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We propose a novel orthogonal simulated annealing algorithm (OSA) for optimization of electromagnetic problems. The algorithm performs best when it employs an intelligent generation mechanism (IGM) based on orthogonal experimental design (OED). The OED-based IGM can efficiently generate a good candidate solution for the next step by using a systematic reasoning method instead of the conventional method of random perturbation. We show empirically that OSA is more efficient in solving parametric optimization problems and in designing optimal electromagnetic devices than some existing optimization methods using simulated annealing algorithms and genetic algorithms.