Solving Inequality-Constrained Binary Optimization Problems on Quantum Annealer

Yonaga, Kouki; Miyama, Masamichi J.; Ohzeki, Masayuki

doi:10.48550/arxiv.2012.06119

Cited by 6 publications

(6 citation statements)

References 19 publications

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“…The second is to optimize using the augmented Lagrangian method and alternating direction method of multipliers (ADMM) without introducing slack variables. Yonaga et al [29] defined an extended Lagrangian by introducing an auxiliary variable in the objective function and proposed a method to obtain a feasible solution while updating the auxiliary variable by applying quantum annealing to QUBO within the ADMM algorithm. This is effective when using quantum annealing because it does not use slack variables, but the computation time increases owing to iterative calculations.…”

Section: H Num : Constraint Term On the Number Of Cluster Elementsmentioning

confidence: 99%

Quantum annealing for the adjuster routing problem

Môri¹,

Furukawa²

2023

Front. Phys.

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In the event of a disaster such as an earthquake, insurance companies basically conduct on-site witnessing. Depending on the scale of the disaster, hundreds of adjusters are dispatched from each office to the affected buildings per day. In such cases, which adjusters will witness which buildings and in what order must be determined, and the route must be optimized to conduct efficient witnessing. In this study, we define this witnessing route decision as an optimization problem and propose the adjuster routing problem (ARP). The ARP can be viewed as an extension of the vehicle routing problem (VRP). We introduce constraints not to be considered in the usual VRP, such as adjuster-building matching and satisfying the desired time. The VRP is an NP-hard optimization problem and is considered difficult to solve on a classical computer. Therefore, we formulated various constraints in QUBO so that quantum annealing can be applied to the ARP. In addition, we conducted numerical experiments with D-Wave. The ARP is a real problem, and our research provides a new example of applications of quantum annealing to real-world problems.

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Section: H Num : Constraint Term On the Number Of Cluster Elementsmentioning

confidence: 99%

Quantum annealing for the adjuster routing problem

Môri¹,

Furukawa²

2023

Front. Phys.

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“…Theoretical background to transform fully connected interactions of quadratic terms into linear terms is present in literature 35,36 . The resulting reformulation has a traditional counterpart in the Lagrangian relaxation of constraints.…”

Section: Qubo Formulationsmentioning

confidence: 99%

“…Instead, when comparing scatter-plots with each other, our results are more insightful: using simple linear penalties lead to a decrease of orders of magnitude in the gap |(z s − min s ′ ∈solvers {z ′ s })/ min s∈solvers {z ′ s }| , in x-axis. Previous analyses [35][36][37] , exploiting more involved linearization techniques, focused on problem size reduction, without proposing comparison with different formulations. Our results show that a linear penalization approach is not only useful to overcome limits in problem size, but has an actual impact on the quality of the solutions produced by the D-Wave QPU.…”

Section: Computing Effortmentioning

confidence: 99%

On good encodings for quantum annealer and digital optimization solvers

Ceselli

Premoli

2023

Sci Rep

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Several optimization solvers inspired by quantum annealing have been recently developed, either running on actual quantum hardware or simulating it on traditional digital computers. Industry and academics look at their potential in solving hard combinatorial optimization problems. Formally, they provide heuristic solutions for Ising models, which are equivalent to quadratic unconstrained binary optimization (QUBO). Constraints on solutions feasibility need to be properly encoded. We experiment on different ways of performing such an encoding. As benchmark we consider the cardinality constrained quadratic knapsack problem (CQKP), a minimal extension of QUBO with one inequality and one equality constraint. We consider different strategies of constraints penalization and variables encoding. We compare three QUBO solvers: quantum annealing on quantum hardware (D-Wave Advantage), probabilistic algorithms on digital hardware and mathematical programming solvers. We analyze their QUBO resolution quality and time, and the persistence values extracted in the quantum annealing sampling process. Our results show that a linear penalization of CQKP inequality improves current best practice. Furthermore, using such a linear penalization, persistence values produced by quantum hardware in a generic way allow to match a specific CQKP metric from literature. They are therefore suitable for general purpose variable fixing in core algorithms for combinatorial optimization.

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“…Several practical applications of quantum annealer have been presented across various fields, such as finance [18][19][20] , traffic 21,22 , logistics 23,24 , manufacturing 9,25 , and marketing 26 , as well as in decoding problems 27,28 . Its potential for solving the optimization problem with inequality constraints has been enhanced 29 , especially in the case that is hard to formulate directly 30 . The comparative study of quantum annealer has also been performed for benchmark tests to solve the optimization problems 31 .…”

Section: Introductionmentioning

confidence: 99%

Travel time optimization on multi-AGV routing by reverse annealing

Haba¹,

Ohzeki²,

Tanaka³

2022

Preprint

Self Cite

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Quantum annealing has been actively researched since D-Wave Systems produced the first commercial machine in 2011. Controlling a large fleet of automated guided vehicles is one of the real-world applications utilizing quantum annealing. In this study, we propose a formulation to control the traveling routes to minimize the travel time. We validate our formulation through simulation in a virtual plant and authenticate the effectiveness for faster distribution compared to a greedy algorithm that does not consider the overall detour distance. Furthermore, we utilize reverse annealing to maximize the advantage of the D-Wave's quantum annealer. Starting from relatively good solutions obtained by a fast greedy algorithm, reverse annealing searches for better solutions around them. Our reverse annealing method improves the performance compared to standard quantum annealing alone and performs up to 10 times faster than the strong classical solver, Gurobi. This study extends a use of optimization with general problem solvers in the application of multi-AGV systems and reveals the potential of reverse annealing as an optimizer.

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Solving Inequality-Constrained Binary Optimization Problems on Quantum Annealer

Cited by 6 publications

References 19 publications

Quantum annealing for the adjuster routing problem

Quantum annealing for the adjuster routing problem

On good encodings for quantum annealer and digital optimization solvers

Travel time optimization on multi-AGV routing by reverse annealing

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