Abstract
This chapter discusses the treatment of expensive optimization problems in Computer-Aided Design (CAD) problems by combining two strategies. First, we perform the whole optimization varying the accuracy with which a given candidate solution is evaluated by the expensive black-box function, rather than using the same accuracy for all evaluations. This idea follows from the fact that evolutionary algorithms, in general, employ more searching effort on the most promising regions of the search domain.We can adopt the same principles for allocating more computational effort when evaluating candidate solutions within these regions. The second strategy is the employment of local approximations within the local search operator of memetic algorithms. Since the points in the data are evaluated with different accuracies, the approximation methodology should give greater weight to samples evaluated with higher precision. The chapter proceeds to the formal analysis of approximation-based memetic algorithms, in which we investigate the effect of the local search operators on the global convergence properties of evolutionary algorithms viaMarkov chain theory, and also study the computational complexity of the approximation-based local search operator. The chapter concludeswith the illustration of the methodology in the design of electromagnetic devices, as an example of an expensive optimization problem.
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Guimarães, F.G., Lowther, D.A., Ramírez, J.A. (2010). Analysis of Approximation-Based Memetic Algorithms for Engineering Optimization. In: Tenne, Y., Goh, CK. (eds) Computational Intelligence in Expensive Optimization Problems. Adaptation Learning and Optimization, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10701-6_7
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