Basin Hopping with Occasional Jumping

TL;DR

This paper introduces an enhanced Basin-Hopping algorithm that incorporates occasional jumps at infinite temperature to escape local optima, significantly improving the likelihood of finding global energy minima in complex atomic clusters.

Contribution

The paper proposes a novel modification to the Basin-Hopping algorithm by adding an occasional jumping process to better escape local minima.

Findings

BHOJ outperforms traditional BH in locating global optima.

The jumping process is triggered when hopping stagnates.

Application to Lennard-Jones clusters shows improved success rates.

Abstract

Basin-Hopping (BH) or Monte-Carlo Minimization (MCM) is so far the most reliable algorithms in chemical physics to search for the lowest-energy structure of atomic clusters and macromolecular systems. BH transforms the complex energy landscape into a collection of basins, and explores them by hopping, which is achieved by random Monte Carlo moves and acceptance/rejection using the Metropolis criterion. In this report, we introduce the jumping process in addition to the hopping process in BH. Jumping are invoked when the hopping stagnates by reaching the local optima, and are achieved using the Monte Carlo move at the temperature $T=\infty$ without rejection. Our Basin-Hopping with Occasional Jumping (BHOJ) algorithm is applied to the Lennard-Jones clusters of several notoriously difficult sizes. It was found that the probability of locating the true global optima using BHOJ is significantly higher than the original BH.