In the present study, an attempt is made to search for better solutions for the Hanoi network, BakRyan network, and GoYang network (GYN) through evolutionary algorithms (EAs) such as genetic algorithm (GA) and differential evolution (DE), which are initially validated using the two-loop network. A detailed note on the classification of available benchmark-problems is reported. The major aim of the study is to improve the optimal solution of GYN, which can emerge as a standard benchmark-problem for future studies. On applying the developed EA models, an improved optimal cost compared with the literature is obtained for GYN. From the results, it is found that DE outshines GA by its better convergence capability and robustness in attaining an optimum solution.