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IEEE International Conference on Quantum Computing and Engineering (QCE)

Evaluating Quantum Annealing for Grouping Optimization with all Members' Compatibility

Kazuhiro Saito, Akihiro Kobayashi, Yuichi Ishikawa

Published Sep 1, 2022• 1 citation
Publisher

Abstract

Quantum annealing is a novel computing approach expected to rapidly solve combinatorial optimization problems. Grouping optimization problem is one of the combinatorial optimization problems that maximize group effectiveness by composing groups based on member's attributes, personality, and compatibility. There is no model for the grouping problem where the group effectiveness is calculated by compatibility of three or more members. In this paper, we formulate a general model of the grouping optimization for quantum annealing, and evaluate it assuming collaborative learning on quantum annealing machine in comparison with simulated annealing and hill climbing.

DOI
10.1109/qce53715.2022.00114

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Quantum annealing is a novel computing approach expected to rapidly solve combinatorial optimization problems. Grouping optimization problem is one of the combinatorial optimization problems that maximize group effectiveness by composing groups based on member's attributes, personality, and compatibility. There is no model for the grouping problem where the group effectiveness is calculated by compatibility of three or more members. In this paper, we formulate a general model of the grouping optimization for quantum annealing, and evaluate it assuming collaborative learning on quantum annealing machine in comparison with simulated annealing and hill climbing.
Quantum annealing (QA) is a novel computing approach for solving computationally demanding problems more rapidly than approaches using classical computers by exploiting parallelism in the variable state updates (spin updates). A number of previous studies have shown that QA performs well in benchmarking combinatorial optimization problems, but no works have evaluated QA in the shift scheduling problem. This paper formulates it for QA and evaluates the effectiveness of QA in comparison with other methods on a classical computer. We confirmed that QA is up to about 14 times faster than classical methods in obtaining high-quality solutions for several instances.
This paper investigates the application of quantum annealing for solving complex combinatorial optimization problems. The core claim is that quantum annealing leverages its global search capabilities to efficiently address such problems. The proposed mechanism involves formulating the combinatorial optimization problem as a quantum annealing problem and utilizing the simulated annealing process within quantum annealing to conduct a search for the optimal solution. This research explores the potential of quantum annealing in practical applications, acknowledging that its application in combinatorial optimization is still in its exploratory phase. The algorithm is designed to minimize the energy of a system described by a Hamiltonian, which evolves over time according to the time-dependent Schrödinger equation. The core of the algorithm lies in mapping the problem's constraints and objective function into this Hamiltonian. The search process is governed by quantum fluctuations, represented by the operator H^\hat{H}H^, which encourages transitions to lower energy states, effectively navigating the solution space. The effectiveness of the algorithm is evaluated based on the quality of the solution found and the computational resources required. This work provides a foundational exploration of quantum annealing's potential within the field of combinatorial optimization.
This paper investigates the application of quantum annealing to solve combinatorial optimization problems. The core claim is that quantum annealing algorithms can effectively enhance the efficiency and accuracy of solving such problems. The underlying mechanism involves simulating the quantum annealing process, leveraging the quantum tunneling effect to explore the solution space and identify optimal solutions. This work presents a novel approach by applying quantum annealing to combinatorial optimization, offering a fresh perspective on problem-solving. We explore the theoretical foundations, model the annealing process, and discuss potential challenges and future research directions. The focus is on demonstrating the feasibility and potential benefits of this approach rather than presenting results from experimental implementations.
A combinatorial optimization problem is the problem of minimizing the energy function among many combinations of variables, which is often difficult to solve with conventional classical computers. Recently, Ising machines, including quantum annealers, have gained attention as a promising architecture for efficiently solving combinatorial optimization problems. Among various methods for solving such problems using Ising machines, one prominent approach is the three-stage annealing method. The approach effectively solves a combinatorial optimization problem, utilizing an initial solution, but it performs the annealing process only once. Repeating the annealing process several times may enhance the solution more efficiently. In this paper, we propose a novel hybrid iterative annealing method that consists of an initial process using a classical computer, an annealing process using a quantum annealer, and a correction process/selection process using a classical computer. The proposed method repeats the annealing process and the correction process/selection process until the solution is sufficiently converged. In the experimental evaluations through the three types of typical combinatorial optimization problems, the proposed method shows improvements by up to 54.0% compared to the three-stage annealing method.
This paper presents an adaptive quantum annealing algorithm designed to improve the performance of quantum annealing in solving combinatorial optimization problems. Traditional quantum annealing relies on a fixed annealing schedule, which may not be optimal for all problems. This work introduces a novel approach that utilizes reinforcement learning to dynamically adjust the annealing parameters during the annealing process, based on the observed progress towards a solution. The algorithm learns an optimal annealing schedule by interacting with the quantum annealing system, maximizing the probability of finding a good solution within a given time limit. We demonstrate the theoretical framework and outline the core components of the adaptive algorithm, highlighting its potential advantages over conventional fixed-schedule quantum annealing. The key performance metric is the solution quality (e.g., objective function value) achieved after annealing. The algorithm's effectiveness is evaluated through conceptual analysis and design considerations. This approach aims to bridge the gap between the theoretical potential of quantum annealing and its practical application in solving real-world combinatorial optimization challenges.
A combinatorial optimization problem is the problem of minimizing the energy function among many combinations of variables, which is often difficult to solve with conventional classical computers. Recently, Ising machines, including quantum annealers, have gained attention as a promising architecture for efficiently solving combinatorial optimization problems. Among various methods for solving such problems using Ising machines, one prominent approach is the three-stage annealing method. The approach effectively solves a combinatorial optimization problem, utilizing an initial solution, but it performs the annealing process only once. Repeating the annealing process several times may enhance the solution more efficiently. In this paper, we propose a novel hybrid iterative annealing method that consists of an initial process using a classical computer, an annealing process using a quantum annealer, and a correction process/selection process using a classical computer. The proposed method repeats the annealing process and the correction process/selection process until the solution is sufficiently converged. In the experimental evaluations through the two types of typical combinatorial optimization problems, the proposed method shows improvements by up to 50.5% compared to the three-stage annealing method.