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This paper introduces a novel method for compact representation of sets of n-dimensional binary sequences in a form of compact triplets structures (CTS), supposing both logic and arithmetic interpretations of data. Suitable illustration of…
A conflict graph represents logical relations between binary variables, and effective use of the graph can significantly accelerate branch-and-cut solvers for mixed-integer programming (MIP). In this paper we develop efficient parallel…
This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints…
Automatic coding of International Classification of Diseases (ICD) is a multi-label text categorization task that involves extracting disease or procedure codes from clinical notes. Despite the application of state-of-the-art natural…
Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in this family are derived by aggregating constraints then…
Many real discrete optimization problems (DOPs) are $NP$-hard and contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. Large DOPs can be solved due to their special tructure…
We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous…
We address the issue of generating cutting planes for mixed integer programs from multiple rows of the simplex tableau with the tools of disjunctive programming. A cut from q rows of the simplex tableau is an intersection cuts from a…
In this paper we present a novel mathematical optimization-based methodology to construct tree-shaped classification rules for multiclass instances. Our approach consists of building Classification Trees in which, except for the leaf nodes,…
We propose an efficient motion planning method designed to efficiently find collision-free trajectories for multiple manipulators. While multi-manipulator systems offer significant advantages, coordinating their motions is computationally…
Constant-dimension subspace codes (CDCs), a special class of subspace codes, have attracted significant attention due to their applications in network coding. A fundamental research problem of CDCs is to determine the maximum number of…
This work proposes a novel method to generate C-Tests; a deviated form of cloze tests (a gap filling exercise) where only the last part of a word is turned into a gap. In contrast to previous works that only consider varying the gap size or…
The Classification Tree (CT) is one of the most common models in interpretable machine learning. Although such models are usually built with greedy strategies, in recent years, thanks to remarkable advances in Mixer-Integer Programming…
Balanced search trees are widely used in computer science to efficiently maintain dynamic ordered data. To support efficient set operations (e.g., union, intersection, difference) using trees, the join-based framework is widely studied.…
We introduce and study the combinatorial optimization problem with interaction costs (COPIC). COPIC is the problem of finding two combinatorial structures, one from each of two given families, such that the sum of their independent linear…
Two successful approaches for the segmentation of biomedical images are (1) the selection of segment candidates from a merge-tree, and (2) the clustering of small superpixels by solving a Multi-Cut problem. In this paper, we introduce a…
Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization…
State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a…
Mixed-integer programming (MIP) provides a powerful framework for optimization problems, with Branch-and-Cut (B&C) being the predominant algorithm in state-of-the-art solvers. The efficiency of B&C critically depends on heuristic policies…
The global optimization of classification trees has demonstrated considerable promise, notably in enhancing accuracy, optimizing size, and thereby improving human comprehensibility. While existing optimal classification trees substantially…