Linearization via Ordering Variables in Binary Optimization for Ising Machines

Ising machines are next-generation computers expected for efficiently sampling near-optimal solutions of combinatorial oprimization problems. Combinatorial optimization problems are modeled as quadratic unconstrained binary optimization (QUBO) problems to apply an Ising machine. However, current state-of-the-art Ising machines still often fail to output near-optimal solutions due to the complicated energy landscape of QUBO problems. Furthermore, physical implementation of Ising machines severely restricts the size of QUBO problems to be input as a result of limited hardware graph structures. In this study, we take a new approach to these challenges by injecting auxiliary penalties preserving the optimum, which reduces quadratic terms in QUBO objective functions. The process simultaneously simplifies the energy landscape of QUBO problems, allowing search for near-optimal solutions, and makes QUBO problems sparser, facilitating encoding into Ising machines with restriction on the hardware graph structure. We propose linearization via ordering variables of QUBO problems as an outcome of the approach. By applying the proposed method to synthetic QUBO instances and to multi-dimensional knapsack problems, we empirically validate the effects on enhancing minor embedding of QUBO problems and performance of Ising machines.Comment: 19 pages. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Hybrid Optimization Method Using Simulated-Annealing-Based Ising Machine and Quantum Annealer

Ising machines have the potential to realize fast and highly accurate solvers for combinatorial optimization problems. They are classified based on their internal algorithms. Examples include simulated-annealing-based Ising machines (non-quantum-type Ising machines) and quantum-annealing-based Ising machines (quantum annealers). Herein we propose a hybrid optimization method, which utilizes the advantages of both types. In this hybrid optimization method, the preprocessing step is performed by solving the non-quantum-annealing Ising machine multiple times. Then sub-Ising models with a reduced size by spin fixing are solved using a quantum annealer. The performance of the hybrid optimization method is evaluated via simulations using Simulated Annealing (SA) as a non-quantum-type Ising machine and D-Wave Advantage as a quantum annealer. Additionally, we investigate the parameter dependence of the proposed hybrid optimization method. The hybrid optimization method outperforms the preprocessing SA and the quantum annealing machine alone in fully connected random Ising models.Comment: 6 pages, 6 figure

Fast Hyperparameter Tuning for Ising Machines

In this paper, we propose a novel technique to accelerate Ising machines hyperparameter tuning. Firstly, we define Ising machine performance and explain the goal of hyperparameter tuning in regard to this performance definition. Secondly, we compare well-known hyperparameter tuning techniques, namely random sampling and Tree-structured Parzen Estimator (TPE) on different combinatorial optimization problems. Thirdly, we propose a new convergence acceleration method for TPE which we call "FastConvergence".It aims at limiting the number of required TPE trials to reach best performing hyperparameter values combination. We compare FastConvergence to previously mentioned well-known hyperparameter tuning techniques to show its effectiveness. For experiments, well-known Travel Salesman Problem (TSP) and Quadratic Assignment Problem (QAP) instances are used as input. The Ising machine used is Fujitsu's third generation Digital Annealer (DA). Results show, in most cases, FastConvergence can reach similar results to TPE alone within less than half the number of trials.Comment: This work has been submitted and accepted at IEEE ICCE2023. Copyright will be transferred to IEEE, please cite the DOI on IEEExplore once read