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Modern systems have become increasingly more complex, and their analysis becomes signicantly more complex. Many practical aspects of complex network tools have mainly been applied to critical infrastructure, in particular, to study power systems' resilience. Blackout prevention, system resilience, and restoration consider the ability of the system's self-healing. The self-healing strategies depend, basically, on the existence of extra lines to re-route energy.Some studies suggested that there is an optimum cost-benefit point when adding power lines redundancies to a system considering the systems' resilience. One method to solve this optimisation problem is the use of a metaheuristic algorithm. These algorithms combine exploration and exploitation on the search for a solution. In this paper, a Chu-Beasley genetic algorithm is used to search for the optimum cost-benefit level of redundancy in a system. Thesystem used is from the Repository of Distribution Systems (REDS), and the function used to evaluate the resilience considers an efficiency coecient so that the resilience by cost curve would have a maximum point. This experiment is executed as a topological analysis. The expected results were obtained using estimated curves from Monte-Carlo simulations for a wide range of combination of parameters. The results from three different parameters of efficiency coefficient were compared to the expected values obtained. The results show that there is a best cost-benefit level of redundancy when an efficiency level is determinate. Also, the GA used has excellent performance for finding this point.