Benders' decomposition is a popular mathematical and constraintprogramming algorithm that is widely applied to exploit problem structure arising from real-world applications. While useful for exploiting structure...
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Benders' decomposition is a popular mathematical and constraintprogramming algorithm that is widely applied to exploit problem structure arising from real-world applications. While useful for exploiting structure in mathematical and constraint programs, the use of Benders' decomposition typically requires significant implementation effort to achieve an effective solution algorithm. Traditionally, Benders' decomposition has been viewed as a problem specific algorithm, which has limited the development of general purpose algorithms and software solutions. This paper presents a general purpose Benders' decomposition algorithm that is capable of handling many classes of mathematical and constraint programs and provides extensive flexibility in the implementation and use of this algorithm. A branch-and-cut approach for Benders' decomposition has been implemented within the constraint integer programming solver SCIP using a plugin-based design to allow for a wide variety of extensions and customisations to the algorithm. The effectiveness of the Benders' decomposition algorithm and available enhancement techniques is assessed in a comprehensive computational study. (C) 2020 Elsevier B.V. All rights reserved.
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the S...
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The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP.
Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper fo...
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Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving constraintinteger Programs), which is a mixed-integer linear programming solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, we present the basic concept of having two parallel extensions, and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator), including an implementation of deterministic parallelization. Second, we discuss the difficulties in achieving a good performance that utilizes all resources on an actual computing environment, and the difficulties of performance evaluation of the parallel solvers. Third, we present away to evaluate the performance of new algorithms and parameter settings of the parallel extensions. Finally, we demonstrate the current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer nonlinear programs (MINLPs) in parallel.
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