Determining Initial Bound by "Ray-method" in Branch and Bound Procedure

In this paper we present an algorithm for determining initial bound for the Branch and Bound (B&B) method. The idea of this algorithm is based on the use of “ray” as introduced in the “ray-method” developed for solving integer linear programming problems [11], [12]. Instead of solving an integer programming problem we use the main idea of the ray-method to find an integer feasible solution of an integer linear programming problem along the ray as close to an optimal solution of the relaxation problem as possible. The objective value obtained in this manner may be used as an initial bound for the B&B method. It is well known that getting a “good bound” as soon as possible can often significantly increase the performance of the B&B method.