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The work presented in this paper deals with the determination of material parameters used in internal variable constitutive models. In order to determine the best suited material parameter set, in the less computationally expensive way, two optimization approaches are used: (i) a gradient-based method and (ii) a continuous evolutionary algorithm (EA) method. The first approach uses a combination of the steepest descent gradient and the Levenberg–Marquardt techniques. The performance of this method is known to be highly dependent on the starting set of parameters and its results are often inconsistent. The EA-based technique provides a better way to determine an optimized set of parameters (the overall minimum). Thus, the difficulty of choosing a starting set of parameters for this process is minor. The main application in this work is a 16 parameter thermoelastic–viscoplastic constitutive model. Experimental …