Fuzzy distributional chance-constrained programming for handling stochastic and epistemic uncertainties during flotation processes

Abstract

During the flotation process, a fuzzy distributional chance-constrained programming approach is proposed to design the circuit structure, equipment size and operating conditions considering stochastic and epistemic uncertainties. Stochastic uncertainties are irreducible, such as fluctuations in copper price and circuit feed mass flowrate, and epistemic uncertainties are due to the complicated flotation mechanism. To achieve the probability measure in the chance constraints, a finite number of scenarios are defined for the stochastic uncertainties by using discrete probability distribution sets. Moreover, the epistemic uncertainties are handled by fuzzy sets. In this context, a fuzzy probability-box of profits combining probability theory with fuzzy theory can be obtained to assess the distribution profile. The integral whole optimization of the flotation process is solved by using a rule-oriented genetic algorithm, adapted from the non-dominated sorting genetic algorithm (NSGA-II), and the design rules are embedded in initialization, crossover and mutation. Finally, the sensitivity analysis of epistemic uncertainties on the optimal designs is carried out to get the critical uncertain variable. The method proposed here can fully reflect the flexibility of the process design under mixed uncertainties, and the optimal designs are compromise solutions that take into account the economic indicator and uncertainty quantification.