The growing need for a simplified management of network infrastructures has recently led to the emergence of software-defined networking (SDN), which enables a centralized path calculation. The diversification of services, as well as the need of rapid path deployment, raises, however, challenges in routing algorithms. Moreover, Quality of Service (QoS) requirements and conflicts between them pile up the complexity of the problem. An intuitive method is formulating the problem as an Integer Linear Programming and solving it by an approximation algorithm. This method tends to have a specific design and usually suffers from unacceptable computational delays to provide a sub-optimal solution. Genetic algorithms (GAs) are deemed as a promising solution to cope with highly complex optimization problems. However, the convergence speed and the quality of solutions should be addressed in order to fit into practical implementations. In this paper, we propose a genetic algorithm-based mechanism to address the multi-constrained multi-objective routing problem. Using a repairer to reduce the search space to feasible solutions, results confirm that the proposed mechanism is able to find the Pareto-optimal solutions within a short run-time.