Original scientific paper

THE RAY-METHOD: THEORETICAL BACKGROUND AND COMPUTATIONAL RESULTS

Erik Bajalinov ; Institute of Mathematics and Informatics, University College of Nyíregyháza, Nyíregyháza, Hungary
Anett Rácz ; Faculty of Informatics, Debrecen University, Debrecen, Hungary

Abstract

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.

Keywords

branch and bound; integer programming

Hrčak ID:

96810

URI

https://hrcak.srce.hr/96810

Publication date:

30.12.2012.

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