Self-Adaptive Ising Machines for Constrained Optimization

TL;DR

This paper introduces a self-adaptive Ising machine that dynamically shapes its energy landscape to efficiently solve constrained optimization problems without extensive parameter tuning, outperforming existing methods in benchmarks.

Contribution

A novel self-adaptive Ising machine method that uses Lagrange relaxation to handle constraints, reducing the need for large penalty tuning and improving solution quality and efficiency.

Findings

Outperforms state-of-the-art IMs on quadratic knapsack problems

Requires 7,500x fewer samples than existing methods

Speeds up constrained optimization via adaptive energy landscape shaping

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.