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The trade-off between the color fidelity index (R_f) released recently by the Illuminating Engineering Society of North America (IES) and luminous efficacy of radiation (LER) was investigated by adjusting the peak wavelengths, spectral widths, and intensities of four-channel LEDs utilizing a multiobjective optimization algorithm based on differential evolution in the correlated color temperature (CCT) ranging from 2800 to 6500 K for general lighting. The results indicate that R_f at a specific LER value decreases with the increasing CCT, and vice versa, and that R_f has significant improvements over the Commission Internationale de l'Eclairage (CIE) color rendering index (CRI) in avoiding spectral gaming and evaluating the light sources even with negative CIE general CRI (R_a). Further, the optimal peak wavelengths with regard to R_f were identified as 629 nm, 568 nm, 504 nm, and 447 nm, yielding high color rendering in terms of R_f(93∼94) and R_a(95∼97) and relatively excellent LER (299  lm/W∼339  lm/W) over a wide range of CCTs from 2800 to 6500 K. This suggests that R_f can be compatible with R_a, making it possible to obtain a common set of optimal peak wavelengths for R_f and R_a. Besides, the IES method could assess saturated red and skin tones more fairly than the CIE CRI. With a practical 17-channel LED array covering the resulted four optimal peak wavelengths, the improvements of the IES method over the CIE CRI were validated further.

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