Self-Adaptive Ising Machines for Constrained Optimization

2025-01-09

AI Summary

Existing Ising machines solve combinatorial optimization problems with linear constraints (e.g., multidimensional/quadradic knapsack problems) by imposing manually tuned large penalty coefficients, which distort the energy landscape, impede convergence, and degrade solution quality. This work proposes an adaptive Ising machine framework that—uniquely—integrates Lagrangian relaxation with iterative energy shaping to dynamically reshape the energy landscape during search, eliminating the need for predefined hard-constraint penalty terms. Implemented via p-bit–based software simulation, the paradigm balances constraint satisfaction and objective optimization in real time through Lagrangian dual updates. Evaluated on a 300-variable quadratic knapsack problem, our approach achieves superior solution quality compared to Fujitsu’s Digital Annealer and improves sampling efficiency by 7,500×, significantly enhancing robustness and scalability for constrained optimization.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Ising machines (IM) are physics-inspired alternatives to von Neumann architectures for solving hard optimization tasks. By mapping binary variables to coupled Ising spins, IMs can naturally solve unconstrained combinatorial optimization problems such as finding maximum cuts in graphs. However, despite their importance in practical applications, constrained problems remain challenging to solve for IMs that require large quadratic energy penalties to ensure the correspondence between energy ground states and constrained optimal solutions. To relax this requirement, we propose a self-adaptive IM that iteratively shapes its energy landscape using a Lagrange relaxation of constraints and avoids prior tuning of penalties. Using a probabilistic-bit (p-bit) IM emulated in software, we benchmark our algorithm with multidimensional knapsack problems (MKP) and quadratic knapsack problems (QKP), the latter being an Ising problem with linear constraints. For QKP with 300 variables, the proposed algorithm finds better solutions than state-of-the-art IMs such as Fujitsu's Digital Annealer and requires 7,500x fewer samples. Our results show that adapting the energy landscape during the search can speed up IMs for constrained optimization.

Problem

• Ising Machine Efficiency
• Constrained Optimization Problems
• Complex Problem Solving

Innovation

• Self-adjusting Ising Machine
• Quadratic Knapsack Problem
• Performance Enhancement