Keywords: surrogate models, design optimization, artificial neural networks, differential evolution, evolutionary algorithms.

Engineering design usually necessitates the use of computationally expensive simulation tools, which almost always result to inefficient computational resources for analyzing all the desired combinations of the design variables. This problem becomes much harder when an optimization procedure is used in the design loop, which usually makes a large number of calls to the corresponding simulation tools, in order to map the search space and efficiently search for the optimal solution.

During recent years, it has been shown by many researchers that evolutionary algorithms (EAs) are viable candidates to solve complicated engineering design optimization problems in a large variety of engineering disciplines. However, EAs ask for a considerable amount of evaluation of candidate solutions, usually with high computational cost, especially when complicated physical systems are simulated using numerical solvers. In order to reduce it several techniques have been applied, such as the use of parallel processing, special operators and surrogate models and approximations. Surrogate models are auxiliary simulations that have a lower accuracy compared to the reference simulations of the physical system at hand, but are also less computationally expensive. Such approximations are the low-order polynomials used in response surface methodology, the kriging estimates employed in the design and analysis of computer experiments, and the various types of artificial neural networks. Several studies have shown that it is not known a priori which surrogate model is the best for a specific optimization problem. Taking into account that the training of a surrogate model is usually much cheaper than an exact analysis of a candidate solution, the use of multiple surrogates in parallel may offer advantages compared to the use of a single one.

This chapter demonstrates the effectiveness of combining surrogate models with EAs in solving engineering design optimization problems. A detailed review on the subject is presented first, containing the recent advances on surrogate-assisted optimization, and especially the combination of surrogate models with EA algorithms and the use of surrogate ensembles. The focus of this work is mainly on the use of artificial neural networks; multi-layer perceptron and radial basis function networks are used in this study. However, other types of surrogate models are also reviewed, as well as their use in combination with EAs. The differences between the use of on-line and off-line surrogate models is addressed and the advantages of using local surrogate models that evolve with the EA population is discussed. Case studies from different engineering disciplines are presented to demonstrate the efficiency of such techniques, especially when multiple surrogates are used as an ensemble.

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