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The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality…

While the ultimate goal of solving computationally intractable problems is to find a provably optimal solutions, practical constraints of real-world scenarios often necessitate focusing on efficiently obtaining high-quality, near-optimal…

Quantum Physics · Physics 2025-04-23 Prashanti Priya Angara , Emily Martins , Ulrike Stege , Hausi Müller

This paper studies quantum optimization baselines for the Generalized Traveling Salesman Problem (GTSP), a clustered routing problem that naturally models variant selection and sequencing problems under discrete alternatives. We propose a…

A multi-objective logistics optimization problem from a real-world supply chain is formulated as a Quadratic Unconstrained Binary Optimization Problem (QUBO) that minimizes cost, emissions, and delivery time, while maintaining target…

Optimization and Control · Mathematics 2026-02-06 Raoul Heese , Timothée Leleu , Sam Reifenstein , Christian Nietner , Yoshihisa Yamamoto

Vehicle Routing Problem (VRP) is one of the most complex NP-hard combinatorial optimization problem in transportation and logistics that requires a dynamic solution approach. In this paper we present a new hybrid approach that combines the…

Quantum heuristics offer a potential advantage for combinatorial optimization but are constrained by near-term hardware limitations. We introduce Iterative-QAOA, a variant of QAOA designed to mitigate these constraints. The algorithm…

Encoding hard-constrained optimization problems into a variational quantum algorithm often turns out to be a challenging task. In this work, we provide a solution for the class of open-shop scheduling problems (OSSPs), which we achieve by…

Quantum Physics · Physics 2026-05-18 Lennart Binkowski , Gereon Koßmann , Christian Tutschku , René Schwonnek

Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such…

Quantum Physics · Physics 2025-07-15 David Fitzek , Toheed Ghandriz , Leo Laine , Mats Granath , Anton Frisk Kockum

In this paper, we describe the usage of the Quantum Approximate Optimization Algorithm (QAOA), which is a quantum-classical heuristic, to solve a combinatorial optimization and integer programming task known as Vehicle Routing Problem…

Quantum Physics · Physics 2022-09-26 Utkarsh Azad , Bikash K. Behera , Emad A. Ahmed , Prasanta K. Panigrahi , Ahmed Farouk

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…

The Traveling Salesman Problem (TSP) is one of the most often-used NP-Hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the…

The Traveling Salesperson Problem (TSP) is a fundamental NP-hard optimisation challenge with widespread applications in logistics, operations research, and network design. While classical algorithms effectively solve small to medium-sized…

Quantum Physics · Physics 2025-03-04 Christos Lytrosyngounis , Ioannis Lytrosyngounis

Noisy intermediate-scale quantum (NISQ) hardware is almost universally incompatible with full-scale optimization problems of practical importance which can have many variables and unwieldy objective functions. As a consequence, there is a…

Quantum Physics · Physics 2022-05-10 Sean J. Weinberg , Fabio Sanches , Takanori Ide , Kazumitzu Kamiya , Randall Correll

The unit commitment (UC) problem stands as a critical optimization challenge in the electrical power industry. It is classified as NP-hard, placing it among the most intractable problems to solve. This paper introduces a novel hybrid…

Quantum Physics · Physics 2024-12-17 Bruna Salgado , André Sequeira , Luis Paulo Santos

The aircraft loading optimization problem is a computationally hard problem with the best known classical algorithm scaling exponentially with the number of objects. We propose a quantum approach based on a multi-angle variant of the QAOA…

The intractability of deterministic solutions in solving $\mathcal{NP}$-Hard Combinatorial Optimisation Problems (COP) is well reported in the literature. One mechanism for overcoming this difficulty has been the use of efficient COP…

Quantum Physics · Physics 2022-04-25 Maxine T. Khumalo , Hazel A. Chieza , Krupa Prag , Matthew Woolway

The Traveling Salesperson Problem (TSP), a quintessential NP-hard combinatorial optimisation challenge, is vital for logistics and network design but limited by exponential complexity in large instances. We propose a hybrid…

Quantum Physics · Physics 2025-10-01 Christos Lytrosyngounis , Ioannis Lytrosyngounis

Hybrid quantum-classical algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such…

In the present Noisy Intermediate-Scale Quantum (NISQ), hybrid algorithms that leverage classical resources to reduce quantum costs are particularly appealing. We formulate and apply such a hybrid quantum-classical algorithm to a power…

Many relevant problems in industrial settings result in NP-hard optimization problems, such as the Capacitated Vehicle Routing Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP). Even with today's most powerful…

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