In many engineering optimization problems, the number of function evaluations is severely limited by time or cost. These problems pose a special challenge to the field of global optimization, since existing methods often require more function evaluations than can be comfortably afforded. One way to address this challenge is to fit response surfaces to data collected by evaluating the objective and constraint functions at a few points. These surfaces can then be used for visualization, tradeoff analysis, and optimization. In this paper, we introduce the reader to a response surface methodology that is especially good at modeling the nonlinear, multimodal functions that often occur in engineering. We then show how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule. The key to using response surfaces for global optimization lies in balancing the need to exploit the approximating surface (by sampling where it is minimized) with the need to improve the approximation (by sampling where prediction error may be high). Striking this balance requires solving certain auxiliary problems which have previously been considered intractable, but we show how these computational obstacles can be overcome.

/pdf/efficient-global-optimization-of-expensive-black-box-4m8fv6oubz.pdf

Efficient Global Optimization of Expensive Black-Box Functions

Big Data applications are typically associated with systems involving large numbers of users, massive complex software systems, and large-scale heterogeneous computing and storage architectures. The construction of such systems involves many distributed design choices. The end products (e.g., recommendation systems, medical analysis tools, real-time game engines, speech recognizers) thus involve many tunable configuration parameters. These parameters are often specified and hard-coded into the software by various developers or teams. If optimized jointly, these parameters can result in significant improvements. Bayesian optimization is a powerful tool for the joint optimization of design choices that is gaining great popularity in recent years. It promises greater automation so as to increase both product quality and human productivity. This review paper introduces Bayesian optimization, highlights some of its methodological aspects, and showcases a wide range of applications.

/pdf/taking-the-human-out-of-the-loop-a-review-of-bayesian-4olcznoudw.pdf

Taking the Human Out of the Loop: A Review of Bayesian Optimization

Introduction to linear and nonlinear programming

This paper presents a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have non-obvious failure modes. Understanding these failure modes is essential for the development of practical algorithms that fulfill the intuitive promise of the response surface approach.

/pdf/a-taxonomy-of-global-optimization-methods-based-on-response-2hv1dk7s60.pdf

A Taxonomy of Global Optimization Methods Based on Response Surfaces

Foundations Of Statistics

Basic Concepts and Ideas.- Global Random Search: Fundamentals and Statistical Inference.- Global Random Search: Extensions.- Methods Based on Statistical Models of Multimodal Functions.

http://hpc-education.unn.ru/files/conference_hpc/2015/Zhigljavsky.pdf

Stochastic Global Optimization

A review of statistical models for global optimization is presented. Rationality of the search for a global minimum is formulated axiomatically and the features of the corresponding algorithm are derived from the axioms. Furthermore the results of some applications of the proposed algorithm are presented and the perspectives of the approach are discussed.

A review of statistical models for global optimization

Non-Convex Multi-Objective Optimization

/pdf/operations-research-theory-and-applications-2qbizgy7l5.pdf

Antanas Žilinskas

Papers

Stochastic Global Optimization

A review of statistical models for global optimization

Non-Convex Multi-Objective Optimization

Operations research: theory and applications

On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions