T he uncapacitated facility location (UFL) problem is one of the most famous and most studied problems in the operations research literature. Given a set of potential facility locations and a set of customers, the goal is to find a subset of facility locations to open and to allocate each customer to open facilities so that the facility opening plus customer allocation costs are minimized. In our setting, for each customer the allocation cost is assumed to be a linear or separable convex quadratic function. Motivated by recent UFL applications in business analytics, we revise approaches that work on a projected decision space and hence are intrinsically more scalable for large-scale input data. Our working hypothesis is that many of the exact (decomposition) approaches that were proposed decades ago and discarded soon after need to be redesigned to take advantage of the new hardware and software technologies. To this end, we "thin out" the classical models from the literature and use (generalized) Benders cuts to replace a huge number of allocation variables by a small number of continuous variables that model the customer allocation cost directly. Our results show that Benders decomposition allows for a significant boost in the performance of a mixed-integer programming solver. We report the optimal solution of a large set of previously unsolved benchmark instances widely used in the available literature. In particular, dramatic speedups are achieved for UFL problems with separable quadratic allocation costs, which turn out to be much easier than their linear counterparts when our approach is used.
The Steiner tree problem is a challenging NP-hard problem. Many hard instances of this problem are publicly available, that are still unsolved by state-of-theart branch-and-cut codes. A typical strategy to attack these instances is to enrich the polyhedral description of the problem, and/or to implement more and more sophisticated separation procedures and branching strategies. In this paper we investigate the opposite viewpoint, and try to make the solution method as simple as possible while working on the modeling side. Our working hypothesis is that the extreme hardness of
Bilevel optimization problems are very challenging optimization models arising in many important practical contexts, including pricing mechanisms in the energy sector, airline and telecommunication industry, transportation networks, optimal expansion of gas networks, critical infrastructure defense, and machine learning. In this paper, we present a new general purpose branch-and-cut framework for the exact solution of mixed-integer bilevel linear programs (MIBLP), which constitute a very significant subfamily of bilevel optimization problems. Our framework introduces several new classes of valid inequalities to speed-up the solver, along with a very effective bilevel-specific preprocessing procedure. A very extensive computational study is presented, where we evaluate the performance of various solution methods on a common testbed of more than 800 instances from the literature-this is by far the most extensive computational analysis ever performed for exact MIBLP solvers. Our new algorithm consistently outperforms (often by a large margin) all alternative state-of-the-art methods from the literature, including methods which exploit problem specific information for special instance classes. In particular, it allows to solve to optimality more than 300 instances previously unsolved instances from literature.
In this work we present a branch-and-bound (B&B) framework for the asymmetric prizecollecting Steiner tree problem (APCSTP). Several well-known network design problems can be transformed to the APCSTP, including the Steiner tree problem (STP), prize-collecting Steiner tree problem (PCSTP), maximum-weight connected subgraph problem (MWCS) and the nodeweighted Steiner tree problem (NWSTP). The main component of our framework is a new dual ascent algorithm for the rooted APCSTP, which generalizes Wong's dual ascent algorithm for the Steiner arborescence problem. The lower bounds and dual information obtained from the algorithm are exploited within powerful bound-based reduction tests and for guiding primal heuristics. The framework is complemented by additional alternative-based reduction tests. All tests are applied in every node of the B&B tree. Extensive computational results on benchmark instances for the PCSTP, MWCS and NWSTP indicate the framework's effectiveness, as most instances from literature are solved to optimality within seconds, including most of the (previously unsolved) largest instances from the recent DIMACS Challenge on Steiner Trees. In many cases the framework even manages to outperform recently proposed state-of-the-art exact and heuristic algorithms. Since the network design problems addressed in this work are frequently used for modeling various real-world applications (e.g., in bioinformatics), the presented B&B framework will also be made publicly available.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.