Application of AI search technique to binary integer programming problem

Abstract

In integer programming the fact that branch-and-bound method which is the one of the most general method has the restriction on the capacity of memory is its limitation. To overcome this limitation we apply the Artifitial Intelligence (AI) search technique to integer programming problem. By applying A$^\star$ algorithm which is the one of AI search techniques to branch-and-bound method, we try to combine OR and AI. Containing heuristic value which is a nonnegative estimate of the optimal value of the subproblem makes the solution procedure efficient. That is, h-value plays a role in finding an optimal solution and preventing needless branching. Especially when heuristic function guarantees to obtain its lowr bound, we cannot fail to obtain an optimal solution. We adopt Lagrangean relaxation among various relaxations as heuristic function and by using Lagrangean multipliers we can generate a good surrogate constraint. This surrogate constraint generates minimal cover and extendible set and both make our proposed algorithm efficient in separation too. Computational results are reported.