In the context of algorithmic parameter optimization, there is much room for efficient usage of computational resources. We consider the OPAL framework in which a nonsmooth optimization problem models the parameter identification task, and is solved by a mesh adaptive direct search solver. Each evaluation of trial parameters requires the processing of a potentially large number of independent tasks. We describe and evaluate several strategies for using parallelism in this setting. Our test scenario consists in optimizing five parameters of a trust-region method for smooth unconstrained minimization.