A Concurrent Efficient Global Optimization Algorithm Applied to Engineering Problems

One of the major difficulties in applying optimization to real engineering problems is that each function evaluation requires a complete model simulation which is in general computationally expensive. Moreover, some problems are known to be multimodal with several local minima. A common approach to tackle these problems is to construct cheap global approximation models of the responses often called metamodels or surrogates. These are based on simulation results obtained for a limited number of designs using global data fitting such as DACE. The optimization algorithm repetitive analysis needs are all performed using the cheap metamodels. In this study a two-stage approach is employed based on the Efficient Global Optimization algorithm, EGO, due to Jones. First an initial sample of designs is obtained using some Design of Experiments (DOE) technique such as Latin Hypercube. Parallel simulation runs for the initial sample are used to construct a kriging metamodel. In the second stage the metamodel is used to guide the search for promising designs which are added to the sample in order to update the model until a suitable termination criterion is fulfilled. The selection of designs which are adaptively added to the sample should balance the need for improving the value of the objective function with that of improving the quality of the prediction so that one does not get trapped in a local minimum. In the EGO algorithm this balance is achieved through the use of the Expected Improvement merit function. In this study the original EGO algorithm is modified to exploit parallelism. The algorithm is also modified to include general nonlinear constraints. The modified algorithm is applied to two example problems. The first is a small multimodal, two-variable structural design problem that can be graphically represented. The second is an eight-variable polymer injection problem in oil reservoir engineering.

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