A new integrated computational HEA design strategy is proposed. It combines a multi-objective genetic algorithm with (i) statistical criteria to guide the formation of a single phase, supplemented by computational thermodynamics (Thermo-Calc) and (ii) models for the estimation of alloy yield stress via solid solution hardening, to be maximised, and alloy density, to be minimised. This strategy is applied to the design of face-centered-cubic (FCC) HEAs and yields several thousands of new alloys. An alloy featuring an interesting combination of predicted stability, strength and density, Al₁₀Co₁₇Fe₃₄Mo₅Ni₃₄ (at%), is chosen among them, fabricated by vacuum arc melting and experimentally tested. The microstructure of this new HEA consists in a single FCC solid solution, as evidenced by X-ray diffraction (XRD), scanning electron microscopy (SEM) and X-ray energy dispersive spectroscopy (EDS) mapping. With a density of 7.95 g⋅cm^{- 3}, a Vickers hardness of 1.78 GPa, a yield stress of 215 MPa and an ultimate tensile strength of 665 MPa in the annealed state, its properties surpass those of existing FCC HEAs of comparable density.