Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design

Benders decomposition is a broadly used exact solution method for stochastic programs, which has been increasingly applied to solve transportation and logistics planning problems under uncertainty. However, this strategy comes with important drawbacks, such as a weak master problem following the relaxation step that confines the dual cuts to the scenario subproblems. In this paper, we propose a partial Benders decomposition methodology, based on the idea of including explicit information from the scenario subproblems in the master. To investigate the benefits of this methodology, we apply it to solve a general class of two-stage stochastic multicommodity network design models. Specifically, we solve the challenging variant of the model where both the demands and the arc capacities are stochastic. Through an extensive experimental campaign, we clearly show that the proposed methodology yields significant benefits in computational efficiency, solution quality, and stability of the solution process.

A Learning-Based Matheuristic for Stochastic Multicommodity Network Design

This paper proposes a solution approach for the multicommodity capacitated fixed-charge network design problem with uncertain demand modeled as a two-stage stochastic program. The proposed learning-based matheuristic combines heuristic search techniques with mathematical programming. It provides a systematic approach to identifying structures of good-quality solutions by gradually considering scenarios and their influences on design decisions. Extensive computational experiments illustrate the efficiency of the proposed matheuristic in obtaining high-quality solutions with limited computational efforts.

MIP Neighborhood Search Heuristics for a Capacitated Fixed-Charge Network Design Problem

The fixed-charge capacitated multicommodity network design problem is a fundamental optimization problem arising in many network configurations. The solution of the problem provides an appropriate network design as well as routes of multicommodity flows aimed at minimizing the total cost, which is the sum of the flow costs and fixed-charge costs over a network with limited arc capacities. In the present paper, we introduce a combined approach with a capacity scaling procedure for finding an initial feasible solution and an MIP neighborhood search for improving the solutions. Besides, we modify the procedure for application to large-scale problems. Computational experiments demonstrate the effectiveness of the proposed approach, and high-quality solutions are obtained for two problem sets from the literature.

Benders Cut Classification via Support Vector Machines for Solving Two-Stage Stochastic Programs

We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones significantly improving bounds over iterations as valuable cuts. We propose a learning-enhanced Benders decomposition (LearnBD) algorithm, which adds a cut classification step in each iteration to selectively generate cuts that are more likely to be valuable cuts. The LearnBD algorithm includes two phases: (i) sampling cuts and collecting information from training problems and (ii) solving testing problems with a support vector machine (SVM) cut classifier. We run the LearnBD algorithm on instances of capacitated facility location and multicommodity network design under uncertain demand. Our results show that SVM cut classifier works effectively for identifying valuable cuts, and the LearnBD algorithm reduces the total solving time of all instances for different problems with various sizes and complexities.