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.
Approximation methods are often used to construct surrogate models, which can replace expensive computer simulations for the purposes of optimization. One of the most important aspects of such optimization techniques is the choice of model updating strategy. In this paper we employ parallel updates by searching an expected improvement surface generated from a radial basis function model. We look at optimization based on standard and gradient-enhanced models. Given N p processors, the best N p local maxima of the expected improvement surface are highlighted and further runs are performed on these designs. To test these ideas, simple analytic functions and a finite element model of a simple structure are analysed and various approaches compared.Key words gradient-enhanced approximations, parallel optimization, radial basis functions IntroductionThe problem of optimization using high fidelity computer simulations is common to many engineering design problems. These simulations are based on mathematical models of some system of interest. Examples include finite element (FE) analysis for structural engineering problems or Navier-Stokes models in computational fluid dynamics (CFD). Optimization is a highly repetitive process requiring many analyses of the model under consideration. If Revised version of the paper presented at the Third ISSMO/AIAA Internet Conference on Approximations in Optimization October 14-25, 2002 this model itself is computationally expensive, direct optimization algorithms can rarely be employed, as a highly repetitive analysis of a high fidelity model becomes too time consuming to be practical.To overcome this problem cheap approximating models (often termed "surrogate models") are sought. These are based on a limited number of calls to the high fidelity model. Once constructed, the surrogate model can replace the original high fidelity model for the purposes of optimization.The first strategic decision that needs to be made relates to the design of experiments (DoE) to be used to provide training data for the approximation method. There are many such methods available to the designerwe will briefly review some of them in the next section. Their common feature is that they try to fill the design space in some sense, as it is commonly recognized that in the absence of any a priori knowledge on the problem under consideration, uniformity of the design points throughout the region of interest is favourable.Regarding the approximation methods, these can be applied locally or globally. Local approximations, such as polynomial response surfaces (see, e.g. Myers and Montgomery 1995), are defined over a specific region of interest, namely about the current best design. Optimization proceeds using a move limit or trust region strategy: we optimize only over the region where the model is valid. Successive local approximations are used to guide the search to a stationary point. Convergence is guaranteed, although only to a local optimum.Global approximations on the other hand try to capture t...
The use of optimal orthogonal array latin hypercube designs is proposed. Orthogonal arrays were proposed for constructing latin hypercube designs by Tang (1993). Such designs generally have better space filling properties than random latin hypercube designs. Even so, these designs do not necessarily fill the space particularly well. As a result, we consider orthogonal-array-based latin hypercube designs that try to achieve optimality in some sense. Optimization is performed by adapting strategies found in Morris & Mitchell (1995) and Ye et al. (2000). The strategies here search only orthogonal-array-based latin hypercube designs and, as a result, optimal designs are found in a more efficient fashion. The designs found are in general agreement with existing optimal designs reported elsewhere.
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