During alloy and process design, it is often desired to identify regions of design or process variables for which certain calculated functions have optimal values under various constraints, for example: compositions of minimum liquidus temperature in an N-component alloy; compositions where the amount of precipitate in a given phase is maximized or minimized during annealing or rolling; other calculated functions such as densities, vapour pressures and viscosities; or the overall cost. The present work reports on the development of software, linked to the FactSage thermodynamic and properties database system, to perform such calculations. The software uses the Mesh Adaptive Direct Search algorithm (MADS) designed to solve non-smooth optimization problems for which the objectives and constraints are typically outputs of computer simulations. Numerical results for several examples are presented.