A Hybrid Mathematical Programming Model for Densities of Alkanol + Alkanediol Mixtures Using Bacterial Foraging Optimization Algorithm

In this work, the densities of pure and binary mixtures of 1-pentanol or 1-decanol with 1,2-ethanediol or 1,2-propanediol or 1,3-butanediol or 2,3-butanediol were measured at atmospheric pressure and temperatures between 288.15K and 313.15K. For the considered system, two types of models were applied: black box and phenomenological. The black box model is represented by Artificial Neural Networks (ANNs) optimized with an improved version of Bacterial Foraging Optimization (iBFO). The phenomenological models are represented by Spencer-Danner and Li equations. In addition, in order to better fit the Spencer-Danner and Li equations to the obtained experimental data, the free parameters of these models were included in an iBFO algorithm. The average absolute error of the best ANN obtained was 2.82%, while the new forms of the Spencer-Danner and Li equations had an improvement from 26.31% and 26.51% respectively to 3.51% and 4.01% respectively. These results indicate the flexibility and efficiency of iBFO, which can provide good solutions for various cases.