For mixed-integer linear programming and linear programming it is well known that symmetries can have a negative impact on the performance of branch-and-bound and linear optimization algorithms. A common strategy to handle symmetries in linear programs is to reduce the dimension of the linear program by aggregating symmetric variables and solving a linear program of … Read more
Inverse optimization problems are bilevel optimization problems in which the leader modifies the follower’s objective such that a prescribed feasible solution becomes an optimal solution of the follower. They capture hierarchical decision-making problems like parameter estimation tasks or situations where a planner wants to steer an agent’s choice. In this work, we study integral inverse … Read more
This paper introduces Zimpler, a free tool built on the ZIMPL modeling language to streamline the solution of mixed-integer linear programs (MILP). Zimpler extends existing ZIMPL workflows by integrating native data sources—such as Excel spreadsheets—without requiring manual conversion to text-based tables. In addition, it supports solution refinement by adapting solver outputs into alternative formats, including … 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 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
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
This paper addresses an operational planning challenge in two-tier robotized sorting systems (T-RSS), an emerging alternative to traditional conveyor-based sorting in e-commerce delivery stations. Designed to be compact and space-efficient, T-RSS use an upper tier to sort parcels from loading stations to drop-off points, which connect to roll containers on a lower tier where parcels … Read more