Abstract Implied-integer detection is a well-known presolving technique that is used by many Mixed-Integer Linear Programming solvers. Informally, a variable is said to be implied integer if its integrality is enforced implicitly by integrality of other variables and the constraints of a problem. In this case, algorithms used in MILP software can choose whether they treat it as an integer or continuous variable. In this work we formalize the definition of implied integrality by taking a polyhedral perspective. Our main result characterizes implied integrality as occurring when a subset of integer variables is fixed to integer values and the polyhedron on the remaining variables is integral. While integral polyhedra are well-understood theoretically, existing detection methods infer implied integrality only for one variable at a time. We introduce new detection methods based on the detection of integral polyhedra, extending existing techniques to multiple variables. Additionally, we discuss the computational complexity of recognizing implied integers. We conduct experiments using a new detection method that uses totally unimodular submatrices to identify implied integrality. For the MIPLIB 2017 collection dataset our results indicate that, on average, 18.8 % of the variables are classified as implied integer after presolving, compared to just 3.3 % identified by state-of-the-art techniques. Moreover, we are able to reduce the average percentage of variables whose integrality needs to be enforced after presolving from 70.2% to 59.0%.

Abstract This article addresses the linear optimization problem to maximize the total costs that can be shared among a group of agents, while maintaining stability in the sense of the core constraints of a cooperative transferable utility game, or TU game. When maximizing total shareable costs, the cost shares must satisfy all constraints that define the core of a TU game, except for being budget balanced. The article first gives a fairly complete picture of the computational complexity of this optimization problem, its relation to optimization over the core itself, and its equivalence to other, minimal core relaxations that have been proposed earlier. We then address minimum cost spanning tree (MST) games as an example for a class of cost sharing games with non‐empty core. While submodular cost functions yield efficient algorithms to maximize shareable costs, MST games have cost functions that are subadditive, but generally not submodular. Nevertheless, it is well known that cost shares in the core of MST games can be found efficiently. In contrast, we show that the maximization of shareable costs is ‐hard for MST games and derive a 2‐approximation algorithm. Our work opens several directions for future research.

A series-parallel matrix is a binary matrix that can be obtained from an empty matrix by successively adjoining rows or columns that are copies of an existing row/column or have at most one one-entry. Equivalently, series-parallel matrices are representation matrices of graphic matroids of series-parallel graphs, which can be recognized in linear time. We propose an algorithm that, for an m-by-n matrix A with k nonzeros, determines in expected time whether A is series-parallel or returns a minimal non–series-parallel submatrix of A. We complement the developed algorithm by an efficient [Formula: see text]implementation and report about computational results. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant OCENW.M20.151]. Supplemental Material: The software that supports the findings of this study is available at the GitHub software repository ( https://github.com/discopt/cmr-series-parallel ).

Abstract We consider the multilinear polytope which arises naturally in binary polynomial optimization. Del Pia and Di Gregorio introduced the class of odd $$\beta $$ β -cycle inequalities valid for this polytope, showed that these generally have Chvátal rank 2 with respect to the standard relaxation and that, together with flower inequalities, they yield a perfect formulation for cycle hypergraph instances. Moreover, they describe a separation algorithm in case the instance is a cycle hypergraph. We introduce a weaker version, called simple odd $$\beta $$ β -cycle inequalities, for which we establish a strongly polynomial-time separation algorithm for arbitrary instances. These inequalities still have Chvátal rank 2 in general and still suffice to describe the multilinear polytope for cycle hypergraphs. Finally, we report about computational results of our prototype implementation. The simple odd $$\beta $$ β -cycle inequalities sometimes help to close more of the integrality gap in the experiments; however, the preliminary implementation has substantial computational cost, suggesting room for improvement in the separation algorithm.

We consider, for complete bipartite graphs, the convex hulls of characteristic vectors of all matchings, extended by a binary entry indicating whether the matching contains two specific edges. This polytope is associated with the quadratic matching problem with a single linearized quadratic term. We provide a complete irredundant inequality description, which settles a conjecture by Klein [ Combinatorial Optimization with One Quadratic Term, Ph.D. thesis, TU Dortmund, Dortmund, Germany]. In addition, we also derive facetness and separation results for the polytopes. The completeness proof is based on a geometric relationship to a matching polytope of a nonbipartite graph. Using standard techniques, we finally extend the result to capacitated $b$-matchings.

We contribute a methodical approach in the context of IS design science research to develop UI prototypes for evaluations in practice-oriented research.Based on previous research on improving IS support for early product cost optimization, we present and discuss our methodical approach to derive UI prototypes based on an evaluated requirements model.The objective of the outlined approach comprising different steps is to derive a clickable UI prototype that is feasible for further artifact evaluation within institutional environments.Together with experts from the practice of software engineering we iterated through the working steps of the elaborated approach to determine its feasibility to derive a prototype and moreover, generate visual examples for each step to improve the approach's comprehensibility.In addition to the description of the approach itself we point to significant hurdles that have arisen with the application of it in order to generate learnings for other research projects.

The system we propose allows the classification of future performances of high-technology venture investments on the basis of limited, successively available information. Our system helps investors to decide whether to invest in a young High-Technology Venture (HTV) or not. In order to cope with uncertain data we apply a Fuzzy-Rule-based Classifier. As we want to attain an objective and clear decision making process we implement a learning algorithm that learns rules from given real-world examples. The availability of data on early-stage investments is typically limited. For this reason we equipped our system with a bootstrapping mechanism which multiplies the number of examples without changing their inherent quality and structure. All these features make an operational and reliable investment decision support system in the context of early stage venture capital investments possible.

The system we propose allows the classification of future performances of high-technology venture investments on the basis of very limited information. Our system thus helps investors to decide whether to invest in a young High-Technology Venture (HTV) or not. In order to cope with uncertain data we apply a Fuzzy Rule based Classifier. As we want to attain an objective and clear decision making process we implement a learning algorithm that learns rules from given real-world examples. The availability of data on early-stage investments is typically limited. For this reason we equipped our system with a bootstrapping mechanism which multiplies the number of examples without changing the inherent quality or structure of the examples. To enhance the performance of the IDSS we apply a specifically designed Particle Swarm Optimization algorithm (PSO). We show the efficacy of this approach by comparing the classification power and other metrics of the PSO-optimized system with the corresponding characteristics of the original IDSS.