Accelerating benders decomposition with heuristicmaster problem solutions

Abstract

ABSTRACT. In this paper, a general scheme for generating extra cuts during the execution of a Benders decomposition algorithm is presented. These cuts are based on feasible and infeasible master problem solutions generated by means of a heuristic. This article includes general guidelines and a case study with a fixed charge network design problem. Computational tests with instances of this problem show the efficiency of the strategy. The most important aspect of the proposed ideas is their generality, which allows them to be used in virtually any Benders decomposition implementation.

Multicommodity Network Flows With Nonconvex Arc Costs

“…Another direction of active research to solve capacitated network design problems has been the use of Benders decomposition to derive dual subproblems and new family of valid cuts (see [25,41] for a general presentation and [24] for a survey on the uncapacitated and capacitated fixed-charge design problems) and various enhancements of that classical approach have been motivated by the network design models (see [26,32,62,63,83]). Generalized Benders decomposition can be too an interesting solution procedure to exactly solve difficult capacity and flow assignment problems with convex flow costs [64], as the subproblems reduce to convex multicommodity network flow problems for which efficient algorithms have been proposed (see [77] for a survey).…”

Stochastic Benders decomposition for the supply chain investment planning problem under demand uncertainty

“…(4) to (9). The objective function (4) represents freight costs between the nodes, inventory costs, and the cost of shortfall.…”

“…Cutting-plane schemes has been successfully used in solving large-scale problems since the pioneering paper of Geoffrion & Graves (1974), e.g., the uncapacitated network design problem with undirected arcs (Magnanti et al, 1986, Costa et al, 2012, the stochastic transportationlocation problems (Franca, 1982) The objective of this paper is to present a mathematical model for the optimization of the supply chain investment planning problem applied to the petroleum products supply chain. Uncertainties related to product demand levels are considered, thus, the stochastic programming framework is adopted as modeling approach.…”

Joint PEV Charging Network and Distributed PV Generation Planning Based on Accelerated Generalized Benders Decomposition

“…Note that this approach will not affect the optimal solution because the feasible set of the original master problem is a subset of the relaxed master problem. Thus, the optimality cuts generated for the latter is also valid for the former [23].…”