A parallel algorithm for the 0?1 knapsack problem

Abstract

Research efforts on parallel exact algorithms for the 0–1 knapsack problem have up to now concentrated on solving small problems (at most 1,000 objects) and in many cases results have only been obtained by simulation of the parallel algorithm. After a brief review of a well known sequential branch-and-bound algorithm we discuss a new parallel algorithm for the 0–1 knapsack problem which exploits the potential parallelism that exists during the backtracking steps of the branch-and-bound algorithm. We report results for our parallel algorithm on a transputer network for problems with up to 20,000 objects. The speedup obtained is nearly linear for 2, 4, and 8 processors except when there is a strong correlation between the profit and weight of the objects.