A Hybrid Approach of Bundle and Benders Applied Large Mixed Linear Integer Problem

Abstract

Consider a large mixed integer linear problem where structure of the constraint matrix is sparse, with independent blocks, and coupling constraints and variables. There is one of the groups of constraints to make difficult the application of Benders scheme decomposition. In this work, we propose the following algorithm; a Lagrangian relaxation is made on the mentioned set of constraints; we presented a process heuristic for the calculation of the multiplier through the resolution of the dual problem, structured starting from the bundle methods. According to the methodology proposed, for each iteration of the algorithm, we propose Benders decomposition where quotas are provided for the value function and $\epsilon$-subgradient.