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The fitting of metal optical properties is a topic that has applications in advanced simulations of spectroscopy, plasmonics, and optical engineering. In particular, the finite difference time domain method (FDTD) requires an analytical model of dispersion that verifies specific conditions to produce a full spectrum in a single run. Combination of Drude and Lorentz models, and Drude and critical points models, are known to be efficient, but the number of parameters to be adjusted for fitting data can prevent accurate results from simulated annealing or Nelder-Mead. The complex number relative permittivities of Au, Ag, Al, Cr, and Ti from either Palik or Johnson and Christy experimental data in the visible domain of wavelengths are successfully fitted by using the result of the particle swarm optimization method with FDTD constraint, as a starting point for the Nelder-Mead method. The results are well positioned compared to those that can be found in the literature. The results can be used directly for numerical simulations in the visible domain. The method can be applied to other materials, such as dielectrics, and to other domain of wavelengths. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.