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This paper outlines an original algorithm of neural optimization backed by three-dimensional full-wave finite-difference time-domain (FDTD) simulation and suitable for viable computer-aided design of complex microwave (MW) systems. The frequency response of an S-parameter is optimized with a decomposed radial basis function (RBF) network capable of dealing with various MW devices. The key feature of the optimization is the dynamic generation of as much FDTD data as the network needs to find a solution satisfying the constraints or the stopping criteria. Other functions contributing to the reduction of computational cost include a choice of an RBF type, radius optimization of the Gaussian RBF, optimization of the regularization parameter, etc. Performance of the algorithm is illustrated by its application to the systems, which can be adequately described only with the full-wave numerical analysis: a double waveguide window, a loaded MW oven, and a patch antenna with two long slits. In all these examples, the network demonstrates excellent generalizing capabilities with the use of relatively small data sets, and the optimized solutions are obtained within fairly reasonable time. The algorithm is shown to be advantageous over conventional gradient and nongradient local-optimization techniques because it is independent of the starting point and having the potential to find the "best" local optimum in the specified domain. Finally, parameters of FDTD simulations and the network operations influencing the computational cost of the optimization are thoroughly discussed.