A multiobjective approach in constructing a predictive model for Fischer-Tropsch synthesis

Fischer-Tropsch synthesis (FTS) is an important chemical process that produces a wide range of hydrocarbons. The exact mechanism of FTS is not yet fully understood, so prediction of the FTS products distribution is a not a trivial task. So far, artificial neural network (ANN) has been successfully applied for modeling varieties of chemical processes whenever sufficient and well-distributed training patterns are available. However, for most chemical processes such as FTS, acquiring such amount of data is very time-consuming and expensive. In such cases, neural network ensemble (NNE) has shown a significant generalization ability. An NNE is a set of diverse and accurate ANNs trained for the same task, and its output is a combination of outputs of these ANNs. This paper proposes a new NNE approach called NNE-NSGA-II that tries to prune this set by a modified nondominated sorting genetic algorithm to achieve an optimum subset according to 2 conflicting objectives, which are minimizing root-mean-square error in training and unseen data sets. Finally, a comparative study is performed on a single best ANN, a regular NNE, NNE-NSGA, and 3 popular ensemble of decision trees called random forest, stochastic gradient boosting, and AdaBoost.R2. The results show that in training data set, stochastic gradient boosting and AdaBoost.R2 have better fitted the samples; however, for the predicted FTS products in unseen data set, NNEs methods specially NNE-NSGA-II have considerably improved the generalization ability in comparison with the other competing approaches.