Enhancing global optimization for bimetallic clusters: an adaptive multi-strategy differential evolution algorithm

Abstract

In this paper, we develop an adaptive multi-strategy differential evolution (AMSDE) algorithm to identify the lowest-energy structures of bimetallic clusters. The proposed AMSDE algorithm utilizes adaptive population sizing and diverse search strategies by formulating global exploration, local exploitation and diversity preservation into three cooperative and dynamically evolving populations. This scheme effectively mitigates premature convergence to local minima and significantly accelerates the overall convergence process. Comprehensive simulations demonstrate that our algorithm achieves faster convergence, higher stability, and lower energy compared to traditional algorithms across clusters of varying sizes. Based on the results of AMSDE, we systematically evaluate the energy, structural stability, and electronic properties of these Pt–Ni clusters with small sizes (3–12 atoms), which serve as ideal models for uncovering atomic-scale structural evolution. The analysis is further extended to medium-sized magic-number clusters (13, 19 and 23 atoms), known for their exceptional stability, to elucidate the structural preferences and stability trends. This work not only introduces an efficient structural optimization framework for nanoalloy clusters but also provides atomistic insights into the stability and electronic behavior of Pt–Ni clusters across a representative size range, facilitating the rational design of advanced catalytic materials.