This paper compares the performance of a group of intelligent algorithms such as the genetic algorithm (GA), particle swarm optimization (PSO), and repulsive particle swarm optimization (RPSO) based on the optimization of thermo-economic indicators such as the payback period (PBP), the levelized energy cost (LEC), the specific investment cost (SIC), and also in the optimization of the thermodynamic process (net power output) of an energy recovery system in a 2 MW natural gas internal combustion engine based on an organic Rankine cycle. Four parameters were considered to analyze and compare the performance of these algorithms: integral of squared error (ISE), integral of absolute error (IAE), integral of time-weighted absolute error (ITAE), and the integral of time-weighted squared error (ITSE). Analyses of variances (ANOVA) were proposed for each of the parameters studied. The PSO and RPSO algorithms presented the best performance in terms of the mean and the standard deviation of the ISE, IAE, ITAE, and ITSE parameters. Significant differences were not found between the three algorithms in terms of the parameters considered. However, significant differences did exist when comparing groups (pairs) of algorithms considering a significance level of 5%. The ANOVA analysis showed that ITAE was the most affected parameter by population size, while the IAE and ITSE parameters were the less affected. In the optimization, the PSO algorithm obtained the best performance in terms of convergence with values of 0.1110 USD/kWh (LCOE), 4.6971 years (PBP), 1114 USD/kWh (SIC), and 173.64 kW (Wnet). PSO-based algorithms obtained better performance in computational terms compared with the genetic algorithms.