Work

Solving combinatorial optimization problems through stochastic Landau-Lifshitz-Gilbert dynamical systems

Year: 2025

Type: article

Abstract: We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of three-dimensional (3D) rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization problems that use simple continuous relaxation of the objective function followed by gradient-descent minimization are inherently unable to avoid local optima, thus producing poor-quality solutions. Our method considers the physical dynamics of macrospins capable of escaping from local minima, thus facilitating the discovery of high-quality, nearly optimal solutions, as supported by extensive numerical simulations on a prototypical quadratic unconstrained binary optimization (QUBO) problem. Our method produces solutions that compare favorably with those obtained using state-of-the-art minimization algorithms (such as simulated annealing) while offering the advantage of being physically realizable by means of arrays of stochastic magnetic tunnel-junction devices.

Source: Physical Review Research

DOI: 10.1103/physrevresearch.7.013129

Authors: Dairong Chen, Andrew D. Kent, Dries Sels, Flaviano Morone

Institutions: New York University, Flatiron Institute

Language: English

Topic: Metaheuristic Optimization Algorithms Research

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funders: New York University, Flatiron Health, Office of Naval Research, Air Force Office of Scientific Research