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A tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max $k$-cut problem is a fundamental combinatorial optimization problem with…
Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…
The paper proposes a quantum algorithm for the traveling salesman problem (TSP) based on the Grover Adaptive Search (GAS), which can be successfully executed on IBM's Qiskit library. Under the GAS framework, there are at least two…
The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a…
Multi-objective optimization (MOO) is a well-studied problem for several important recommendation problems. While multiple approaches have been proposed, in this work, we focus on using constrained optimization formulations (e.g., quadratic…
We propose and evaluate a quantum-inspired algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, which are mathematically equivalent to finding ground states of Ising spin-glass Hamiltonians. The algorithm…
Achieving ubiquitous global connectivity requires integrating satellite and terrestrial networks, particularly to serve remote and underserved regions. In this work, we investigate the design and optimization of Space-Terrestrial Integrated…
We study the costs and benefits of different quantum approaches to finding approximate solutions of constrained combinatorial optimization problems with a focus on Maximum Independent Set. In the Lagrange multiplier approach we analyze the…
The quantum approximate optimization algorithm (QAOA) is designed to determine optimum and near optimum solutions of quadratic (and higher order) unconstrained binary optimization (QUBO or HUBO) problems, which in turn accurately model…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…
Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require…
Quantum computing is a promising technology to address combinatorial optimization problems, for example via the quantum approximate optimization algorithm (QAOA). Its potential, however, hinges on scaling toy problems to sizes relevant for…
Traveling salesman problems (TSP) are one of the well-known combinatorial optimization problems that many groups tackle to solve. This problem appears in many types of combinational optimization, such as scheduling, route optimization, and…
Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific…
Hard combinatorial optimization problems, often mapped to Ising models, promise potential solutions with quantum advantage but are constrained by limited qubit counts in near-term devices. We present an innovative quantum-inspired framework…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
This study proposes a novel method for simplifying inequality constraints in Higher-Order Binary Optimization (HOBO) formulations. The proposed method addresses challenges associated with Quadratic Unconstrained Binary Optimization (QUBO)…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…
The rapid progress of physical implementation of quantum computers paved the way for the design of tools to help users write quantum programs for any given quantum device. The physical constraints inherent in current NISQ architectures…