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Fuzzy distributional robust optimization for flotation circuit configurations based on uncertainty theories
Minerals Engineering ( IF 4.8 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.mineng.2020.106433
Yu Liang , Dakuo He , Xinchao Su , Fuli Wang

Abstract 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 superstructure, 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.

中文翻译:

基于不确定性理论的浮选电路配置模糊分布鲁棒优化

摘要 提出了浮选回路配置模糊分布鲁棒优化,以根据经济绩效分布曲线寻找最优浮选回路配置,并通过不确定性理论确定最佳和最差分布。所有可行的浮选回路都由一个上部结构表示,单个单元由浮选模拟器模拟。这里考虑的不确定性涉及进料流、铜价和模型参数,定义为模糊数。在可能性和必要性理论下,这项工作通过模糊模拟获得了利润的不确定性分布,并在这样的背景下定义了模糊熵。不确定性下的过程优化通过模糊期望值转换为等效的确定性公式,并通过非支配排序遗传算法获得帕累托最优解。考虑模糊熵的意义在于设计者的目标是在更少的系统不确定性下实现更好的利润分配。该方法避免了随机规划方法中将不确定参数划分为有限数量的场景,可以获得更优化的设计。结果表明,这些技术的结合可以通过使用随机和认知不确定性下的利润分布曲线提供更好的浮选设计,这在现有研究中很少见。该方法避免了随机规划方法中将不确定参数划分为有限数量的场景,可以获得更优化的设计。结果表明,这些技术的结合可以通过使用随机和认知不确定性下的利润分布曲线提供更好的浮选设计,这在现有研究中很少见。该方法避免了随机规划方法中将不确定参数划分为有限数量的场景,可以获得更优化的设计。结果表明,这些技术的结合可以通过使用随机和认知不确定性下的利润分布曲线提供更好的浮选设计,这在现有研究中很少见。
更新日期:2020-09-01
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