Simultaneous optimization of the performance of flotation circuits and their simplification using the jumping gene adaptations of genetic algorithm

The elitist non-dominated sorting genetic algorithm with the modified jumping gene operator (NSGA-II-mJG) is used to optimize the performance of froth flotation circuits. Four example optimization problems (Mehrotra and Kapur, 1974; Green, 1984; Dey et al., 1989) [Mehrotra, S.P., Kapur, P.C., 1974. Optimal–sub-optimal synthesis and design of flotation circuits. Sep. Sci. 9, 167–184; Green, J.C.A., 1984. The optimization of flotation networks. Int. J. Miner. Process. 13, 83–103; Dey, A.K., Kapur, P.C., Mehrotra, S.P., 1989. A search strategy for optimization of flotation circuits. Int. J. Miner. Process. 26, 73-93.] of varying complexity are solved using single-objective functions. In one example, the overall recovery of the concentrate stream is maximized for a desired grade of the concentrate and a fixed total cell volume. The interconnecting cell linkage parameters (fraction flow rates) and the mean cell residence times are the decision variables. In all these cases, the optimal solutions obtained using NSGA-II-mJG are superior to those obtained by earlier techniques (which converged to local optimal solutions). Thereafter, a few two-objective optimization problems are solved. In these, the performance of the circuit is optimized, and simultaneously, the number of connecting streams is minimized so as to give simple circuits. Pareto optimal sets of equally good (non-dominating) solutions are obtained. This is probably the first study involving the multi-objective optimization of flotation circuits with one aim being to simplify them.     

A multiobjective steepest descent method with applications to optimal well control

Multiobjective optimization deals with mathematical optimization problems where two or more objective functions (cost functions) are to be optimized (maximized or minimized) simultaneously. In most cases of interest, the objective functions are in conflict, i.e., there does not exist a decision (design) vector (vector of optimization variables) at which every objective function takes on its optimal value. The solution of a multiobjective problem is commonly defined as a Pareto front, and any decision vector which maps to a point on the Pareto front is said to be Pareto optimal. We present an original derivation of an analytical expression for the steepest descent direction for multiobjective optimization for the case of two objectives. This leads to an algorithm which can be applied to obtain Pareto optimal points or, equivalently, points on the Pareto front when the problem is the minimization of two conflicting objectives. The method is in effect a generalization of the steepest descent algorithm for minimizing a single objective function. The steepest-descent multiobjective optimization algorithm is applied to obtain optimal well controls for two example problems where the two conflicting objectives are the maximization of the life-cycle (long-term) net-present-value (NPV) and the maximization of the short-term NPV. The results strongly suggest the multiobjective steepest-descent (MOSD) algorithm is more efficient than competing multiobjective optimization algorithms.     

A variable-control well placement optimization for improved reservoir development

Determination of well locations and their operational settings (controls) such as injection/production rates in heterogeneous subsurface reservoirs poses a challenging optimization problem that has a significant impact on the recovery performance and economic value of subsurface energy resources. The well placement optimization is often formulated as an integer-programming problem that is typically carried out assuming known well control settings. Similarly, identification of the optimal well settings is usually formulated and solved as a control problem in which the well locations are fixed. Solving each of the two problems individually without accounting for the coupling between them leads to suboptimal solutions. Here, we propose to solve the coupled well placement and control optimization problems for improved production performance. We present an alternating iterative solution of the decoupled well placement and control subproblems where each subproblem (e.g., well locations) is resolved after updating the decision variables of the other subproblem (e.g., solving for the control settings) from previous step. This approach allows for application of well-established methods in the literature to solve each subproblem individually. We show that significant improvements can be achieved when the well placement problem is solved by allowing for variable and optimized well controls. We introduce a well-distance constraint into the well placement objective function to avoid solutions containing well clusters in a small region. In addition, we present an efficient gradient-based method for solving the well control optimization problem. We illustrate the effectiveness of the proposed algorithms using several numerical experiments, including the three-dimensional PUNQ reservoir and the top layer of the SPE10 benchmark model.     

Extremum solutions to the limit equilibrium method subjected to physical admissibility

In the slope stability analysis, the interslice force calculated by the method of slices is the internal force of the slope in the limit equilibrium state, which is vital to the design of reinforcement. However, none of the existing methods can guarantee a priori the interslice force is reasonable. Starting from the global analysis procedure, an optimization problem for maximizing the factor of safety is posed under the constraints that the system of forces in the sliding body is physically admissible. In the problem, both the factor of safety and the normal stress along the slip surface are taken as the independent variables. With weak nonlinearity and no numerical problems inherent in the methods of slices, the optimization problem can be solved by those conventional optimization techniques. No assumption is made regarding the interslice forces, but the system of forces from the optimization problem is physically admissible. To bracket the factor of safety, meanwhile, the minimum of the factor of safety is calculated through a minimization process under the same constraints as the maximization process. It is illustrated that for smooth slip surfaces, the solutions to the maximum and the minimum almost coincide, and for non-smooth slip surfaces, the interval of the solution is very narrow.     

On optimization algorithms for the reservoir oil well placement problem

Determining optimal locations and operation parameters for wells in oil and gas reservoirs has a potentially high economic impact. Finding these optima depends on a complex combination of geological, petrophysical, flow regimen, and economical parameters that are hard to grasp intuitively. On the other hand, automatic approaches have in the past been hampered by the overwhelming computational cost of running thousands of potential cases using reservoir simulators, given that each of these runs can take on the order of hours. Therefore, the key issue to such automatic optimization is the development of algorithms that find good solutions with a minimum number of function evaluations. In this work, we compare and analyze the efficiency, effectiveness, and reliability of several optimization algorithms for the well placement problem. In particular, we consider the simultaneous perturbation stochastic approximation (SPSA), finite difference gradient (FDG), and very fast simulated annealing (VFSA) algorithms. None of these algorithms guarantees to find the optimal solution, but we show that both SPSA and VFSA are very efficient in finding nearly optimal solutions with a high probability. We illustrate this with a set of numerical experiments based on real data for single and multiple well placement problems.     

基于区域分解法的水文地质参数寻优研究

在建立地下水流模型的过程中，水文地质参数寻优一直是较为复杂的步骤之一，具体难点包括寻优方法的取用，为保持总体平衡所引起的参数峰值异常以及总体寻优需要大量的计算机时等问题。本文运用区域分解法（Domain Decomposition method，DDM）的基本思想，将整个区域的参数寻优问题分解为各参数分区内的子域问题求解，通过寻找整个区域上的Nash均衡最终获得各子域上的最优参数。实验算例及其结果证明应用该方法实现水文地质参数自动寻优，不但具有高度的可靠性，同时优化问题的规模减小。此举不但减少了求解过程所需要的CPU时间，而且提高了参数拟合度。     

遗传算法在非线性地下水经济管理模型中的应用

通常采用基于梯度的数学规划方法求解地下水管理模型,如线性规划和非线性规划。但对于高度非线性、非凸的优化问题,尤其是涉及到经济或环境的地下水管理模型,传统方法难以有效地寻找全局最优解。本文介绍了一种求解非线性地下水资源管理模型的遗传算法,并以山东羊庄盆地分布参数地下水系统非线性管理模型为例,给出了用遗传算法在求解这类问题的一般步骤。结果表明该方法能快速有效地找到全局最优解。     

State of the art in the conceptual design of flotation circuits

The present study summarizes reports on optimal flotation circuits design over the period from 1989 to present. A review is made on the resolution characteristics of each study, leading to a classification of the approaches into four different groups, in which conclusions are based on either (A) mathematical solutions without binary variable, (B) mathematical solutions with binary variable, (C) heuristic solutions, or (D) genetic algorithms. These groups aim at a common scheme of resolution, varying in both flotation and milling models employed, characteristics of their superstructures, and functions which each study proposes to optimize, as well as the effects of the application of each strategy on the form of the solution of the circuit (selection of stages, selection of equipment, and dimensions of equipment).Within these either implicit or explicit multi-objective optimization problems there are challenges strongly related to the obtaining of better flotation and milling/classification models, as well as the treatment of uncertainty related to important parameters (kinetics, composition, external economic factors) and changes in previously established configurations using methods in which the designer's criteria influence the application of models and restrictions on the problem. Also, the incorporation of environmental issues needs more attention.     

新型捕收剂RA-92在低品位碳酸锰矿选矿中的应用

微细粒低品位锰矿由于颗粒间的非选择性聚集、浮选药剂用量大、浮选效率低等技术难题而致使其利用困难,造成大量浪费。在品位低于13%的锰矿浮选技术研究中,捕收剂最受关注,前人已研究了多种类型的捕收剂,所得精矿品位在16.9%~18.3%之间,回收率为56%~97%,回收率比较理想,但精矿品位总体不高。本文将新型捕收剂RA-92应用于湖南凤凰-花垣地区低品位碳酸锰矿(锰品位为10.7%)的选矿工艺中,实验研究了磨矿细度、pH值、抑制剂和捕收剂用量对浮选效果的影响,在最佳工艺条件下,精矿品位由原矿的10.7%提升至17.4%,回收率达到80.2%。研究表明RA-92对碳酸锰矿具有良好的捕收性能,浮选工艺相对简单且捕收剂用量少,浮选成本较低,可为此种捕获剂在微细粒低品位碳酸盐锰矿选矿中的应用得到推广。     

Optimizing for grade or profit in mineral processing circuits — Circuit analysis

Circuit analysis is applied to the general optimization of mineral processing circuits. Four functions are defined: feed, selectivity, composition and criteria. After defining the criteria function that is to be optimized, the general method of optimization is shown in closed form. Two examples are given. That optimum grade and recovery do not coincide is proven.     

三峡水库围堰发电期调度模拟优化研究

汛限水位是协调综合利用水库防洪和兴利矛盾的重要参数。三峡水库围堰发电期调度规则将汛期水库水位控制在134．9-135．4m运行,本文将汛期(6-9月)按旬划分为12个分期,建立模拟模型和动态规划模型;采用宜昌站120年实测日流量序列,通过所建模型计算,得到了优化的分期汛限水位方案。模型实现了模拟和优化的有机结合,将带机遇约束的多目标优化问题转化为确定性约束条件下的单目标优化问题,降低了复杂性。结果表明,模型在不增加防洪风险的前提下,发电效益增加了2．21％(2005 年)和2．32％(2006年)。     

A compartment model for the mass transfer inside a conventional flotation cell

A model is developed by taking into account the simultaneous mechanisms of true flotation and entrainment in a conventional flotation cell. The total volume of the cell is divided into three compartments: pulp collection zone, pulp quiescent zone and froth region, with the mechanisms being modeled as occurring at the same time but originating at different places: true flotation from the collection zone and entrainment from the quiescent one. A particle is referred to as suspended in water or attached to an air bubble, depending upon its original state before crossing the pulp–froth interface (whether or not it remains in that state all the way to the concentrate launder). The model is obtained by solving a set of equations describing the mass conservation of solids and water between adjacent compartments. The principal mass transfer factors are identified as: the flotation rate constant, the mean residence time in the collection zone, the froth recovery of attached particles, the degree of entrainment through the froth and the water recovery from the feed to the concentrate. The development presented here allows the intricate nature of the mass transfer in a flotation cell to be reduced to one single equation, overcoming the need of numerical methods for simulation purposes. Moreover, it is shown that reliable prediction of grade and recovery can be obtained without detailed information on the pulp hydrodynamics or on any froth sub-process either than drainage, bubble bursting and bubble coalescence.     

Simultaneous and sequential approaches to joint optimization of well placement and control

Determining optimal well placement and control is essential to maximizing production from an oil field. Most academic literature to date has treated optimal placement and control as two separate problems; well placement problems, in particular, are often solved assuming some fixed flow rate or bottom-hole pressure at injection and production wells. Optimal placement of wells, however, does depend on the control strategy being employed. Determining a truly optimal configuration of wells thus requires that the control parameters be allowed to vary as well. This presents a challenging optimization problem, since well location and control parameters have different properties from one another. In this paper, we address the placement and control optimization problem jointly using approaches that combine a global search strategy (particle swarm optimization, or PSO) with a local generalized pattern search (GPS) strategy. Using PSO promotes a full, semi-random exploration of the search space, while GPS allows us to locally optimize parameters in a systematic way. We focus primarily on two approaches combining these two algorithms. The first is to hybridize them into a single algorithm that acts on all variables simultaneously, while the second is to apply them sequentially to decoupled well placement and well control problems. We find that although the best method for a given problem is context-specific, decoupling the problem may provide benefits over a fully simultaneous approach.     

Optimum design of stone column-improved soft soil using multiobjective optimization technique

A combined simulation–optimization-based methodology is proposed to identify the optimal design parameters for granular bed–stone column-improved soft soil. The methodology combines a finite difference-based simulation model and an evolutionary multiobjective optimization model. A combined simulation–optimization methodology is developed for two different formulations: (a) the minimization of maximum settlement and the minimization of differential settlement subject to stress constraints; (b) the minimization of maximum settlement, the minimization of differential settlement and the maximization of the degree of consolidation subject to stress constraints. The developed methodology is applied to an illustrative system. Different scenarios are evaluated to examine critical field conditions. The solution results show that the modular ratio and the ultimate stress carrying capacity of the stone column are the most important parameters for optimal design. The obtained results also show the potential applicability of the developed methodology.     

基于连续不确定区域的蚁群算法求解水文地质逆问题

本文在介绍求解复杂组合优化问题而提出的蚁群算法的基础上,提出一种基于连续不确定区域的蚁群算法。该方法将连续变量优化问题转化为一个组合优化问题,进而将蚁群算法求解。通过两个水文地质逆问题的求解,表明该方法在参数识别中计算结果可靠,具有较好的计算效率。     

河北某斑岩型钼矿提高选矿指标试验研究

河北省某钼矿为单一斑岩型钼矿,主要金属矿物为辉钼矿。为了进一步提高钼精矿的品位和回收率,试验采用混合捕收剂(煤油∶2号油=2∶1)和新型捕收剂PE-100相结合的方法,粗选时可使粗精矿的回收率提高2个百分点,品位也略有提高。为节约生产成本,试验采用阶段磨矿阶段选别的选矿工艺,即原矿磨矿(-0.074mm占60%)后,经一次粗选,一次扫选,粗精矿再磨(-0.038mm占85%)后再进行5次精选,最终获得钼精矿品位w(Mo)=50.007%,回收率为89.90%的较好指标。     

A MILP model for design of flotation circuits with bank/column and regrind/no regrind selection

A method for the design of flotation circuits is presented. The design problem is represented by several superstructures. The first superstructure represents separation tasks (STS), which include: feed processing superstructure (FPS), concentrate processing superstructure (CPS), and tail processing superstructure (TPS). The FPS commonly uses a single stage, i.e., rougher. The CPS represents the circuit needed to carry out the cleaner task, and the TPS represents the circuit needed to carry out the scavenger task. These superstructures are flow networks between several separation stages. In each separation stage two kinds of cells are allowed, bank and column. In several streams in the CPS and TPS, the incorporation of regrind mills is also included.     

水文模型参数多目标率定及最优非劣解优选

针对概念性水文模型参数众多、相互制约,且多目标参数优化率定最优参数求解困难、易受决策者主观因素影响的问题,采用多目标优化算法对水文模型参数进行率定,得到模型参数最优非劣解集,在此基础上,引入最小最大后悔值决策理论,并结合Pareto支配基本理论,提出了一种多目标最优非劣解选取准则。以柘溪流域为研究对象,采用三目标MOSCDE优化率定新安江模型的参数,并与单目标SCE-UA优化结果进行对比分析。结果表明,提出的非劣解选取方法可以有效从大规模非劣解集中筛选出最优非劣解,大大缩短参数率定耗时。     

阶段磨选工艺在白云鄂博磁铁矿选矿中的应用

白云鄂博磁铁矿是由沉积变质并经多期热液叠加形成,矿石矿物间嵌布关系复杂,嵌布粒度细.为进一步提高白云鄂博磁铁矿选矿铁精矿品位,降低有害杂质含量,采用阶段磨选工艺流程后的铁精矿品位达到66.91％,回收率为73.12％,与原连续磨矿分级—弱磁选—反浮选工艺流程相比,精矿品位和回收率同时提高,选别指标有了明显改善.