BR 
EN Comparing Multi-Objective Surrogate Models For Binary Petroleum Well Placement
Resumo
Optimization problems often involve expensive computational calculations. For example, in petroleum well place-ment problems, optimization techniques are applied to reservoir simulation models to identify the optimal number and positions of exploration wells. Each evaluation of a well placement plan requires extensive calculations of differential equations to forecast fluid behavior. To enhance the quality of the optimization techniques without increasing the computational burden, re-searchers have explored combining optimization methods with Surrogate Models, approximation techniques used in regression problems to replace expensive objective functions with more computationally efficient evaluations. However, since most of the research on surrogate modeling has been performed for single-objective problems, surrogate modeling for multi-objective problems remains a challenging task. For this reason, this paper provides a comparative analysis of three supervised learning techniques, Random Forest (RF), Multi-Layer Perceptron (MLP), and k-Nearest Neighbors (k-NN) when applied as multi-objective surrogate models to approximate the real objective function val-ues of five datasets of a real-world expensive discrete petroleum well placement problem. We also investigate if an ensemble of these three methods surpasses their individual performances. The results demonstrate that the ensemble prediction outperforms the individual methods in 4 out of 5 datasets in terms of Root Mean Square Error, while k-NN provides the best Mean Absolute Error in 4 out of 5 datasets. Nonetheless, the Friedman and Bonferroni-Dunn tests indicate that there are only statistically significant differences between MLP and the remaining methods. Therefore, the choice between k-NN, RF, or the ensemble is indifferent.