An Enhanced Nested Partitions Method

Combinatorial optimization problems arise in many applications such as task assignment, facility location, and elevator scheduling. One powerful method to address those difficult problems is the nested partitions method (NP). This method, however, cannot use historical information because it is required that the sampling of different iterations should be independent in order to guarantee global convergence. In this paper, the convergence property of the NIP method is enhanced by relaxing the independent sampling requirement with a much milder one so that historical information can be utilized without impairing algorithm convergence. Novel insights about how to effectively utilize historical information are obtained by representing the NIP method in the viewpoint of the estimation of distribution algorithms (EDAs). The convergence result of the enhanced NP method is further extended to derive global convergence for a large class of population-based methods, population distribution-based methods.