A Multiple Coefficients Trial Method to Solve Combinatorial Optimization Problems for Simulated-annealing-based Ising Machines

Kota, Takehara; Oku, Daisuke; Matsuda, Yoshiki; Tanaka, Shu; Togawa, Nozomu

doi:10.1109/icce-berlin47944.2019.8966167

Cited by 8 publications

(6 citation statements)

References 10 publications

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“…The penalty function is constructed by L2 regularization [36] which is an equally weighted sum of 2N errors measured by the L2-distance from the feasible region. The ground states of the penalty function are a set of states satisfying the 2N one-hot constraint [28], [46]. QUBO can be mapped to the isomorphic Ising problem and solved by finding the ground state of a total Hamiltonian ℋ of the form in eq.…”

Section: A Qubo Problemmentioning

confidence: 99%

“…QUBO can be mapped to the isomorphic Ising problem and solved by finding the ground state of a total Hamiltonian ℋ of the form in eq. ( 11) [46]. ℋ describes the Hamiltonian of the Ising spins that have linear terms in spin variables associated with external fields acting on each spin and the quadratic terms associated with interactions between two spins.…”

Section: A Qubo Problemmentioning

confidence: 99%

“…We prepared the local field strength and the coupling coefficient between spins using normalized matrix 𝑑 * according to the prescription given in Refs. [28] and [46]. Explicit forms of ℋ 𝑐 (𝒔) and ℋ 𝑝 (𝒔) are given as follows:…”

Section: A Qubo Problemmentioning

confidence: 99%

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Rejection-Free Monte Carlo Simulation of QUBO and Lechner–Hauke–Zoller Optimization Problems

Nambu

2022

IEEE Access

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Many studies have attempted to develop simple and efficient methods for solving global optimization problems. Simulated annealing (SA) has been recognized as a powerful tool for performing this task. In this study, we implemented a rejection-free Monte Carlo (RFMC) algorithm, which is a kernel of rejection-free SA (RFSA). We showed its validity and advantage in obtaining globally optimal solution for quadratic unconstrained binary optimization (QUBO) and spin-glass problem embedded in the Lechner-Hauke-Zoller (LHZ) architecture. Landscapes of success probabilities of finding the globally optimal solution as well as feasible solutions were evaluated as a function of a set of hyper-parameters used to characterize the weights of cost and penalty functions. We demonstrated that the efficiency of RFMC was greatly enhanced compared to that of standard MC. Furthermore, we found that the landscapes for QUBO and those for LHZ problem show considerably different views. When we focus on a specific class of problems, the smaller the problem size, the more scattered is the success probability. We also show that the success probabilities can be further improved by avoiding inefficiencies due to cycling of state transitions using short-term memory mechanisms. We suggest a reasonable strategy to tune hyper-parameters and find the correct global solution using RFSA.

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Section: A Qubo Problemmentioning

confidence: 99%

Section: A Qubo Problemmentioning

confidence: 99%

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Rejection-Free Monte Carlo Simulation of QUBO and Lechner–Hauke–Zoller Optimization Problems

Nambu

2022

IEEE Access

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“…Especially, PyQUBO is a software package that supports these formulations [19]. Also, the method to determine the hyperparameters used in the formulations has been proposed [20]. In Phase 2, a logical Ising model is embedded onto a physical Ising model (or a real annealing machine).…”

Section: Introductionmentioning

confidence: 99%

How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins

Oku

Tawada

Tanaka

et al. 2022

IEEE Trans. Comput.

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“…The idea behind this is that, if a TSP solution is penalised by the maximum distance between any two cities, feasibility of the optimal solution can always be achieved. In Takehara et al [2019], the authors used a multi-trial approach. The values used were within a range de ned using the minimum and the maximum distance between any two locations.…”

Section: Introductionmentioning

confidence: 99%

Penalty Weights in QUBO Formulations: Permutation Problems

Ayodele

2022

Lecture Notes in Computer Science

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Optimisation algorithms designed to work on quantum computers or other specialised hardware have been of research interest in recent years. Commercial solvers that use quantum or quantuminspired methods, such as Fujitsu's Digital Annealer (DA) and D-wave's Quantum Annealer, can solve optimisation problems faster than algorithms implemented on general purpose computers. However, they can only optimise problems that are in binary and quadratic form. Quadratic Unconstrained Binary Optimisation (QUBO) is therefore a common formulation used by these solvers. There are many combinatorial optimisation problems that are naturally represented as permutations e.g. travelling salesman problem. Encoding permutation problems using binary variables however presents some challenges. Many QUBO solvers are single ip solvers, it is therefore possible to generate solutions that cannot be decoded to a valid permutation. To create bias towards generating feasible solutions, we use penalty weights. The process of setting static penalty weights for various types of problems is not trivial. This is because values that are too small will lead to infeasible solutions being returned by the solver while values that are too large may lead to slower convergence. In this study, we explore some methods of setting penalty weights within the context of QUBO formulations. We propose new static methods of calculating penalty weights which lead to more promising results than existing methods.

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A Multiple Coefficients Trial Method to Solve Combinatorial Optimization Problems for Simulated-annealing-based Ising Machines

Cited by 8 publications

References 10 publications

Rejection-Free Monte Carlo Simulation of QUBO and Lechner–Hauke–Zoller Optimization Problems

Rejection-Free Monte Carlo Simulation of QUBO and Lechner–Hauke–Zoller Optimization Problems

How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins

Penalty Weights in QUBO Formulations: Permutation Problems

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