Quantum Relaxation for Solving Multiple Knapsack Problems

• URL: http://arxiv.org/abs/2404.19474v2
• Date: Tue, 30 Jul 2024 08:35:21 GMT
• Title: Quantum Relaxation for Solving Multiple Knapsack Problems
• Authors: Monit Sharma, Yan Jin, Hoong Chuin Lau, Rudy Raymond,
• Abstract summary: Combinatorial problems are a common challenge in business, requiring finding optimal solutions under specified constraints. In this study, we investigate a hybrid quantum-classical method for constrained optimization problems. Our proposed method relies on relaxations to local quantum Hamiltonians, defined through commutative maps.
• Score: 7.003282322403712
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Combinatorial problems are a common challenge in business, requiring finding optimal solutions under specified constraints. While significant progress has been made with variational approaches such as QAOA, most problems addressed are unconstrained (such as Max-Cut). In this study, we investigate a hybrid quantum-classical method for constrained optimization problems, particularly those with knapsack constraints that occur frequently in financial and supply chain applications. Our proposed method relies firstly on relaxations to local quantum Hamiltonians, defined through commutative maps. Drawing inspiration from quantum random access code (QRAC) concepts, particularly Quantum Random Access Optimizer (QRAO), we explore QRAO's potential in solving large constrained optimization problems. We employ classical techniques like Linear Relaxation as a presolve mechanism to handle constraints and cope further with scalability. We compare our approach with QAOA and present the final results for a real-world procurement optimization problem: a significant sized multi-knapsack-constrained problem.

Related papers

• Parallel Quantum Local Search via Evolutionary Mechanism [0.9208007322096533]
  We propose an innovative Parallel Quantum Local Search (PQLS) methodology that leverages the capabilities of small-scale quantum computers. Our approach transcends this constraint by simultaneously executing multiple QLS pathways and aggregating their most effective outcomes at certain intervals to establish a generation'' Our findings demonstrate the profound impact of parallel quantum computing in enhancing the resolution of Ising problems.
  arXiv  Detail & Related papers  (2024-06-10T16:35:52Z)
• Q-CHOP: Quantum constrained Hamiltonian optimization [2.7022651232296946]
  We propose a new quantum algorithm for constrained optimization, which we call quantum constrained Hamiltonian optimization (Q-CHOP) The basic idea is to enforce a Hamiltonian constraint at all times, thereby restricting evolution to the subspace of feasible states. We benchmark Q-CHOP against the commonly-used adiabatic algorithm with constraints enforced using a penalty term.
  arXiv  Detail & Related papers  (2024-03-08T20:03:59Z)
• Optimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methods [52.0617030129699]
  We introduce a novel theoretical framework for analyzing the effectiveness of DeepMatching Networks and Reinforcement Learning methods. Our main contribution holds for a broad class of problems including Max-and Min-Cut, Max-$k$-Bipartite-Bi, Maximum-Weight-Bipartite-Bi, and Traveling Salesman Problem. As a byproduct of our analysis we introduce a novel regularization process over vanilla descent and provide theoretical and experimental evidence that it helps address vanishing-gradient issues and escape bad stationary points.
  arXiv  Detail & Related papers  (2023-10-08T23:39:38Z)
• A Hybrid Quantum-Classical Approach to the Electric Mobility Problem [0.8796261172196743]
  We suggest a hybrid quantum-classical routine for the NP-hard Electric Vehicle Fleet Charging and Allocation Problem. We benchmark the performance of the decomposition technique with classical and quantum-inspired metaheuristics. The major advantage of the proposed approach is that it enables quantum-based methods for this realistic problem with many inequality constraints.
  arXiv  Detail & Related papers  (2023-10-04T12:14:56Z)
• Quantum-Assisted Solution Paths for the Capacitated Vehicle Routing Problem [0.0]
  We discuss the Capacitated Vehicle Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP) Even with today's most powerful classical algorithms, the CVRP is challenging to solve classically. Quantum computing may offer a way to improve the time to solution.
  arXiv  Detail & Related papers  (2023-04-19T13:03:50Z)
• Multiobjective variational quantum optimization for constrained problems: an application to Cash Management [45.82374977939355]
  We introduce a new method for solving optimization problems with challenging constraints using variational quantum algorithms. We test our proposal on a real-world problem with great relevance in finance: the Cash Management problem. Our empirical results show a significant improvement in terms of the cost of the achieved solutions, but especially in the avoidance of local minima.
  arXiv  Detail & Related papers  (2023-02-08T17:09:20Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines [81.4597482536073]
  Quantum approximate optimization algorithms (QAOAs) utilize the power of quantum machines and inherit the spirit of adiabatic evolution. We propose QAOA-in-QAOA ($textQAOA2$) to solve arbitrary large-scale MaxCut problems using quantum machines. Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale optimization problems.
  arXiv  Detail & Related papers  (2022-05-24T03:49:10Z)
• Classically-Boosted Quantum Optimization Algorithm [0.0]
  We explore a natural approach to leveraging existing classical techniques to enhance quantum optimization. Specifically, we run a classical algorithm to find an approximate solution and then use a quantum circuit to search its "neighborhood" for higher-quality solutions. We demonstrate the applications of CBQOA to Max 3SAT and Max Bisection, and provide empirical evidence that it outperforms previous approaches on these problems.
  arXiv  Detail & Related papers  (2022-03-25T23:36:14Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as 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 algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.