  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.
