Efficiency of Various Stochastic Optimization Algorithms in High Frequency Electromagnetic Applications
We present the efficiency of various probabilistic algorithms, including the standard genetic algorithm, micro-genetic algorithm, evolutionary strategy, randomly initialized hill climbing, and mutation based algorithms for the optimization of electromagne
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Abstract We present the efficiency of various probabilistic algorithms, including the standard genetic algorithm, micro-genetic algorithm, evolutionary strategy, randomly initialized hill climbing, and mutation based algorithms for the optimization of electromagnetic devices operating at microwave and optical frequencies. Single fitness evaluations are costly because the electromagnetic field computation time is usually long. We therefore need to find strategies that provide optimal solutions in under a few hundred fitness evaluations. This constraint considerably affects the design of the optimizer. In order to obtain reliable guidelines, various optimization algorithms have been applied to three optimization problems.
1 Introduction As opposed to traditional, empirical design approaches, modern design of electromagnetic devices is based on field simulations. If the problem size is small enough, one can directly link field solvers with efficient optimizers to perform the design task. The process is finished when a certain convergence criterion is met. The scope of this paper is to outline numerical difficulties when applying this process to modern engineering problems, to present the efficiency of various stochastic optimization algorithms applied to several different examples, and finally to sugJ. Smajic ABB Switzerland Ltd., Corp. Research, Segelhofstrasse 1, CH-5405 Baden 5 Daettwil, Switzerland [email protected] M. Mishrikey, A. Fallahi, C. Hafner, and R. Vahldieck Lab for Electromagnetic Fields and Microwave Electronics, ETH Zurich, Gloriastrasse 35, 8092 Zurich, Switzerland [email protected], [email protected], [email protected], [email protected] J. Smajic et al.: Efficiency of Various Stochastic Optimization Algorithms in High Frequency Electromagnetic Applications, Studies in Computational Intelligence (SCI) 129, 261–272 (2008) c Springer-Verlag Berlin Heidelberg 2008 www.springerlink.com
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gest an appropriate optimization algorithm for a certain class of problems in high frequency electromagnetic applications. In engineering optimizations, a single fitness evaluation is rather costly as it is based on numerical field computations in 2D and 3D. One option would be to employ a deterministic optimizer such as the well known gradient based steepest descent algorithm, which converges rapidly to the nearest local optimum. For electromagnetics applications however, this is a poor strategy because fitness functions are rarely smooth as a result of inaccuracy and numerical noise of the field solver [1]. As such, stochastic optimization algorithms are best suited for these types of problems. From a design optimization standpoint, two types of optimization problems are important: 1. binary optimization (the device is described with a bit string in which every bit is related to an existing or missing feature of the device, for example the distribution of the defects in a periodic structure) 2. real parameter optimization (the dimensions and material properties of the device a
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