Approximate Muscle Guided Beam Search for Three-Index Assignment Problem
This work addresses the efficiency and solution quality challenges in heuristics for the Three-Index Assignment Problem, offering an incremental improvement for optimization researchers and practitioners.
The paper tackles the NP-hard Three-Index Assignment Problem by developing the Approximate Muscle guided Beam Search (AMBS) heuristic, which achieves a good trade-off between solution quality and running time, enabling competitive solutions on large-scale instances.
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.