The binary Paint Shop Problem (BPSP) is a combinatorial optimization problem which draws inspiration from the automotive paint shop. Its binary nature, making it a good fit for quadraticunconstrainedbinary Optimizat...
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The binary Paint Shop Problem (BPSP) is a combinatorial optimization problem which draws inspiration from the automotive paint shop. Its binary nature, making it a good fit for quadratic unconstrained binary optimization (QUBO) solvers, has been well studied but its industrial applications are limited. In this paper, in order to expand the industrial applications, QUBO formulations for two generalizations of the BPSP, which are the Multi-Car Paint Shop Problem (MCPSP) and the Multi-Car Multi-Color Paint Shop Problem (MCMCPSP), are proposed. Given the multiple colors, the MCMCPSP is no longer natively binary which increases the problem size and introduces additional constraint factors in the QUBO formulation. Resulting QUBOs are solved using Scatter Search (SS). Furthermore, extensions of the SS that can exploit k-hot constrained structures within the formulations are proposed to compensate the additional complexity introduced by formulating non-binary problems into QUBO. Since no public benchmark database currently exists, random problem instances are generated. Viability of the proposed QUBO solving methods for the MCPSP and MCMCPSP, is highlighted through comparison with an integer-based Random Parallel Multi-start Tabu Search (RPMTS) and a greedy heuristic for the problems. The greedy heuristic has negligible computational requirements and therefore serves as a lower bound on the desired performance. The results for both problems show that better results can be obtained than the greedy heuristic and integer-based RPMTS, by using the novel k-hot extensions of the SS to solve the problems as QUBO.
In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to quadratic unconstrained binary optimization (QUBO) problems. In this form, a solution for a QUBO problem involves min...
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In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to quadratic unconstrained binary optimization (QUBO) problems. In this form, a solution for a QUBO problem involves minimizing a quadratic function over binary variables (0/1), where the coefficients can be represented by a symmetric square matrix (or an equivalent upper triangular version). With the QUBO formulation, exploiting new computing architectures, such as Quantum and Digital Annealers, is possible. A more conventional approach consists of developing approximate solvers, which, in this case, are used to tackle the intrinsic complexity. We performed tests to prove the correctness and applicability of classical problems in argumentation and enforcement of argument sets. We compared our approach to two other approximate solvers in the literature during tests. In the final experimentation, we used a Simulated Annealing algorithm on a local machine. Also, we tested a Quantum Annealer from the D-Wave Ocean SDK and the Leap (TM) Quantum Cloud Service.
Quantum annealing has the potential to outperform classical transistor-based computer technologies in tackling intricate combinatorial optimization problems. However, ongoing scientific debates cast doubts on whether ...
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Quantum annealing has the potential to outperform classical transistor-based computer technologies in tackling intricate combinatorial optimization problems. However, ongoing scientific debates cast doubts on whether quantum annealing devices (or quantum annealers) can genuinely provide better problem-solving capabilities than classical computers. The question of whether quantum annealing algorithms (QAAs) running on quantum annealers have computational advantages over classical algorithms (CAs) running on classical computers still remains unclear. This paper aims to clarify the question by classifying and benchmarking QAAs that utilize quadratic unconstrained binary optimization (QUBO) formulas to solve NP-hard problems. It proposes a four-class classification of QUBO formulas and exemplifies each class by QUBO formulas used by QAAs for solving specific NP-hard problems, such as the subset sum, maximum cut, vertex cover, 0/1 knapsack, graph coloring, Hamiltonian cycle, traveling salesperson, and job shop scheduling problems. The classification is based on the following two criteria: (i) Does the number of QUBO variables scale linearly with the problem input size? (ii) Does the QUBO formula have both the constraint term and the optimization term? QAAs are implemented and run on a D-Wave quantum annealer for benchmarking. They are benchmarked against related CAs in terms of the quality of the solution and the time to the solution. The benchmarking results reveal which classes of QUBO formulas are likely to provide advantages to QAAs over CAs. Furthermore, based on the benchmarking results, observations and suggestions are given for each class of QUBO formulas, facilitating the adoption of appropriate actions to improve the performance of QAAs.
Quantum annealers offer a promising approach to solve quadratic unconstrained binary optimization (QUBO) problems, which have a wide range of applications. However, when a user submits its QUBO problem to a third-part...
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ISBN:
(纸本)9798331541378
Quantum annealers offer a promising approach to solve quadratic unconstrained binary optimization (QUBO) problems, which have a wide range of applications. However, when a user submits its QUBO problem to a third-party quantum annealer, the problem itself may disclose the user's private information to the quantum annealing service provider. To mitigate this risk, we introduce a privacy-preserving QUBO framework and propose a novel solution method. Our approach employs a combination of digit-wise splitting and matrix permutation to obfuscate the QUBO problem's model matrix Q, effectively concealing the matrix elements. In addition, based on the solution to the obfuscated version of the QUBO problem, we can reconstruct the solution to the original problem with high accuracy. Theoretical analysis and empirical tests confirm the efficacy and efficiency of our proposed technique, demonstrating its potential for preserving user privacy in quantum annealing services.
We simulate Quantum Annealing on a variational manifold defined by a parametric family of wavefunctions represented by a Restricted Boltzmann Machine architecture. By iteratively lowering the transverse field and opti...
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ISBN:
(纸本)9798331541378
We simulate Quantum Annealing on a variational manifold defined by a parametric family of wavefunctions represented by a Restricted Boltzmann Machine architecture. By iteratively lowering the transverse field and optimizing the neural network parameters, we prove the effectiveness of our methods for a challenging class of real-world quadratic unconstrained binary optimization (QUBO) instances, namely the Job Shop Scheduling Problem. Our methods outperform a straightforward optimization of the same problem without simulated quantum fluctuations. Despite the QUBO model being equivalent to a frustrated Ising spin glass, we obtain exact solutions up to 50-100 binary variables and empirically outperform results obtained with D -Wave quantum annealers.
Routing and wavelength assignment with protection is an important problem in telecommunications. Given an optical network and incoming connection requests, a commonly studied variant of the problem aims to grant a max...
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Routing and wavelength assignment with protection is an important problem in telecommunications. Given an optical network and incoming connection requests, a commonly studied variant of the problem aims to grant a maximum number of requests by assigning lightpaths with minimum network resource usage, while ensuring the provided services remain functional in the case of a single-link failure through dedicated protection paths. We consider a version where alternative lightpaths for requests are assumed to be given as a precomputed set and show that it is NP-hard. We formulate the problem as an Integer Programming (IP) model and also use it as a foundation to develop a quadratic unconstrained binary optimization (QUBO) model. We present necessary and sufficient conditions on objective function parameters to prioritize request granting objective over wavelength-link usage for both models, and a sufficient condition ensuring the exactness of the QUBO model. Moreover, we implement a problem-specific branch-and-cut algorithm for the IP model and employ a new quantum-inspired technology, Digital Annealer (DA), for the QUBO model. We conduct computational experiments on a large suite of nontrivial instances to assess the efficiency and efficacy of all of these approaches as well as two problem-specific heuristics. Although the objective penalty coefficient values that guarantee the exactness of the QUBO model were outside the acceptable range for DA, it always yielded feasible solutions even with smaller values in practice. The results show that the emerging technology DA outperforms the considered techniques coupled with GUROBI in finding mostly significantly better or as good solutions in two minutes compared to two-hour run time, whereas problem-specific heuristics fail to be competitive.
quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (Q...
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ISBN:
(纸本)9781665437868
quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (QA). We present a toolkit of methods to transform almost arbitrary problems to QUBO by (i) approximating them as a polynomial and then (ii) translating any polynomial to QUBO. We showcase the usage of our approaches on two example problems (ratio cut and logistic regression).
Many quantum computing algorithms are being developed with the advent of quantum computers. Solving linear systems is one of the most fundamental problems in almost all of science and engineering. HHL algorithm, a mon...
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ISBN:
(数字)9781510642904
ISBN:
(纸本)9781510642904
Many quantum computing algorithms are being developed with the advent of quantum computers. Solving linear systems is one of the most fundamental problems in almost all of science and engineering. HHL algorithm, a monumental quantum algorithm for solving linear systems on the gate model quantum computers, was invented and several advanced variations have been developed. However, HHL-based algorithms have a lot of limitations in spite of their importance. We address solving linear systems on a D-Wave quantum annealing device. To formulate a quadratic unconstrained binary optimization (QUBO) model for a linear system solving problem, we make use of a linear least-square problem with binary representation of the solution. We validate this QUBO model on the D-Wave system and discuss the results.
The quadratic unconstrained binary optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely diffic...
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The quadratic unconstrained binary optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In order to incorporate the problemspecific insights, a diverse set of solutions meeting an acceptable target metric or goal is the preference in high level decision making. In this paper, we present two alternatives for goalseeking QUBO for minimizing the deviation from a given target as well as a range of values around a target. Experimental results illustrate the efficacy of the proposed approach over Constraint Programming for quickly finding a satisficing set of solutions.
A long-standing challenge in the metaheuristic literature is to devise a way to select parent solutions in evolutionary population-based algorithms to yield better offspring, and thus provide improved solutions to pop...
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A long-standing challenge in the metaheuristic literature is to devise a way to select parent solutions in evolutionary population-based algorithms to yield better offspring, and thus provide improved solutions to populate successive generations. We identify a way to achieve this goal that simultaneously improves the efficiency of the evolutionary process. Our strategy derives from a proposal associated with the scatter search and path relinking evolutionary algorithms that prescribes clustering the solutions and focusing on the two classes of solution combinations where the parents alternatively belong to the same cluster or to different clusters. We demonstrate the efficacy of our approach for selecting parents within this scheme by applying it to the important domain of quadratic unconstrained binary optimization (QUBO), which provides a model for solving a wide range of binaryoptimization problems. Within this setting, we focus on the path relinking algorithm, which together with tabu search has provided one of the most effective methods for QUBO problems. Computational tests disclose that our solution combination strategy improves the best results in the literature for hard QUBO instances.
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