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We introduce a genetic algorithm-based method for structural optimization of multiplicative general parameter (MGP) finite impulse response (FIR) filters. These computationally efficient reduced-rank adaptive filters are robust, suitable for predictive configurations, and they have numerous applications in 50/60 Hz power systems instrumentation. The design process of such filters has three independent stages: Lagrange multipliers-based optimization of the sinusoid-predictive basis filter, genetic algorithm-based search of optimal FIR tap cross-connections and, finally, the online MGP-adaptation phase guided by variations in signal statistics. Thus, our multistage design procedure is a complementary fusion of hard computing (HC) and soft computing (SC) methodologies. Such advantageous fusion (or symbiosis) thinking is emerging among researchers and practicing engineers, and it can potentially lead to competitive combinations of individual HC and SC methods.