This paper applies a genetic algorithm-based optimisation procedure, namely, NSGA-II, to the problem of synthesis of a four-bar mechanism. The internal parameters of NSGA-II are tuned using a Design of Experiments (DoE) procedure to enhance the quality of the final results. Constraints are handled through a penalty formulation. Further, a scaling function is introduced, which transforms the penalty terms in a manner that leads to faster convergence of the solutions. The theoretical developments are illustrated via applications to two well-studied problems in the domain of coupler-curve synthesis. A comparison of the results vis-a-vis existing ones shows that the proposed enhancements of the basic scheme of NSGA-II deliver promising improvements in terms of accuracy, and rate of convergence of the solutions.