Cluster Optimization BGO 01

By Ilias Bilionis1, Yinuo Li

1. Purdue University

Cluster Optimization Using Bayesian Global Optimization

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Version 1.0 - published on 03 Aug 2015

doi:10.4231/D3GF0MX5X cite this

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The Summer Undergraduate Research Fellowship (SURF) Symposium

6 August 2015

Purdue University, West Lafayette, Indiana, USA


Design-Optimization with a Limited Data-Budget

Yinuo Li

School of Electrical and Computer Engineering, Purdue University

Ilias Bilionis and Piyush Pandita

School of Mechanical Engineering, Purdue University


Design-optimization with realistic computer codes is a ubiquitously challenging task. Typically, we have to execute thousands of simulations in order to achieve a globally optimum design. However, since realistic models may take hours or even days to complete a single simulation, global optimization is infeasible for all but the simplest models. We are necessarily limited to just a handful of simulations. Bayesian global optimization (BGO) is a computational framework built upon Gaussian process regression that allows us to actively select which simulations to make in order to reach our objective or its gradients. It only assumes that the objective is measurable at any given design point either experimentally or via a computer simulation. We have implemented BGO in Python and created a nanoHUB tool that applies the concept to the problem of the structure determination of an arbitrary cluster of atoms. The tool works as follows: First, it generates an initial data pool consisting of random structures and their associated energies as well as a test design pool consisting of structures that will be tested for optimality. Then, it constructs a Gaussian process model of the energy surface and employs BGO to find the minimum energy cluster among the test pool. The process runs until either the maximum expected improvement of future simulations falls below a threshold or the number of maximum iterations is reached. 




Gaussian Process, Bayesian Global Optimization, Limited Data-budget, GUI


1. Donald Jones.(2001) A Taxonomy of Global Optimization Methods Based on Response Surfaces. Kluwer Academic Publishers.

2. Donald Jones & Matthlas Schonlau.(1998) Efficient Global Optimization of Expensive, Black-Box Function. Kluwer Academic Publishers.

3. Atomistic simulation environment

4. Gaussian Processes framework in Python (GPy).

5. Carl Edward Rasmussen, & Christopher K. I. Williams. (2006) Gaussian Processes for Machine Learning. Massachusetts Institute of Technology. [Online] Available:

6. Bilionis, Ilias. (2015)  Multivariate Normal Probability Density. Purdue University.[Online] Available:

7. Bilionis, Ilias. (2015)  Gaussian Processes. Purdue University.[Online] Available:




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Researchers should cite this work as follows:

  • Ilias Bilionis, Yinuo Li (2015), "Cluster Optimization BGO 01," (DOI: 10.4231/D3GF0MX5X).

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