Compact heat exchangers are devices responsible for transmitting heat between two fluids that are at different temperatures. These constitute an essential component in many of the processes that facilitate daily life. This paper presents a numerical study of compact heat exchangers with circular tubes and louver fins that use vortex generators. The influence of the inclination angle of the vortex generators on the heat transfer and the pressure drop is determined. A 3D numerical model is used within the laminar regime with Reynolds number equal to 350. Eighteen geometries are constructed according to an experimental design based on the Latin Hypercube technique. The efficiency of the fin is determined by using the Schmidt method. In order to optimize two contrasting objectives (friction factor and Colburn factor) a multi-objective optimization approach was considered by using metaheuristics. This approach allows to obtain a Pareto set with fifteen non-dominated solutions. The area goodness criterion was used to compare the obtained results. It is interesting to remark that the optimization allows finding solutions that intensify heat transfer by 7% with only a 5% increase in pressure loss.