solution can be sharply reduced. Extensive experimental results on the benchmark indicate that the new algorithm is able to obtain solutions with competitive quality and it can be employed on instances with largescale. Work of this paper not only proposes a new efficient heuristic, but also provides a promising method to improve the efficiency of beam search.