The use of multi-objective optimisation techniques in the field of artificial intelligence for designing photonic crystal (PhC) light-emitting diodes (LEDs) is proposed. The extraction ratio and Purcell factor are first identified and considered as the main objectives when designing such LEDs. These two objectives are then optimised simultaneously even though both are in conflict. The proposed method is developed within a framework and applied to a case study. A comparative study shows that the optimised PhC LEDs completely outperform current works in the literature. These results are obtained by just tuning the PhC structural parameters, which can be considered as a substantial achievement in this field.