Optimization Methods For Comprehensive Indicators Of Production-line In Mineral Processing

Metals are extensively used in many industries such as construction, transportation, communications, aircraft and manufacturing industry. The pursuit of industrial development and the progress of technology have made China as an even more mineral resources dependent country than ever before. There are plenty of hematite resources with the nature of low grade and poor separability in China. Hematite resources are mainly processed in the flowsheet consisting of shaft furnace roasting, grinding and magnetic separation cell. In order to produce qualified concentrate products and enhance efficiency, the plant determines the enterprise-wide production indicators (denoted as EPI, e.g., concentrate grade, yields, metal recovery, concentration ratio and production cost over the entire horizon) and decomposes them to production indicators of production-line (denoted as PPI, e.g., concentrate grade, yields, metal recovery, concentration ratio and production cost in the current period) by production planning and scheduling. Based on the above PPI targets, the operational indicators (e.g., magnetic tube recovery rate in roasting cell, particle size in grinding cell, concentrate grade,and tailings grade in magnetic separation cell) for each mineral processing subprocess are determined by the production operation optimization. These operational indicators' targets are then transformed into the setpoints of the production control systems in each subprocess, and the setpoints are tracked.by the control system. At last, the EPI indicators are controlled in the expected target ranges. In the above process, whether the PPI indicators are reasonable or not directly influence the setting of the operational indicators in the lower level and the action of the control systems, and finally influence the yields and quality of the concentrate product. As a consequence, the PPIs optimization decision has important significance for improving the concentrate grade, metal recovery, yields while decreasing the consumption (concentration ratio) and production cost.The PPIs decision making for mineral processing is to improve the concentrate grade, metal recovery, yields and decrease the concentration ratio and production cost as possible, considering the target ranges and production constraints (e.g., raw ore property and combination, equipment capacity, runtime, energy resource consumption, etc.) in different production periods. However, there exist several mutual conflicts among the EPIs. For example, the production of high-grade concentrate requires high-grade and therefore expensive raw ore, leading to increased cost and reduced recovery. Moreover, these indicators are needed to be decomposed in different time scales where the target ranges, production constraints and boundary parameters (e.g., fluctuation of raw ore composition and price, runtime changes for equipment breakdown, etc.) vary with the variation of the market demand and production process. Therefore, the PPIs decision making is a multiobjective nonlinear optimization problem characterized by multi-level, multi-periods, multiple conflicting objectives and complex constraints, it is difficult to optimize the PPIs by the existing optimization approaches. In practice, the PPIs are often set by managers with incoherent empirical knowledge. Because of the arbitrariness and inaccuracy based on managers'experience, the EPI indicators often deviate from the.target range, thus lead to undesirable effects such as poor quality product, high cost, high consumption of resources and so on. As a consequence, it has important theoretical significance and application value to research on how to make optimization decision for PPIs with above features, so as to optimize the total EPIs.Supported by the National Basic Research Program of China (973 project)"the total control strategy and operational control approach for complex manufacturing processes" (No.2009CB320601), the research on optimization approaches for mineral processing PPI indicators decision has been carried out in order to optimize the total EPI indicators for mineral processing enterprise. A software platform based on above optimization approach has been developed to assist the decision making of EPI&PPI. The main contents are summarized as follows:(1) In solving multiobjective optimization problem, classical analytical methods are prone to local optimal and are sensitive to initial points while pure evolutionary algorithms (EAs) show the shortage of slow convergence and weak direction. A gradient driven (MO-G) hybrid operator is proposed. The search direction in the operator is normalized as a strictly convex cone combination of negative gradient direction of each objective, and is provided to move each selected point along some descent direction of the objective functions to the Pareto front, so as to reduce the invalid trial times of crossover arid mutation. Two theorems are established to reveal a descent direction for the improvement of all objective functions. The gradient-based hybrid operator is incorporate in two evolutionary algorithms named the gradient-based NSGA-? (G-NSGA-?) and the gradient-based SPEA2 (G-SPEA2). Experiments on standard test problems, namely ZDT 1-3, CONSTR, SRN, and TNK, have demonstrated that the proposed algorithms can improve the chance of minimizing all objectives compared to pure evolutionary algorithms in solving the multiobjective optimization problems with differentiable objective functions under short running time limitation. The results also show that the proposed hybrid operators have better performance than that of pure gradient-based operators in attaining either a broad distribution or maintaining much diversity of obtained non-dominated solutions. The above methods lay the foundation for optimizing the comprehensive indicators of production-line in mineral processing.(2) Optimization methods for the determination of mineral processing PPIs are proposed, including a multiobjective optimization method for the decision of mineral processing EPIs and a multi-objective optimization decomposition method for the decision of mineral processing PPIs. By the above proposed methods, the EPIs are optimized within the expected objective interval, the feasible and satisfied PPIs are then determined by the rolling horizon based decomposition method.a) In the proposed multiobjective EPI optimization method, a multiobjective EPI model (denoted as MPPP) is presented. The model optimizes five production indices, including its iron concentrate output, the concentrate grade, the concentration ratio, the metal recovery, and the production cost, under given production conditions such as mineral raw materials properties, limited equipment capacity, limited inventories, and energy resources over a specified time horizon. In current researches, many production conditions (e.g., restrictions for resource combination and product quality) and some objectives are not involved in the problem. The multiobjectives of EPI optimization problem are normally aggregated into a single one by weighted-sum aggregation, however, the solution depends largely on the values assigned to the weighting factors and these factors are difficult to be determined reasonably. Therefore, the proposed hybrid multiobjective evolutionary algorithms (G-NSGA-? and G-SPEA2) are utilized to solve the problem MPPP. The experimental results show the effectiveness of the proposed approach.b) In the proposed multiobjective PPI optimization decomposition method, the EPI indicators are decomposed into feasible and satisfied PPI indicators. The decomposing process is characterized by multi-level, multi-periods and conflicting objectives. Traditionally, the production indictors are determined in each period and each level separately. However, the EPI indictors determined by the upper level may be infeasible for the PPI indicators in the lower level. A novel multiobjective 0-1 mixed integer nonlinear programming model is presented for the simultaneous EPI and PPI optimization problem (denoted as O-model). The model optimizes the five EPI indicators meanwhile, considers the conflicting PPI indicators (e.g.,. the concentrate yield, the concentrate grade, the concentration ratio, the metal recovery and the production cost) and many production conditions (e.g., limits for the equipment capacity, the energy resource consumption, the quality requirement and the raw material combination) with different time scale. In order to reduce the computational cost for solving O-model, a rolling horizon based two-level decomposition approach is proposed to separate O-model into an upper level model (H-model) and a lower level model (L-model). An interactive partition (IP) and.MO-G based hybrid evolutionary multiobjective algorithm named as IG-NSGA-II/IG-SPEA2 is proposed to solve both H-model and L-model, where an IP technique is designed to generate the efficient feasible combinational nodes, an ideal solution technique is provided for fathoming the infeasible nodes, an improved MO-G operator is developed to accelerate the evolution process in each selected node, and a cut with all continuous variables is constructed to exclude the previous feasible combination if it is not desired for the decision makers (DMs). The experimental results show the effectiveness of the proposed approach..(3) To assist the optimization decision of the mineral processing PPI indicators, a production indicators optimization software platform for optimizing the mineral processing EPI&PPI indicators is designed and developed. The platform consists of the EPI&PPI indicators objective management module, boundary constraints management module, decision process module, metal balance calculation module, production indicator optimization model library, algorithm library and so on. Moreover, the platform is characterized by modularity, configuration model, extensibility and friendly interface. The model and algorithm libraries in the software are flexible configuration, therefore, the platform can meet the decision demand of the production indicators for different complex production processes.(4) Based on the real production data from a mineral processing plant, experimental research is carried out on the developed system in our laboratory. Simulation results show that the above proposed methods can simultaneously enhance the EPI&PPI indicators under short time limitation. For example, under the given experimental conditions, the PPI indicators value by the system are all within the expected ranges. Furthermore, compared with the results by manual decision, the monthly cumulative EPI indicators are all improved (concentrate grade increased by 0.13%, concentration ratio decreased by 0.009, metal recovery increased by 0.13%, production cost reduced by 5.2 Yuan/ton, yields increased by 1000 tons). The developed software platform shows a good application prospect for it can provide not only decision-making support for planners and schedulers, but also experimental platform for researchers.