A study on diversity for cluster geometry optimization

Abstract

Diversity is a key issue to consider when designing evolutionary approaches for difficult optimization problems. In this paper, we address the development of an effective hybrid algorithm for cluster geometry optimization. The proposed approach combines a steady-state evolutionary algorithm and a straightforward local method that uses derivative information to guide search into the nearest local optimum. The optimization method incorporates a mechanism to ensure that the diversity of the population does not drop below a pre-specified threshold. Three alternative distance measures to estimate the dissimilarity between solutions are evaluated. Results show that diversity is crucial to increase the effectiveness of the hybrid evolutionary algorithm, as it enables it to discover all putative global optima for Morse clusters up to 80 atoms. A comprehensive analysis is presented to gain insight about the most important strengths and weaknesses of the proposed approach. The study shows why distance measures that consider structural information for estimating the dissimilarity between solutions are more suited to this problem than those that take into account fitness values. A detailed explanation for this differentiation is provided.

Analysis of Crossover Operators for Cluster Geometry Optimization

“…More specifically we selected the instances with the following number of atoms N= {30, 38, 47, 61, 68}. This set includes examples that are considered to be difficult to optimize (see, e.g., (Grosso et al, 2007;Pereira & Marques, 2009)). …”

“…In this work we rely on the center of mass distance, a measure that is based on the distance of atoms to the cluster's center of mass (Grosso et al, 2007). Results reported in (Grosso et al, 2007;Pereira & Marques, 2009) confirm that it is effective in accessing the similarity of possible solutions for Morse instances. In general terms, a descendant D is allowed to enter the population if one of the following conditions is satisfied (consult (Lee et al, 2003) for a detailed description of the replacement strategy): i) D is similar to a solution X that belongs to the current population and D is better than X.…”

“…Two recent papers describe approaches to remove the bias from the first phase of local search (Cassioli et al, 2208;. In 2009, Pereira and Marques proposed a simple hybrid EA that is able to discover all putative global optima for short-ranged Morse clusters until 80 atoms (Pereira & Marques, 2009). This is the first completely unbiased population-based method that was able to succeed in this task.…”

“…Since the early 1990's Evolutionary Algorithms (EAs) have been increasingly applied to this task (Deaven & Ho, 1995;Doye et al, 2004;Grosso et al, 2007;Hartke, 2001;Johnston, 2003;Pereira & Marques, 2009;Zeiri, 1995). State-of-the-art methods usually combine a global evolutionary component with a gradient-driven local search procedure.…”

Island models for cluster geometry optimization: how design options impact effectiveness and diversity

“…They also suggested that the enhanced results were in most part the outcome of the increased diversity caused by the adaption of the settings. Later Pereira et al [61] introduced an unbiased hybrid steady-state EA combined with a single phase local optimization method based on a general quasi-Newton method. This study includes mechanisms designed to ensure the maintenance of diversity and demonstrates that its preservation is a key point to efficiently tackle CGO problems.…”