This work used a computational strategy to optimize a pultrusion process. Based on mass and energy balance equations, the mathematical model was implemented into Ansys CFX® and Matlab® tools. A pultrusion die with six heaters and C-section composite geometry was used as a studied case. For the single objective optimization, the sum of the heaters' temperatures was considered as objective function with a minimum degree of cure of 0.9 imposed as a constraint. Particle swarm optimization (PSO) and sequential quadratic programming (SQP) algorithms were considered for single objective optimization. The results indicated that the SQP method could reduce the objective function and computational cost by 1.58% and 30.31%, respectively, concerning the PSO algorithm. However, the results also indicated that the performance of the SQP is highly dependent on the initial temperature estimates. The PSO and NSGA-II algorithms were applied to solve the multi-objective optimization in which pull speed maximization and minimization of heaters' temperatures were defined as objective functions. Results indicated that NSGA-II was 18.8% faster than the PSO strategy. The Pareto curve of the two methods presented a similar profile, evidencing that a higher pull speed requires greater energy consumption. Finally, the results show that the Pareto curve is helpful for predicting the set of resulting optimal points, which also makes it possible to detect unfeasible combinations of temperature and pull speed values.