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 .

Operations researchers have long drawn insight from the structure of constraint coefficient matrices (CCMs) for mixed integer programs (MIPs). We propose a new question: Can pictorial representations of CCM structure be used to identify similar MIP models and instances? In this paper, CCM structure is visualized using digital images, and computer vision techniques are used to detect latent structural features therein. The resulting feature vectors are used to measure similarity between images and, consequently, MIPs. An introductory analysis examines a subset of the instances from strIPlib and MIPLIB 2017, two online repositories for MIP instances. Results indicate that structure-based comparisons may allow for relationships to be identified between MIPs from disparate application areas. Additionally, image-based comparisons reveal that ostensibly similar variations of an MIP model may yield instances with markedly different mathematical structures. Summary of Contribution: This paper presents a methodology for comparing mixed integer programs (MIPs) from any research domain based on the structure of the constraint coefficient matrices for one or more instances of a model. Specifically, computer vision and deep learning techniques are used to extract structural features and measure the similarity between these images. This process is agnostic to application area and instead focuses solely on mathematical structure. As a result, this methodology offers a fundamentally new way for operations researchers to view MIP similarity and highlights similarities between research problems that may have previously been viewed as unrelated.

In Dantzig-Wolfe reformulation of an integer program one convexifies a subset of the constraints, leading to potentially stronger dual bounds from the respective linear programming relaxation. As the subset can be chosen arbitrarily, this includes the trivial cases of convexifying no and all constraints, resulting in a weakest and strongest reformulation, respectively. Our computational study aims at better understanding of what happens in between these extremes. For a collection of integer programs with few constraints we compute, optimally solve, and evaluate the relaxations of all possible (exponentially many) Dantzig-Wolfe reformulations (with mild extensions to larger models from the MIPLIBs). We observe that only a tiny number of different dual bounds actually occur and that only a few inclusion-wise minimal representatives exist for each. This aligns with considerably different impacts of individual constraints on the strengthening the relaxation, some of which have almost no influence. In contrast, types of constraints that are convexified in textbook reformulations have a larger effect. We relate our experiments to what could be called a hierarchy of Dantzig-Wolfe reformulations.

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