THE RAY-METHOD: THEORETICAL BACKGROUND AND COMPUTATIONAL RESULTSReport as inadecuate




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Croatian Operational Research Review, Vol.3 No.1 December 2012. -

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.

branch and bound; integer programming



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Source: http://hrcak.srce.hr/



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