A new computational framework for systematic and optimal alloy design is introduced. It is based on a multi-objective genetic algorithm which allows (i) the screening of vast compositional ranges and (ii) the optimisation of the performance of novel alloys. Alloys performance is evaluated on the basis of their predicted constitutional and thermomechanical properties. To this end, the CALPHAD method is used for assessing equilibrium characteristics (such as constitution, stability or processability) while Gaussian processes provide an estimate of thermomechanical properties (such as tensile strength or creep resistance), based on a multi-variable non-linear regression of existing data. These three independently well-assessed tools were unified within a single C++ routine. The method was applied to the design of affordable nickel-base superalloys for service in power plants, providing numerous candidates with superior expected microstructural stability and strength. An overview of the metallurgy of optimised alloys, as well as two detailed examples of optimal alloys, suggest that improvements over current commercial alloys are achievable at lower costs.