On the Design of Optimization Strategies Based on Global Response Surface Approximation Models

Abstract

Abstract. Striking the correct balance between global exploration of search spaces and local exploitation of promising basins of attraction is one of the principal concerns in the design of global optimization algorithms. This is true in the case of techniques based on global response surface approximation models as well. After constructing such a model using some initial database of designs it is far from obvious how to select further points to examine so that the appropriate mix of exploration and exploitation is achieved. In this paper we propose a selection criterion based on the expected improvement measure, which allows relatively precise control of the scope of the search. We investigate its behavior through a set of artificial test functions and two structural optimization problems. We also look at another aspect of setting up search heuristics of this type: the choice of the size of the database that the initial approximation is built upon.

Recent advances in surrogate-based optimization

“…Subsequently, we have imputed lower and lower values ‡ This is similar to trying a range of weightings between local and global search. Sóbester et al [73] used a weighted expected improvement formulation as part of a twostage approach to achieve similar ends, while Forrester [18] used a weighted statistical lower bound with reinforcement learning to chose the weighting. at x = 0.7572 and re-optimized θ to produce a prediction through these points.…”

Exploration versus exploitation using kriging surrogate modelling in electromagnetic design

“…The Weighted Expected Improvement (WEI) [3] is derived from EI by adding a tuneable parameter which can adjust the weights on exploration and exploitation, whilst the quality of the approximation of the objective function can be improved by incorporating the newly evaluated design vector at each iteration. The WEI utility function used in this work may be written as…”

“…where the tuneable parameter w (0 < w < 1) controls the balance between the two terms (exploration and exploitation), therefore searching globally and locally [3]. The efficiency of the kriging with WEI has been tested with the Schwefel test function [4] as an objective function in the interval [-500 500] for different values of w .…”

Correlation matrices in kriging assisted optimisation of electromagnetic devices

“…Kriging [1][2][3][4] predicts the shape of the objective function by considering the spatial correlation of data based on limited information and thus offers an efficient and inexpensive surrogate to replace the computationally demanding numerical simulation (such as finite elements). The accuracy of the prediction can be estimated by the mean square error in kriging to assist in a decision on where to place the next evaluation point during optimisation iterations.…”

“…where the global function m k=1 b k f k (x) and an additive Gaussian noise ε(x) are integrated to the predicted valuê y(x) of the objective function; θ k is the correlation among the data in the k-direction and p k determines the 'smoothness' of (2). The most popular correlation function is given by the Gauss model where the value of p k is simply taken as equal to 2.…”