In this paper, the general problem of chemical process optimization defined by a computer simulation is formulated. It is generally a nonlinear, non-convex, nondifferentiable optimization problem over a disconnected set. A brief overview of popular optimization methods in the chemical engineering literature is made. The recent mesh adaptive direct search (MADS) algorithm is presented. It is a direct search algorithm, so it uses only function values and does not compute or approximate derivatives. This is useful when the functions are noisy, costly or undefined at some points, or when derivatives are unavailable or unusable. In this work, the MADS algorithm is used to optimize a spent potliner (toxic waste from aluminum production) treatment process. In comparison with the best previously known objective function value, a 37% reduction is obtained even if the model failed to return a value 43% of the time.