Multiple response optimization: Analysis of genetic programming for symbolic regression and assessment of desirability functions

Multiple responses optimization (MRO) consists in the search for the best settings in an problem with conflicting responses. MRO is performed following the steps: experimental design; experimental data gathering; mathematical models building; statistical validation of models; agglutination of the models responses in only one function to be optimized; optimization of agglutinated function; experimental validation of the best conditions. This work selected two MRO cases from literature aiming to compare two methods of mathematical models building and two agglutinating functions to assess the best one among the four possible combinations. The methods used in mathematical models building were the ordinary least squares performed in Minitab (v. 17) and genetic programming performed in Eureqa Formulize (v. 1.24.0). The assessment of the best method for building mathematical models was performed using the Akaike Information Criterion. The responses agglutination were performed using the desirability and modified desirability functions. In all MRO cases, the optimization step was performed by generalized reduced gradient method on Microsoft ExcelTM software. The average percentage distance between predicted and experimental results was used to both assess the best agglutination function and verify the effect of the method used in the building of the mathematical models about its fitness to estimate the best condition close to that one obtained on experimental validation step. The obtained results suggest as the better strategy for multiple responses optimization the use, jointly, of genetic programming to mathematical models building and the modified desirability function to responses agglutination.