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We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…
We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison…
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…
Uncertainty in surgery durations continues to be difficult to account for in operating room scheduling. In particular, it remains complex to accurately incorporate uncertainty in surgical overtime constraints within mixed-integer linear…
Optimization problems characterized by both discrete and continuous variables are common across various disciplines, presenting unique challenges due to their complex solution landscapes and the difficulty of navigating mixed-variable…
The No-Three-In-Line problem asks for the maximum number of points that can be placed on an n by n grid with no three collinear, representing a famous problem in combinatorial geometry. While classical methods like Integer Linear…
To create efficient-high performing processes, one must find an optimal design with its corresponding controller that ensures optimal operation in the presence of uncertainty. When comparing different process designs, for the comparison to…
We present a two-level branch-and-bound (BB) algorithm to compute the optimal gripper pose that maximizes a grasp metric in a restricted search space. Our method can take the gripper's kinematics feasibility into consideration to ensure…
This work is a benchmark study for quantum-classical computing method with a real-world optimization problem from industry. The problem involves scheduling and balancing jobs on different machines, with a non-linear objective function. We…
While mixed-integer linear programming and convex programming solvers have advanced significantly over the past several decades, solution technologies for general mixed-integer nonlinear programs (MINLPs) have yet to reach the same level of…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
The usability of Reinforcement Learning is restricted by the large computation times it requires. Curriculum Reinforcement Learning speeds up learning by defining a helpful order in which an agent encounters tasks, i.e. from simple to hard.…
Quantified Integer Programming (QIP) bridges multiple domains by extending Quantified Boolean Formulas (QBF) to incorporate general integer variables and linear constraints while also generalizing Integer Programming through variable…
Rental-based business models and increasing sustainability requirements intensify the need for efficient strategies to manage large machine and vehicle fleet renewal and upgrades. Optimized fleet upgrade strategies maximize overall utility,…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…
Scheduling problems are a fundamental class of combinatorial optimization problems that underpin operational efficiency in manufacturing, logistics, and service systems. While operations research has traditionally developed solver-centric…
We explore a reinforcement learning strategy to automate and accelerate h/p-multigrid methods in high-order solvers. Multigrid methods are very efficient but require fine-tuning of numerical parameters, such as the number of smoothing…
Lagrangian relaxation stands among the most efficient approaches for solving a Mixed Integer Linear Programs (MILP) with difficult constraints. Given any duals for these constraints, called Lagrangian Multipliers (LMs), it returns a bound…