We study a two-stage admission and assignment problem under uncertainty arising in university admission systems. In the first stage, applicants are admitted to an initial two-year program. In the second stage, admitted applicants are assigned to degree programs through an articulation mechanism subject to capacity constraints. Uncertainty stems from the academic performance of admitted applicants … Read more
We present an exact formulation of the symmetric Traveling Salesman Problem (TSP) that replaces the classical edge-selection view with a surface-building approach. Instead of selecting edges to form a cycle, the model selects a set of connected triangles where the boundary of the resulting surface forms the tour. This method yields a mixed-integer linear programming … Read more
We introduce and study a novel generalization of the classical Knapsack Problem (KP), called the Colored Knapsack Problem (CKP). In this problem, the items are partitioned into classes of colors and the packed items need to be ordered such that no consecutive items are of the same color. We establish that the problem is weakly … Read more
In modern Formula~1, strict regulations and highly optimized cars limit performance gains through hardware, increasing the importance of strategic decision-making. This work tackles the problem of computing a race strategy that minimizes total race time by jointly optimizing tire stints, compound selection, fuel load, and Energy Recovery System (ERS) deployment. We present a high-performance simulation … Read more
We present a brief structural equivalence between the symmetric TSP and a constrained Group Steiner Tree Problem (cGSTP) defined on a simplicial incidence graph. Given the complete weighted graph on the city set V, we form the bipartite incidence graph between triangles and edges. Selecting an admissible, disk-like set of triangles induces a unique boundary … Read more
We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and incorporates the known components, such as hard constraints, via a constraint reasoning module, yielding a constrained learning scheme. The trained model generates new solutions that are structurally … Read more
ArticleDownload View PDF
We present a constructive procedure for certifying the infeasibility of a mixed-integer program (MIP) using recursion on a sequence of sets that describe the sets of barely feasible right-hand sides. Each of these sets corresponds to a monotonic superadditive function, and the pointwise limit of this sequence is a functional certificate for MIP infeasibility. Our … Read more
ArticleDownload View PDF
Probing is an important presolving technique in mixed-integer programming solvers. It selects binary variables, tentatively fixes them to 0 and 1, and performs propagation to deduce additional variable fixings, bound tightenings, substitutions, and implications. In this work, we propose clique probing instead of probing on individual variables, we select cliques, a set of binary variables … Read more