A Branch and Bound Algorithm for the Knapsack Problem

A branch and bound algorithm for solution of the “knapsack problem,” max ∑ v_ix_i where ∑ w_ix_i ≦ W and x_i = 0, 1, is presented which can obtain either optimal or approximate solutions. Some characteristics of the algorithm are discussed and computational experience is presented. Problems involving 50 items from which approximately 25 items were loaded were solved in an average of 0.07 minutes each by a coded version of this algorithm for the IBM 7094 computer.