Single temperature for Monte Carlo optimization on complex landscapes

TL;DR

This paper introduces a novel Monte Carlo optimization strategy that uses landscape statistics to set a single optimal temperature, outperforming traditional methods in complex, rugged landscapes.

Contribution

It presents a new approach for MC optimization that explicitly matches temperature to landscape irregularities, improving efficiency over existing algorithms.

Findings

Single-temperature MC outperforms other MC algorithms in certain landscapes.

The method effectively identifies optimal temperature based on landscape statistics.

Results suggest relevance to biological processes like protein folding.

Abstract

We propose a new strategy for Monte Carlo (MC) optimization on rugged multidimensional landscapes. The strategy is based on querying the statistical properties of the landscape in order to find the temperature at which the mean first passage time across the current region of the landscape is minimized. Thus, in contrast to other algorithms such as simulated annealing (SA), we explicitly match the temperature schedule to the statistics of landscape irregularities. In cases where this statistics is approximately the same over the entire landscape, or where non-local moves couple distant parts of the landscape, single-temperature MC will outperform any other MC algorithm with the same move set. We also find that in strongly anisotropic Coulomb spin glass and traveling salesman problems, the only relevant statistics (which we use to assign a single MC temperature) is that of irregularities in low-energy funnels. Our results may explain why protein folding in nature is efficient at room temperatures.