Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial optimization

Area of Science:

• Computational physics
• Optimization algorithms
• Machine learning

Background:

• Combinatorial optimization problems are widespread in industry but computationally challenging.
• Mapping these problems to Ising models has driven the development of specialized solvers.
• Recent quantum and classical computing advances offer new approaches to optimization.

Purpose of the Study:

• To benchmark various physics-inspired optimization algorithms.
• To compare their performance against simulated annealing on Ising problems.
• To investigate the impact of numerical methods and network structures on performance.

Main Methods:

• Benchmarking coherent Ising machines, gain-dissipative algorithms, simulated bifurcation machines, and Hopfield networks.
• Utilizing random Ising problems with planted solutions for evaluation.
• Comparing performance against simulated annealing using a unified software stack.
• Analyzing the effects of different numerical integration techniques and graph connectivities.

Main Results:

• Performance evaluation of stochastic driven nonlinear dynamical systems against simulated annealing.
• Identification of factors influencing algorithm efficiency, such as numerical integration and graph topology.
• Comparative analysis of novel optimization paradigms for Ising-type problems.

Conclusions:

• Physics-inspired algorithms offer alternative approaches to solving hard optimization problems.
• Understanding the influence of numerical and structural parameters is crucial for algorithm selection.
• This work provides a valuable overview of emerging optimization paradigms.