The recent performance improvements in mixed-integer programming (MIP) have been accompanied by a significantly increased complexity of the codes of MIP solvers, which poses challenges in fixing implementation errors. In this paper, we introduce MIP-DD, a solver-independent tool, which to the best of our knowledge is the first open-source delta debugger for MIP. Delta debugging is a hypothesis-trial-result approach to isolate the cause of a solver failure. MIP-DD simplifies MIP instances while maintaining the undesired behavior. Preliminary versions already supported and motivated fixes for many bugs in the SCIP releases 8.0.1 to 8.1.1. In these versions, MIP-DD successfully contributed to 24 out of all 51 documented MIP-related bugfixes even for some long-known issues. In selected case studies we highlight that instances triggering fundamental bugs in SCIP can typically be reduced to a few variables and constraints in less than an hour. This makes it significantly easier to manually trace and check the solution process on the resulting simplified instances. A promising future application of MIP-DD is the analysis of performance bottlenecks, which could very well benefit from simple adversarial instances. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: This work was partially supported by the German Research Foundation [Grant RA 1033/3-1] and the German Federal Ministry of Education and Research [Grant 05M20ZBM]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0844 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0844 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Presolving has become an essential component of modern mixed integer program (MIP) solvers, both in terms of computational performance and numerical robustness. In this paper, we present PaPILO, a new C++ header-only library that provides a large set of presolving routines for MIP and linear programming problems from the literature. The creation of PaPILO was motivated by the current lack of (a) solver-independent implementations that (b) exploit parallel hardware and (c) support multiprecision arithmetic. Traditionally, presolving is designed to be fast. Whenever necessary, its low computational overhead is usually achieved by strict working limits. PaPILO’s parallelization framework aims at reducing the computational overhead also when presolving is executed more aggressively or is applied to large-scale problems. To rule out conflicts between parallel presolve reductions, PaPILO uses a transaction-based design. This helps to avoid both the memory-intensive allocation of multiple copies of the problem and special synchronization between presolvers. Additionally, the use of Intel’s Threading Building Blocks library aids PaPILO in efficiently exploiting recursive parallelism within expensive presolving routines, such as probing, dominated columns, or constraint sparsification. We provide an overview of PaPILO’s capabilities and insights into important design choices. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: This work has been financially supported by Research Campus MODAL, funded by the German Federal Ministry of Education and Research [Grants 05M14ZAM, 05M20ZBM], and the European Union’s Horizon 2020 research and innovation programme under grant agreement No 773897 (plan4res). The content of this paper only reflects the author’s views. The European Commission / Innovation and Networks Executive Agency is not responsible for any use that may be made of the information it contains. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0171 ), as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0171 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

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 .