Constraint Handling in Efficient Global Optimization

This is the author accepted manuscript. The final version is available from ACM via the DOI in this record.Real-world optimization problems are often subject to several constraints which are expensive to evaluate in terms of cost or time. Although a lot of effort is devoted to make use of surrogate models for expensive optimization tasks, not many strong surrogate-assisted algorithms can address the challenging constrained problems. Efficient Global Optimization (EGO) is a Kriging-based surrogate-assisted algorithm. It was originally proposed to address unconstrained problems and later was modified to solve constrained problems. However, these type of algorithms still suffer from several issues, mainly: (1) early stagnation, (2) problems with multiple active constraints and (3) frequent crashes. In this work, we introduce a new EGO-based algorithm which tries to overcome these common issues with Kriging optimization algorithms. We apply the proposed algorithm on problems with dimension d ≤ 4 from the G-function suite [16] and on an airfoil shape example.This research was partly funded by Tekes, the Finnish Funding Agency for Innovation (the DeCoMo project), and by the Engineering and Physical Sciences Research Council [grant numbers EP/N017195/1, EP/N017846/1]

Predictive Entropy Search for Efficient Global Optimization of Black-box Functions

We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance

Efficient global optimization: Motivation, variations and applications

A popular optimization method of a black box objective function is Efficient Global Optimization (EGO), also known as Sequential Model Based Optimization, SMBO, with kriging and expected improvement. EGO is a sequential design of experiments aiming at gaining as much information as possible from as few experiments as feasible by a skillful choice of the factor settings in a sequential way. In this paper we will introduce the standard procedure and some of its variants. In particular, we will propose some new variants like regression as a modeling alternative to kriging and two simple methods for the handling of categorical variables, and we will discuss focus search for the optimization of the infill criterion. Finally, we will give relevant examples for the application of the method. Moreover, in our group, we implemented all the described methods in the publicly available R package mlrMBO

An extension of Chebfun to two dimensions

An object-oriented MATLAB system is described that extends the capabilities of Chebfun to smooth functions of two variables defined on rectangles. Functions are approximated to essentially machine precision by using iterative Gaussian elimination with complete pivoting to form “chebfun2” objects representing low rank approximations. Operations such as integration, differentiation, function evaluation, and transforms are particularly efficient. Global optimization, the singular value decomposition, and rootfinding are also extended to chebfun2 objects. Numerical applications are presented