A decomposition approach for the scheduling of a steel plant production

In this paper we present a decomposition strategy for solving large scheduling problems using mathematical programming methods. Instead of formulating one huge and unsolvable MILP problem, we propose a decomposition scheme that generates smaller programs that can often be solved to global optimality. The original problem is split into subproblems in a natural way using the special features of steel making and avoiding the need for expressing the highly complex rules as explicit constraints. We present a small illustrative example problem, and several real-world problems to demonstrate the capabilities of the proposed strategy, and the fact that the solutions typically lie within 1–3% of the global optimum.     

Iterative approach to weir drainage

Understanding liquid drainage in foam is an important step in determining the performance of a froth flotation system. The geometry of the flotation vessel has a major impact on drainage and thereby performance. In particular it is known that in a vessel geometry with sloping walls, a thin boundary layer of wet foam can appear near the wall, containing a high speed liquid jet that is sliding downwards. Although a zeroth order theory exists describing this liquid jet (Eur. Phys. J. E 8 (2002) 517), it has a number of unsatisfactory features which need to be rectified. The jet structure predicted does not match correctly onto the known state of the foam far from the wall. Also important physical mechanisms influencing the speed and liquid content of the jet are neglected. These problems can be corrected by iteratively improving the zeroth order solutions. The iterative approach indicates that bulk foam motion is an important effect influencing the jet boundary layer, and indeed that the foam is wetter at the wall than previously predicted.     

迭代遗传算法及其用于生物反应器补料优化

针对化工动态优化的数值求解问题,提出将迭代思想与遗传操作相结合,构建迭代遗传算法.算法首先对时间区间和控制搜索域实施离散化,进而应用遗传操作搜索离散问题的最优控制策略.逐步收缩搜索域并迭代以消减离散化带来的偏差,不断改善寻优结果,增强算法的稳健性.实例测试表明该算法简便、可行、高效,已成功地应用于Lee-Ramirez生物反应器补料流率的优化,运算结果优于文献值,显示了迭代遗传算法的优越性.迭代遗传算法尤其适用于系统的梯度信息不可得的情况.     

An integrated self sufficient multipurpose plant for seawater desalination

A multipurpose plant is described, which produces drinking water and chemicals from seawater. The most important part of the plant consists in a combined MSF/VT evaporator, which operates on a high economy ratio and enables also a high concentration of the brine. These two facts are due to a special treatment of the evaporator feedwater by chemical agents produced from the concentrated brine. A surplus of these chemicals can be sold. The energy supply of the complex is assured by an adequate power station, which provides process steam and electricity at such a ratio as to minimize fuel cost.     

MILP scheduling model for multipurpose batch processes considering various intermediate storage policies

MILP (Mixed Integer Linear Programming) scheduling models for non-sequential multipurpose batch processes are presented. Operation sequences of products have to be made in each unit differently by considering production route of each product under a given intermediate storage policy to reduce idle time of units and to raise the efficiency of the process. We represent the starting and finishing time of a task in each unit with two coordinates for a given storage policy. One is based on products, and the other is based on operation sequences. Then, using binary variables and logical constraints, we match the variables used in the two coordinates into one. We suggest MILP models considering sequence dependent setup times to guarantee the optimality of the solutions. Two examples are presented to show the effectiveness of the suggested models.     

A solution approach to the design of multi-period,multipurpose batch plants

A deterministic model for multipurpose, multiperiod batch plants was presented in a linearized form to predict the future design according to the change of demand by using a modified Benders’ Decomposition. The OSL code offered by the IBM corporation as optimizer was employed for solving several example problems. The decomposition method was successful, showing remarkable reduction in the computing times as compared with those of the direct solution method. Also the heuristic used as a solution approach for the multiperiod model provided an efficient methodology to the block-structured problem by dividing the large overall problem into the manageable single period blocks.     

Economic optimal control applied to a solar seawater desalination plant

This paper discusses the formulation of an optimal control strategy taking into account economic objectives in the fresh water production process through a solar seawater desalination plant. It contributes both a linearised model of the solar-field dynamics and a simplified model of the produced distillate as a function of the outlet solar field water temperature. Then such linear models are used to design an economic receding horizon optimal controller. In particular, it comprises incomes related to the production of fresh water and the costs dealing with the electricity. Several simulations validate the proposed models and show the performance of the proposed economic optimal control strategy. In both cases, actual disturbances from physical experiments have been included in the simulations. Notice that the AQUASOL facility available at the Plataforma Solar de Almería (Spain) has been considered in this work as testbed.     

一种用水驱曲线确定油田单井最佳提液时机的方法

本文在对油田单井提液理论和应用现状进行分析的基础上,研究并提出一种用于判断单井最佳提液时机的新方法。该方法首先对单井动态生产数据进行甲型处理,并通过甲型水驱曲线拟合相对渗透率曲线的油相、水相指数和水油流度比;再由此作出无因次采油、采液指数曲线图并进行最佳提液时机分析。所提出的理论和方法对油田开发把握单井提液措施的有利时机,提高作业成功率具有一定的实际应用价值。     

A zonohedral approach to optimal colours

This article demonstrates that the CIE XYZ colour solid is a zonoid. An approximating zonohedral colour solid is constructed explicitly from a set of generating vectors, which are integrals of colour‐matching functions over narrow intervals of the visible spectrum. The zonohedral approach yields an intuitive, constructive proof of the Optimal Colour Theorem: the reflectance function of an optimal colour takes on only the values 0 or 1, with at most two transition wavelengths. In addition, zonohedral techniques can simplify computations: for example, optimal colours can be found without calculating transition wavelengths. Finally, zonohedra provide a simple, unified approach to colour space and eliminate much of the confusion arising from chromaticity diagrams. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2013     

A novel approach to scheduling multipurpose batch plants using unit‐slots

Several models for scheduling multipurpose batch plants exist in the literature. The models using unit‐specific event points have shown better solution efficiency on various literature examples. This article presents a novel approach to scheduling multipurpose batch plants, which uses unit‐slots instead of process‐slots to manage shared resources such as material storage. We develop two slightly different models that are even more compact and simpler than that of Sundaramoorthy and Karimi, Chem Eng Sci. 2005;60:2679–2702. Although we focus on material as a shared resource, our multi‐grid approach rationalizes, generalizes, and improves the current multi‐grid approaches for scheduling with shared resources. Our models allow nonsimultaneous transfers of materials into and out of a batch. We show by an example that this flexibility can give better schedules than those from existing models in some cases. Furthermore, our approach uses fewer slots (event‐points) on some examples than even those required by the most recent unit‐specific event‐based model. Numerical evaluation using literature examples shows significant gains in solution efficiency from the use of unit‐slots except where the number of unit‐slots required for the optimal solution equals that of process slots. We also highlight the importance of constraint sequencing in GAMS implementation for evaluating mixed‐integer linear programming based scheduling models fairly. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Tracking the predefined optimal policies for multiple-fraction batch distillation by using adaptive control

Predefined optimal policies will be tracked with control systems to realize the optimum of multiple-fraction batch distillation. Adaptive control is proposed to carry out this task. Characteristics of batch distillation control are analyzed and a proper system is designed for controlling such processes. Besides tracking the optimal reflux ratio profile, the maximum vapor load will be maintained during the batch. In addition, a changing temperature profile of the condenser should be followed to reduce the operating energy with a possibly minimum subcooling. Recursive least square estimation (RLSE) with a variable forgetting factor is applied to the on-line identification of the plant to follow the changing dynamics of the process. Generalized predictive control (GPC) is used to track the predefined policies. The effectiveness of the control strategy is verified with a pilot batch column and the tracking performance is compared with that of PID controllers.     

A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants

Many continuous-time formulations have been proposed during the last decades for short-term scheduling of multipurpose batch plants. Although these models establish advantages over discrete-time representations, they are still inefficient in solving moderate-size problems, such as maximization of profit in long horizon, and minimization of makespan. Unlike existing literature, this paper presents a new precedence-based mixed integer linear programming (MILP) formulation for short-term scheduling of multipurpose batch plants. In the new model, multipurpose batch plants are described with a modified state-task network (STN) approach, and binary variables express the assignments and sequences of batch processing and storing. To eliminate the drawback of precedence-based formulations which commonly include large numbers of batches, an iterative procedure is developed to determine the appropriate number of batch that leads to global optimal solution. Moreover, four heuristic rules are proposed to selectively prefix some binary variables to 0 or 1, thereby reducing the overall number of binary variables significantly. To evaluate model performance, our model and the best models reported in the literature (S&K model and I&F model) are utilized to solve several benchmark examples. The result comparison shows that our model is more effective to find better solution for complex problems when using heuristic rules. Note that our approach not only can handle unlimited intermediate storage efficiently as well as the I&F model, but also can solve scheduling problems in limited intermediate storage more quickly than the S&K model.     

Stochastic approach for the calculation of anti-solvent addition policies in crystallization operations: An application to a bench-scale semi-batch crystallizer

This work discusses a stochastic approach for the calculation of robust anti-solvent addition policies for controlling the mean crystal size (MCS) and prediction of the crystal size distribution (CSD) in semi-batch crystallization operations. The proposed strategy is based on a structured-like population balance where uncertainties associated with the start-up condition and random fluctuations along the semi-batch operation can be taken into account in a very natural way. To include and quantify the effect of the uncertainties, a deterministic crystal growth model is embedded into a Fokker–Planck equation (FPE) resulting in a stochastic model for the MCS dynamics. This approach uses the generalized logistic equation (GLE) that has an adequate mathematical structure that suits the dynamic characteristic of the crystal growth. The numerical solution of the resulting FPE provides the most likely MCS evolution for a given anti-solvent flow-rate. The effects of the anti-solvent are incorporated into the parameters of the FPE and they are computed as linear piece-wise interpolating functions of the anti-solvent flow-rate. The strategy uses a PI-like regulator in closed-loop mode with the FPE to calculate the anti-solvent addition flow-rates for different set-point targets in the MCS. To validate the model and assess the merits of the proposed strategy, the crystallization of sodium chloride in water using ethanol as anti-solvent is performed in an experimental bench-scale semi-batch crystallizer. The implementation of the calculated anti-solvent policies resulted in a good control of the MCS despite modelling mismatch and uncertainties present during the crystallization operation.     

Design of multipurpose production facilities: A RTN decomposition-based algorithm

A general mathematical formulation for the design of multipurpose facilities has recently been presented by Barbosa-Póvoa and Pantelides (1997). The model proposed permits a detailed consideration of the design problem taking account of trade-offs between capital costs, revenues and operational flexibility. The optimal solution involves the selection of the required processing and storage equipment items and the required levels of provision of other production resources such as utilities, manpower, cleaning and transportation equipment.In order to guarantee solution optimality, the above design formulation has to consider a large number of equipment items, out of which it will select the ones that will actually be incorporated in the plant. This may result in large mixed-integer linear programming (MILP) problems that are expensive to solve.This paper presents a decomposition approach for the solution of large batch process design problems. The approach involves the iterative solution of a master problem (representing a relaxation of the original design problem) and a design sub-problem (in which several of the design decisions are already fixed).An example illustrating the effectiveness of the proposed decomposition approach is presented.     

基于MKPLS和SQP方法的间歇过程迭代优化控制

采用多向核偏最小二乘（MKPLS）方法建立间歇过程的模型并进行操作条件的优化。由于存在模型失配和未知扰动，基于MKPLS模型的最优控制轨迹在实际对象上往往难以实现最优的产品质量指标。本文利用间歇过程批次间的重复特性与序贯二次规划（SQP）优化算法中迭代计算的相似特点，提出了一种基于MKPLS模型的批次间优化调整策略，使得经过逐步优化调整得到的控制轨迹作用于实际对象时，可以得到更优的质量指标。该方法的有效性在苯乙烯聚合反应器和乙醇流加发酵过程的仿真对象上得到了验证。     

涤纶长丝装置改纺锦纶长丝

将涤纶长丝装置改纺锦纶长丝 ,着重介绍了装置的切片输送加料系统、纺丝部分的单体抽吸装置及熔体预过滤器、卷绕头部分的电器仪表和压缩空气系统等设备的改造 ,改造后的装置可生产 90～ 186dtex锦纶长丝 ,且 POY合格品率大于等于 99.8%。