A variable depth search algorithm with branching search for the generalized assignment problem

In this paper, we propose a variable depth search (VDS) algorithm for the generalized assignment problem (GAP), which is one of the representative combinatorial optimization problems, and is known to be NP-hard. The VDS is a generalization of the local search. The main idea of VDS is to change the size of the neighborhood adaptively so that the algorithm can effectively traverse larger search space within reasonable computational time. In our previous paper, we proposed a simple VDS algorithm for the GAP, and obtained good results. To further improve the performance of the VDS, we examine the effectiveness of incorporating branching search processes to construct the neighborhoods. Various types of branching rules are examined, and it is observed that appropriate choices of branching strategies improve the performance of VDS. Comparisons with other existing heuristics are also conducted using benchmark instances. The proposed algorithm is found to be quite effective.