The rational design of photonic nanostructures consists of anticipating their optical response from systematic variations of simple models. This strategy, however, has limited success when multiple objectives are simultaneously targeted, because it requires demanding computational schemes. To this end, evolutionary algorithms can drive the morphology of a nano-object towards an optimum through several cycles of selection, mutation and cross-over, mimicking the process of natural selection. Here, we present a numerical technique that can allow the design of photonic nanostructures with optical properties optimized along several arbitrary objectives. In particular, we combine evolutionary multi-objective algorithms with frequency-domain electrodynamical simulations to optimize the design of colour pixels based on silicon nanostructures that resonate at two user-defined, polarization-dependent wavelengths. The scattering spectra of optimized pixels fabricated by electron-beam lithography show excellent agreement with the targeted objectives. The method is self-adaptive to arbitrary constraints and therefore particularly apt for the design of complex structures within predefined technological limits.