THE RAY-METHOD: THEORETICAL BACKGROUND AND COMPUTATIONAL RESULTS

In our talk we present an algorithm for determining initial bound for the Branch and Bound (B&B) method. The idea of the algorithm is based on the use of the "ray" introduced in the "ray-method" developed for solving integer programming problems [13], [14]. Instead of solving a common integer programming problem we use the main idea of the ray-method to find an integer feasible solution of integer linear programming (ILP) problem along the ray as close to optimal solution of relaxation problem, as possible. Objective value obtained in this way may be used as an initial bound for B&B method. The algorithm has been implemented in the frame of educational package WinGULF [3] for linear and linear-fractional programming and has been tested on various ILP problems. Then inspired by the results obtained we implemented the method using the so-called callable library of CPLEX package by IBM. omputational experiments with the algorithm proposed show that such preprocessing procedure in many cases results an integer feasible solution very close to the solution of relaxation problem. Initial bound for branch and bound method determined in this way often can significantly decrease the size of the binary tree to be searched and in this manner can improve performance of the B&B method

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