The spectral power distributions of tri- and tetrachromatic clusters of Light-Emitting-Diodes, composed of simulated and commercially available LEDs, were optimized with a genetic algorithm to maximize the luminous efficacy of radiation and the colour quality as assessed by the memory colour quality metric developed by the authors. The trade-off of the colour quality as assessed by the memory colour metric and the luminous efficacy of radiation was investigated by calculating the Pareto optimal front using the NSGA-II genetic algorithm. Optimal peak wavelengths and spectral widths of the LEDs were derived, and over half of them were found to be close to Thornton’s prime colours. The Pareto optimal fronts of real LED clusters were always found to be smaller than those of the simulated clusters. The effect of binning on designing a real LED cluster was investigated and was found to be quite large. Finally, a real LED cluster of commercially available AlGaInP, InGaN and phosphor white LEDs was optimized to obtain a higher score on memory colour quality scale than its corresponding CIE reference illuminant.