Problem hardness of diluted Ising models: Population Annealing versus Simulated Annealing

TL;DR

This paper compares population annealing and simulated annealing in solving diluted Ising models, revealing an easy-hard-easy transition in problem difficulty and demonstrating population annealing's superior efficiency near the hardest instances.

Contribution

It introduces a detailed analysis of the problem hardness transition in diluted Ising models and evaluates the efficiency of population annealing versus simulated annealing.

Findings

Population annealing outperforms simulated annealing near the hardness peak.

An easy-hard-easy transition in problem difficulty is observed as dilution varies.

Adaptive inverse temperature schedules improve efficiency and robustness.

Abstract

Population annealing is a variant of the simulated annealing algorithm that improves the quality of the thermalization process in systems with rough free-energy landscapes by introducing a resampling process. We consider the diluted Sherrington-Kirkpatrick Ising model using population annealing to study its efficiency in finding solutions to combinatorial optimization problems. From this study, we find an easy-hard-easy transition in the model hardness as the problem instances become more diluted, and associate this behaviour to the clusterization and connectivity of the underlying Erd\H{o}s-R\'enyi graphs. We calculate the efficiency of obtaining minimum energy configurations and find that population annealing outperforms simulated annealing for the cases close to this hardness peak while reaching similar efficiencies in the easy limits. Finally, it is known that population annealing can be used to define an adaptive inverse temperature annealing schedule. We compare this adaptive method to a linear schedule and find that the adaptive method achieves improved efficiencies while being robust against final temperature miscalibrations.