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The break minimization problem is a fundamental problem in sports scheduling. Recently, its quadratic unconstrained binary optimization (QUBO) formulation has been proposed, which has gained much interest with the rapidly growing field of…
This paper presents a new hybrid classical-quantum approach to solve Mixed Integer Linear Programming (MILP) using neutral atom quantum computations. We apply Benders decomposition (BD) to segment MILPs into a master problem (MP) and a…
Optimization problems is one of the most challenging applications of quantum computers, as well as one of the most relevants. As a consequence, it has attracted huge efforts to obtain a speedup over classical algorithms using quantum…
Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the…
Hydro unit commitment is the problem of maximizing water use efficiency while minimizing start-up costs in the daily operation of multiple hydro plants, subject to constraints on short-term reservoir operation, and long-term goals. A…
In this paper, we propose novel mixed-integer linear programming (MIP) formulations to model decision problems posed as influence diagrams. We also present a novel heuristic that can be employed to warm start the MIP solver, as well as…
This paper studies binary linear programming problems in the presence of uncertainties that may cause solution values to change during implementation. This type of uncertainty, termed implementation uncertainty, is modeled explicitly…
The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem (which we call unimodular…
We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in $\{0, \pm 1\}$. While semidefinite programming (SDP) techniques are well established for $\{0,1\}$-…
Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this context, we consider the…
We expand our novel computational method for unit commitment (UC) to include long-horizon planning. We introduce a fast novel algorithm to commit hydro-generators, provably accurately. We solve problems with thousands of generators at 5…
Power systems Unit Commitment (UC) problem determines the generator commitment schedule and dispatch decisions for power networks based on forecasted electricity demand. However, with the increasing penetration of renewables and stochastic…
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…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number of…
We consider sensitivity analysis for Mixed Binary Quadratic Programs (MBQPs) with respect to changing right-hand-sides (rhs). We show that even if the optimal solution of a given MBQP is known, it is NP-hard to approximate the change in…
Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization. As solving large-scale combinatorial optimization problems is challenging, primal heuristics have been developed to quickly…
The p-center problem consists in selecting p centers among M to cover N clients, such that the maximal distance between a client and its closest selected center is minimized. For this problem we propose two new and compact integer…
Resource scheduling is critical in many industries, especially in power systems. The Unit Commitment problem determines the on/off status and output levels of generators under many constraints. Traditional exact methods, such as…
This paper presents a comprehensive theoretical analysis of six distinct Mixed-Integer Programming (MIP) formulations for preventive Generator Maintenance Scheduling (GMS), a critical problem for ensuring the reliability and efficiency of…