Accelerating benders decomposition: multiple cuts via multiple solutions

Abstract

Benders decomposition (BD) is a well-known approach that has been successfully applied to various mathematical programming problems. According to previous studies, slow convergence is the main drawback of this method. In this paper, multi-solution of the master problem has been applied to accelerate the BD algorithm and improve both lower and upper bounds by simultaneously adding multiple feasibility and optimality cuts. A novel integration of Benders cuts was used to prevent the growth of master problem. Computational experiments were applied to a series of logistics facility location problems. Our numerical experiments resulted in a 61% decrease in the total number of iterations and up to 73% reduction in the solution time, confirming the outstanding performance of the proposed method.