Fuzzy robust optimization for handling feed stream and model parameter uncertainties during comminution process

Abstract

Uncertainty analysis of an industrial grinding optimization process involving various sources of uncertainties and multiple numbers of objective functions has been studied in this work. Two primary sources of uncertainties, e.g. (1) operational parameters such as feed size distributions that are subjected to uncertainty due to varied range of feed sources that the industrial grinding process handles, and (2) model parameters that are obtained by the regression analysis of experimental data and subjected to regression and experimental errors, have been considered. Moreover, obtaining statistical distributions for these uncertain parameters are practically challenging. Hence, these parameters are considered as fuzzy numbers and the embedded uncertain multi-objective optimization problem has been analyzed using credibility based fuzzy robust optimization (FRO) technique. This technique helps in converting the uncertain fuzzy optimization formulation into a deterministic equivalent form, which can be further utilized to obtain the Pareto solutions by well-developed evolutionary algorithms. Initially, PO solutions are obtained by considering the uncertainty in different sets of uncertain parameters separately. This is followed by the study of amalgamated effect of uncertain parameters on PO solutions. Along with this, different fuzzy measures e.g. credibility, possibility, necessity etc. are utilized to observe their effects on final solutions. PO solutions obtained from possibility and necessity based FRO show the optimistic and pessimistic attitudes of risk, respectively. This provides a key to a decision maker to select any point based on the existing risk appetite. As compared to the deterministic results, the robust Pareto solutions show potential improvements of 26% and 16% in throughput and mid-size fractions, respectively. This generic approach not only provides the solution for robust range of operation based on the risk appetite of the enterprise, but also helps a decision maker to decide which parameters, amidst the set of uncertain parameters, are more sensitive to the results utilizing various fuzzy measures such as credibility, possibility and necessity. Along with this, the PO solutions obtained with robust optimization are compared with the solutions obtained by Expected Value Model (EVM).