Optimization by Record Dynamics

TL;DR

This paper introduces Record Dynamics Optimization (RDO), a new local search algorithm inspired by barrier-crossing behavior in glassy systems, and demonstrates its effectiveness in solving spin-glass ground state problems compared to Parallel Tempering.

Contribution

The paper presents RDO, a novel optimization algorithm based on record dynamics, which is simpler to implement and provides insights into the configuration space structure.

Findings

RDO achieves solution quality comparable to Parallel Tempering.

RDO offers additional geometrical information about the configuration space.

The effectiveness of RDO supports the hierarchical organization of the system's configuration space.

Abstract

Large dynamical changes in thermalizing glassy systems are triggered by trajectories crossing record sized barriers, a behavior revealing the presence of a hierarchical structure in configuration space. The observation is here turned into a novel local search optimization algorithm dubbed Record Dynamics Optimization, or RDO. RDO uses the Metropolis rule to accept or reject candidate solutions depending on the value of a parameter akin to the temperature, and minimizes the cost function of the problem at hand through cycles where its `temperature' is raised and subsequently decreased in order to expediently generate record high (and low) values of the cost function. Below, RDO is introduced and then tested by searching the ground state of the Edwards-Anderson spin-glass model, in two and three spatial dimensions. A popular and highly efficient optimization algorithm, Parallel Tempering (PT) is applied to the same problem as a benchmark. RDO and PT turn out to produce solution of similar quality for similar numerical effort, but RDO is simpler to program and additionally yields geometrical information on the system's configuration space which is of interest in many applications. In particular, the effectiveness of RDO strongly indicates the presence of the above mentioned hierarchically organized configuration space, with metastable regions indexed by the cost (or energy) of the transition states connecting them.