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
When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-network structure has been employed to find good solutions within a reasonable time limit. For … Read more
Capacity Planning problems are a class of optimization problems used in diverse industries to improve resource allocation and make investment decisions. Solving real-world instances of these problems typically requires significant computational effort. To tackle this, we propose machine-learning-aided column generation methods for solving large-scale capacity planning problems. Our goal is to accelerate column generation by … Read more
This paper surveys optimization problems arising in agriculture, energy systems, and water-energy coordination from an operations research perspective. These problems are commonly formulated as integer nonlinear programs, mixed-integer nonlinear programs, or combinatorial set optimization models, characterized by nonlinear physical constraints, discrete decisions, and intertemporal coupling. Such structures pose significant computational challenges in large-scale and repeated-solution … Read more
Benders’ decomposition (BD) is a framework for solving optimization problems by removing some variables and modeling their contribution to the original problem via so-called Benders cuts. While many advanced optimization techniques can be applied in a BD framework, one central technique has not been applied systematically in BD: symmetry handling. The main reason for this … Read more
This paper investigates a presolving method for handling symmetries in mixed-binary programs, based on inequalities computed from so-called Schreier-Sims tables. We show that an iterative application of this method together with merging variables will produce an instance for which the symmetry group is trivial. We then prove that the problem structure can be preserved for … Read more
Inverse optimization (IO) has emerged as a powerful framework for analyzing prescriptive model parameters that rationalize observed or prescribed decisions. Despite the prevalence of discrete decision-making models, existing work has primarily focused on continuous and convex models, for which the corresponding IO problems are far easier to solve. This paper makes three contributions that broaden … Read more
The Stochastic Unit Commitment (SUC) problem models the scheduling of power generation units under uncertainty, typically using a two-stage stochastic program with integer first-stage and continuous second-stage variables. We propose a new Benders decomposition approach that leverages an extended formulation based on interval variables, enabling decomposition by both unit and time interval under mild technical … Read more