Keywords: differential evolution, surrogate model, structural optimization, nearest neighbors, linear regression.

As a result of the increasing competitiveness in industry, as well as the identification of new scientific challenges of growing complexity, significant effort has been invested in recent years to develop effective techniques to deal with computationally expensive simulation models. Nature inspired metaheuristics can help overcome the challenges presented including multiple objectives, mixed types of design variables, low regularity of the objective functions, a large number of nonlinear implicit constraints, and expensive and/or unreliable gradients.

Among the various nature inspired metaheuristics available, differential evolution (DE) is a relatively new optimization technique which has generated interest among a number of researchers from different fields. Although good solutions can be obtained, DE requires, similarly to other nature inspired techniques, many evaluations of the objective function. This becomes a serious drawback to their application in situations where expensive simulations are required. The user's computational budget then places a strong limit to the number of calls to the expensive simulation model, making it necessary to modify the search process in order to increase the convergence speed of the optimization procedure.

One way to alleviate that situation is to use a surrogate model (or metamodel), replacing the computationally intensive original simulator evaluation by a relatively inexpensive approximation of the objective function and constraint checking. Here, the use of a similarity-based surrogate model is proposed in order to improve the DE's overall performance for computationally expensive problems. The offspring are generated by means of different variants, and only the best one, according to the surrogate model, is evaluated by the simulator.

Computational experiments were performed to assess the performance of the proposed procedure using six different constrained optimization problems involving five structures with continuous as well as discrete design variables. The results show that the use of a similarity-based surrogate model improves the performance of DE for most test-problems, especially when using r-nearest neighbors with with r set equal to 0.001. The use of a simple local linear regressor produced relatively lower quality results for most problems, although producing the best results in two of the six test-problems.

It is important to note that the results from the literature which presented a better (smaller) final weight were obtained with a much larger (often one-order magnitude) number of simulations. In addition, the proposed technique alleviates the user from the task of defining, a priori, which type of variant to use in the DE.

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