In this chapter a hybrid algorithm is constructed, implemented and tested for the optimization of graph drawing employing a multiobjective approach. The multiobjective optimization problem for graph drawing consists of three objective functions: minimizing the number of edge crossing, minimizing the graph area, and minimizing the aspect ratio. The population of feasible solutions is generated using a hybrid algorithm and at each step a Pareto front is calculated. This hybrid algorithm combines a global search algorithm (EDA — Estimation of Distribution Algorithm) with a local search Algorithm (HC — Hill Climbing) in order to maintain a balance between the exploration and exploitation. Experiments were performed employing planar and non-planar graphs. A quality index of the obtained solutions by the hybrid MOEA-HCEDA (Multiobjective Evolutionary Algorithm - Hill Climbing & Univariate Marginal Distribution Algorithm) is constructed based on the Pareto front defined in this chapter. A factorial experiment using the algorithm parameters was performed. The factors are number of generations and population size, and the result is the quality index. The best combination of factors levels is obtained.