Fuzzy distributional robust optimization for flotation circuit configurations based on uncertainty theories

Fuzzy distributional robust optimization for flotation circuit configurations is proposed to find optimal flotation circuit configurations based on the distribution profiles of economic performance, and the best and worst distributions can be identified by uncertainty theories. All feasible flotation circuits are represented by a super-structure, and single cell is simulated by a flotation simulator. Uncertainties considered here involve the feed stream, copper price and model parameters, defined as fuzzy numbers. Under possibility and necessity theories, this work obtains uncertainty distributions of profits by fuzzy simulation and defines the fuzzy entropy within such a context. Process optimization under uncertainties is converted into an equivalent deterministic formulation by fuzzy expected values, and Pareto optimal solutions are obtained by nondominated sorting genetic algorithm. The significance of considering the fuzzy entropy lies in the fact that designers aim to achieve a better profit distribution under less system uncertainty. The proposed method avoids dividing the uncertain parameters into a limited number of scenarios in stochastic programming methodology and can obtain more optimal designs. The results show that the combination of these techniques can provide better flotation designs by using the distribution profiles of profits under stochastic and epistemic uncertainties, which is rare in existing studies.