Sequential and Parallel Branch-and-Bound Search under Limited-Memory Constraints

Abstract

Branch-and-bound (B&B) best-first search (BFS) is a widely applicable method that requires the least number of node expansions to obtain optimal solutions to combinatorial optimization problems (COPs). However, for many problems of interest, its memory requirements are enormous and can far exceed the available memory capacity on most systems. To circumvent this problem, a number of limited-memory search methods have been proposed that are either based purely on depth-first search (DFS) or combine BFS with DFS. We survey and compare previous sequential and parallel limited-memory search methods, and discuss their suitability for solving different types of COPs. We also propose a new limited-memory search method, iterative extrapolated-cost bounded search (IES*), that performs a sequence of cost-bounded depth-first searches from the root node of the search space. In this method, cost bounds for successive iterations are set to an estimated optimal-solution cost obtained by extrapolating from search experience in previous iterations. We provide accurate and fast, approximate methods suitable for extrapolating the optimal-solution cost for lower-bound cost functions with a range of growth rates Finally, we propose an efficient approach to parallelizing IES* that is applicable, with minor modifications, to other iterative cost-bounded DFS methods like IDA* and DFS*. An important feature of this approach is the asynchronous execution of the different iterations of IES* by processors to minimize idling. We provide a method for determining cost bounds independently in different processors; these cost bounds vary from processor to processor, and decrease from an initial larger value to the true cost bound for the iteration. Further, to minimize unnecessary node expansions that can occur because of the asynchronous operation and because of the initial loose upper bounds, we propose an efficient load balancing technique. This technique distributes work of earlier iterations with higher priority among processors. As a result, different processors are likely to execute IES* iterations that are as close to each other as possible, and also the individual cost bounds for the same IES* iteration in different processors approach the true cost bound rapidly. This decreases the possibility of unnecessary work in parallel IES*, thus leading to an efficient parallelization.

S. Dutt was supported by NSF grant MIP-9210049, and this research was done while N. Mahapatra was a Ph.D. student at the University of Minnesota.