50 research outputs found
A Neural Benders Decomposition for the Hub Location Routing Problem
In this study, we propose an imitation learning framework designed to enhance
the Benders decomposition method. Our primary focus is addressing degeneracy in
subproblems with multiple dual optima, among which Magnanti-Wong technique
identifies the non-dominant solution. We develop two policies. In the first
policy, we replicate the Magnanti-Wong method and learn from each iteration. In
the second policy, our objective is to determine a trajectory that expedites
the attainment of the final subproblem dual solution. We train and assess these
two policies through extensive computational experiments on a network design
problem with flow subproblem, confirming that the presence of such learned
policies significantly enhances the efficiency of the decomposition process
A Benders Based Rolling Horizon Algorithm for a Dynamic Facility Location Problem
This study presents a well-known capacitated dynamic facility location problem (DFLP) that satisfies the customer demand at a minimum cost by determining the time period for opening, closing, or retaining an existing facility in a given location. To solve this challenging NP-hard problem, this paper develops a unique hybrid solution algorithm that combines a rolling horizon algorithm with an accelerated Benders decomposition algorithm. Extensive computational experiments are performed on benchmark test instances to evaluate the hybrid algorithm’s efficiency and robustness in solving the DFLP problem. Computational results indicate that the hybrid Benders based rolling horizon algorithm consistently offers high quality feasible solutions in a much shorter computational time period than the stand-alone rolling horizon and accelerated Benders decomposition algorithms in the experimental range
Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition
In this paper, we study chance constrained mixed integer program with
consideration of recourse decisions and their incurred cost, developed on a
finite discrete scenario set. Through studying a non-traditional bilinear mixed
integer formulation, we derive its linear counterparts and show that they could
be stronger than existing linear formulations. We also develop a variant of
Jensen's inequality that extends the one for stochastic program. To solve this
challenging problem, we present a variant of Benders decomposition method in
bilinear form, which actually provides an easy-to-use algorithm framework for
further improvements, along with a few enhancement strategies based on
structural properties or Jensen's inequality. Computational study shows that
the presented Benders decomposition method, jointly with appropriate
enhancement techniques, outperforms a commercial solver by an order of
magnitude on solving chance constrained program or detecting its infeasibility
Solving the optimum communication spanning tree problem
This paper presents an algorithm based on Benders decomposition to solve the optimum communication spanning tree problem. The algorithm integrates within a branch-and-cut framework a stronger reformulation of the problem, combinatorial lower bounds, in-tree heuristics, fast separation algorithms, and a tailored branching rule. Computational experiments show solution time savings of up to three orders of magnitude compared to state-of-the-art exact algorithms. In addition, our algorithm is able to prove optimality for five unsolved instances in the literature and four from a new set of larger instances.Peer ReviewedPostprint (author's final draft
Integrating network design and frequency setting in public transportation networks : a survey
This work reviews the literature on models which integrate the network design and the frequency setting phases in public transportation networks. These two phases determine to a large extent the service for the passengers and the operational costs for the operator of the system. The survey puts emphasis on modelling features, i.e., objective cost components and constraints, as well as on algorithmic aspects. Finally, it provides directions for further research