Mixed-integer Algorithms for the (0,1) Knapsack Problem

An enumerative scheme is presented for the (0,1) knapsack problem as a specialization of the state enumeration method. Techniques are explored for rendering search procedures more efficient by systematic use of information generated during execution of the algorithm. The inequalities of Benders and Gomory-Johnson are exploited to yield implicit enumeration tests in the special case of the knapsack problem. In a comparative study of eight algorithms and of the utility of certain approximations and inequalities, computational results are given for twelve knapsack problems, each having ten (0,1) variables. The effectiveness of these enumerative algorithms are thus tested in a relatively simple framework.