Local Energy Distribution Based Hyperparameter Determination for Stochastic Simulated Annealing

Abstract

This paper presents a local energy distribution based hyperparameter determination for stochastic simulated annealing (SSA). SSA is capable of solving combinatorial optimization problems faster than typical simulated annealing (SA), but requires a time-consuming hyperparameter search. The proposed method determines hyperparameters based on the local energy distributions of spins (probabilistic bits). The spin is a basic computing element of SSA and is graphically connected to other spins with its weights. The distribution of the local energy can be estimated based on the central limit theorem (CLT). The CLT-based normal distribution is used to determine the hyperparameters, which reduces the time complexity for hyperparameter search from $\mathcal {O}(n^{3})$ of the conventional method to $\mathcal {O}(1)$. The performance of SSA with the determined hyperparameters is evaluated on the Gset and K2000 benchmarks for maximum-cut problems. The results show that the proposed method achieves mean cut values of approximately 98% of the best-known cut values.

Keywords

• Combinatorial optimization
• Hamiltonian
• Ising model
• maximum-cut problem
• simulated annealing
• stochastic computing