Computational Enhancement in the Application of the Branch and Bound Method for Linear Integer Programs and Related Models

Abstract

In this paper, a reformulation that was proposed for a knapsack problem has been extended to single and bi-objective linear integer programs. A further reformulation by adding an upper bound constraint for a knapsack problem is also proposed and extended to the bi-objective case. These reformulations significantly reduce the number of branch and bound iterations with respect to these models. Numerical illustrations have been presented and computational experiments have been carried out to compare the behaviour before and after the reformulation. For this purpose, Tora software was used.

Keywords

• Reformulation
• Branch and bound
• General linear integer programs
• Knapsack problem
• Bi-objective models
• Non-dominated point set