油轮到达时间不确定条件下的原油调度优化

原油调度是炼油企业生产的第一个环节,它直接影响后续生产过程的稳定性和经济性.文中采用连续时间建模方法.建立了油轮到达时间不确定条件下的原油从到港、卸载、储存、调合到进料全过程的随机规划机会约束调度优化模型,模型的优化目标是最小化给定调度时界内的总操作费用.采用直方图法对油轮迟到时间进行回归,得到油轮迟到时间的概率密度函数和分布函数,并引入置信水平,将模型中的不确定性约束转化为确定性约束,使得油轮到达时间不确定条件下的随机规划机会约束模型转变为可以求解的确定性混合整数非线性规划模型.针对原油调度模型的特点,采用广义Benders分解算法将原模型分解为两个混合整数线性规划问题和一个非线性规划问题进行迭代求解.避免了直接求解混合整数非线性规划问题的复杂性.最后,将建立的模型和算法应用于背景企业的原油调度过程,结果表明模型和算法都有良好的实用性.     

基于状态设备网络的改进间歇生产调度模型

建立有效的间歇生产调度模型一直是生产调度问题研究的热点,基于特定事件点的连续时间建模方法是优化短期间歇生产调度问题的有效工具。基于状态设备网络和特定事件点概念,建立非线性的连续时间间歇生产调度模型。为了解决非线性引起的求解困难,该模型使用替代方法线性化模型中的双线性项,替代法不仅将建立的混合整数非线性规划模型转化为混合整数线性规划模型,且由于其不包含大M松弛项,能使模型搜索空间更紧凑,模型求解效率更高。通过3个实例对比实验表明了基于状态设备网络描述的改进间歇生产调度模型搜索高效性。另外,模型中还给出了不同存储条件下,基于状态设备网络描述的间歇生产调度模型约束,扩展了模型适用性。     

基于状态设备网络的改进间歇生产调度模型

建立有效的间歇生产调度模型一直是生产调度问题研究的热点,基于特定事件点的连续时间建模方法是优化短期间歇生产调度问题的有效工具。基于状态设备网络和特定事件点概念,建立非线性的连续时间间歇生产调度模型。为了解决非线性引起的求解困难,该模型使用替代方法线性化模型中的双线性项,替代法不仅将建立的混合整数非线性规划模型转化为混合整数线性规划模型,且由于其不包含大M松弛项,能使模型搜索空间更紧凑,模型求解效率更高。通过3个实例对比实验表明了基于状态设备网络描述的改进间歇生产调度模型搜索高效性。另外,模型中还给出了不同存储条件下,基于状态设备网络描述的间歇生产调度模型约束,扩展了模型适用性。     

考虑多类型不确定性的蒸汽动力系统运行优化

针对蒸汽动力系统中包含的多类型不确定性,根据基于时间表达、基于发生概率表达和基于集合表达划分不确定变量。多周期离散化操作解决基于时间表达的不确定变量;在各个周期内,耦合机会约束规划和鲁棒优化解决基于发生概率表达和基于集合表达的不确定变量,建立了机会约束鲁棒优化模型。以某石化企业蒸汽动力系统实例为背景,将该模型和传统模型的最优操作方案进行对比和分析。结果表明,该模型权衡系统经济性和稳定性,可获得在复杂不确定性下具有可接受风险的鲁棒性决策。     

基于特定单元事件点的改进间歇生产调度模型

建立有效的间歇调度模型一直是生产调度问题调度研究的热点,而连续时间模型是优化短期间歇生产调度问题的有效工具。基于特定单元事件点的概念,建立一种改进的间歇调度连续时间混合整数线性规划(MILP)模型。该调度模型引入了新变量,使模型处理物料在不同设备间的传输过程更加灵活。结果表明,提出的改进模型只需要较少的事件点,就可以快速有效处理无限中间存储(UIS)间歇调度问题。     

过程工业不确定条件下的计划与调度优化

过程工业的计划与调度优化是提高企业综合效益的有效途径,然而各种不确定因素的存在导致在确定性条件假设下得到的“最优”生产计划或调度次优或者不可实施。本文对当前过程工业不确定条件下计划与调度优化的研究进展进行了综述,并对系统建模和优化技术面临的挑战和下一步的发展趋势进行了分析。     

操作时间不确定的间歇过程最优化设计(Ⅰ)不限制等待时间过程

对操作时间不确定的不限制等待时间的间歇过程的优化设计问题 ,提出一种在操作时间不确定条件下确定过程的限定循环时间的方法。该方法使模型的限定循环时间变为相互独立的 ,从而可将原过程转化为更新过程 ,并根据更新过程原理建立了优化该过程的期望值模型。算例表明考虑操作时间不确定性的优化结果要好于不考虑操作时间不确定性的优化结果。通过Monte-Carlo模拟表明采用新模型优化的结果在实际生产时是可行的     

基于PSO的间歇生产鲁棒统计过程监控

间歇过程广泛应用于精细化工产品、生物化工产品等高附加值产品的制备.为提高间歇生产的可重复性,提高批次之间产品的一致性,多向主元分析法(MPCA)广泛应用于间歇生产过程的监控.针对MPCA统计监控模型容易受到建模数据中离群点影响的不足,提出了一种基于微粒群优化算法(PSO)的鲁棒MPCA分析方法,并进一步给出了相应鲁棒监控统计量的计算方法.对于链霉素发酵过程的监控表明,相对于普通MPCA,鲁棒MPCA在建模数据中存在离群点时仍能够给出正确的统计监控模型,从而有效减少了建模过程对数据的要求.     

聚氯乙烯生产过程全流程调度

研究了电石法制聚氯乙烯(PVC)全流程生产调度问题, 包括从电石生产、盐水电解到氯乙烯(VCM)聚合产品出厂各环节, 其中电石生产和VCM聚合是间歇过程, 其他生产环节是连续过程, 是一个混杂系统调度问题。本文针对过程特性对该问题进行了合理假设, 以包括电耗、库存、产品型号切换、交货延迟等的成本最小为目标, 建立了基于离散时间表示的混合整数线性规划(MILP)调度优化模型, 并针对一个案例进行了调度优化求解和分析, 验证了模型的可行性。     

基于马尔可夫链的蒸汽动力系统两阶段随机规划

现有的解决蒸汽动力系统蒸汽需求不确定性的优化方法有随机规划和鲁棒优化,但二者不能同时兼顾稳定性和经济性。本文提出一种基于马尔可夫链的两阶段随机规划去解决这个问题。第一阶段基于空间距离表达划分不确定变量,通过聚类算法划分成不同工况。第二阶段基于状态切换概率构建马尔可夫链,通过场景生成和削减的方法预测蒸汽的需求值。以某煤制气企业蒸汽动力系统为实例建立相应的优化模型,将预测的蒸汽值带入优化模型求解,得出的最优操作方案与随机规划和鲁棒优化法进行对比和分析。结果表明,本优化方法综合了随机规划经济性高和鲁棒优化稳定性高的优点,稳定性和经济性都介于随机规划和鲁棒优化的中间,为解决蒸汽动力系统的不确定优化问题提供了新思路。     

A computational framework and solution algorithms for two‐stage adaptive robust scheduling of batch manufacturing processes under uncertainty

A novel two‐stage adaptive robust optimization (ARO) approach to production scheduling of batch processes under uncertainty is proposed. We first reformulate the deterministic mixed‐integer linear programming model of batch scheduling into a two‐stage optimization problem. Symmetric uncertainty sets are then introduced to confine the uncertain parameters, and budgets of uncertainty are used to adjust the degree of conservatism. We then apply both the Benders decomposition algorithm and the column‐and‐constraint generation (C&CG) algorithm to efficiently solve the resulting two‐stage ARO problem, which cannot be tackled directly by any existing optimization solvers. Two case studies are considered to demonstrate the applicability of the proposed modeling framework and solution algorithms. The results show that the C&CG algorithm is more computationally efficient than the Benders decomposition algorithm, and the proposed two‐stage ARO approach returns 9% higher profits than the conventional robust optimization approach for batch scheduling. © 2015 American Institute of Chemical Engineers AIChE J, 62: 687–703, 2016     

Theoretical and computational comparison of continuous‐time process scheduling models for adjustable robust optimization

Coping with uncertainty in system parameters is a prominent hurdle when scheduling multi‐purpose batch plants. In this context, our previously introduced multi‐stage adjustable robust optimization (ARO) framework has been shown to obtain more profitable solutions, while maintaining the same level of immunity against risk, as compared to traditional robust optimization approaches. This paper investigates the amenability of existing deterministic continuous‐time scheduling models to serve as the basis of this ARO framework. A comprehensive computational study is conducted that compares the numerical tractability of various models across a suite of literature benchmark instances and a wide range of uncertainty sets. This study also provides, for the first time in the open literature, robust optimal solutions to process scheduling instances that involve uncertainty in production yields. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3055–3070, 2018     

Robust optimization and stochastic programming approaches for medium-term production scheduling of a large-scale steelmaking continuous casting process under demand uncertainty

Scheduling of steelmaking-continuous casting (SCC) processes is of major importance in iron and steel operations since it is often a bottleneck in iron and steel production. In practice, uncertainties are unavoidable and include demand fluctuations, processing time uncertainty, and equipment malfunction. In the presence of these uncertainties, an optimal schedule generated using nominal parameter values may often be suboptimal or even become infeasible. In this paper, we introduce robust optimization and stochastic programming approaches for addressing demand uncertainty in steelmaking continuous casting operations. In the robust optimization framework, a deterministic robust counterpart optimization model is introduced to guarantee that the production schedule remains feasible for the varying demands. Also, a two-stage scenario based stochastic programming framework is investigated for the scheduling of steelmaking and continuous operations under demand uncertainty. To make the resulting stochastic programming problem computationally tractable, a scenario reduction method has been applied to reduce the number of scenarios to a small set of representative realizations. Results from both the robust optimization and stochastic programming methods demonstrate robustness under demand uncertainty and that the robust optimization-based solution is of comparable quality to the two-stage stochastic programming based solution.     

考虑需求不确定性的化工生产计划与调度集成

生产计划与调度是化工供应链优化中两个重要的决策问题。为了提高生产决策的效率,不仅要对计划与调度进行集成,而且要考虑不确定性的影响。对于多周期生产计划与调度问题,首先在每个生产周期内,分别建立计划与调度的确定性模型,通过产量关联对二者进行集成。然后考虑需求不确定性,使用有限数量的场景表达决策变量,建立二阶段随机规划模型。最后运用滚动时域求解策略,使计划与调度结果在迭代过程中达到一致。实例结果表明,在考虑需求不确定性时,与传统方法相比,随机规划方法可以降低总费用,结合计划与调度的分层集成策略,实现了生产操作性和经济性的综合优化。     

Multi‐stage adjustable robust optimization for process scheduling under uncertainty

Variations in parameters such as processing times, yields, and availability of materials and utilities can have a detrimental effect in the optimality and/or feasibility of an otherwise “optimal” production schedule. In this article, we propose a multi‐stage adjustable robust optimization approach to alleviate the risk from such operational uncertainties during scheduling decisions. We derive a novel robust counterpart of a deterministic scheduling model, and we show how to obey the observability and non‐anticipativity restrictions that are necessary for the resulting solution policy to be implementable in practice. We also develop decision‐dependent uncertainty sets to model the endogenous uncertainty that is inherently present in process scheduling applications. A computational study reveals that, given a chosen level of robustness, adjusting decisions to past parameter realizations leads to significant improvements, both in terms of worst‐case objective as well as objective in expectation, compared to the traditional robust scheduling approaches. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1646–1667, 2016     

A hybrid evolutionary algorithm for solving two-stage stochastic integer programs in chemical batch scheduling

This contribution deals with the solution of two-stage stochastic integer programs with discrete scenarios (2-SIPs) that arise in chemical batch scheduling under uncertainty. Since the number of integer variables in the second-stage increases linearly with the number of scenarios considered, the real world applications usually give rise to large scale deterministic equivalent mixed-integer linear programs (MILPs) which cannot be solved easily without incorporating decomposition methods or problem specific knowledge.In this paper a new hybrid algorithm is proposed to solve 2-SIPs based on stage decomposition: an evolutionary algorithm performs the search on the first-stage variables while the second-stage subproblems are solved by mixed-integer programming. The algorithm is tested for a real-world scheduling problem with uncertainties in the demands and in the production capacity. Numerical experiments have shown, that the new algorithm is robust and superior to state-of-the-art solvers if good solutions are needed in short CPU-times.     

On the global and efficient solution of stochastic batch plant design problems

The presence of uncertainty in product demands of batch plant design formulations with fixed structure and continuous equipment sizes transforms them into large-scale nonconvex nonlinear programs. This paper describes recent developments towards the efficient solution of such mathematical models. Two global optimization algorthms, a specialized GOP algorithm and a reduced space branch and bound algorithm, are presented and applied to this class of batch plant design models. It is shown that, by taking advantage of the special structure of the resulting mathematical formulations, encouraging computational results can be obtained from both algorithms for problem sizes that would otherwise be practically unsolvable with conventional global optimization techniques. An efficient, specialized Gaussian quadrature technique is also described for the case of product demands following normal probability distribution functions with which reduced model size and improved estimation of the expected profit integral are achieved. These developments are tested on example problems from the literature covering single batch plant configuration with various scheduling policies and flexible configurations with alternative production sequences.     

Scheduling of crude oil operations under demand uncertainty: A robust optimization framework coupled with global optimization

Scheduling of crude oil operations is an important component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transform the problem into a challenging, nonconvex, mixed‐integer nonlinear programming (MINLP) optimization model. In practice, uncertainties are unavoidable and include demand fluctuations, ship arrival delays, equipment malfunction, and tank unavailability. In the presence of these uncertainties, an optimal schedule generated using nominal parameter values may often be suboptimal or even become infeasible. In this article, the robust optimization framework proposed by Lin et al. and Janak et al. is extended to develop a deterministic robust counterpart optimization model for demand uncertainty. The recently proposed branch and bound global optimization algorithm with piecewise‐linear underestimation of bilinear terms by Li et al. is also extended to solve the nonconvex MINLP deterministic robust counterpart optimization model and generate robust schedules. Two examples are used to illustrate the capability of the proposed robust optimization approach, and the extended branch and bound global optimization algorithm for demand uncertainty. The computational results demonstrate that the obtained schedules are robust in the presence of demand uncertainty. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2373–2396, 2012     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

A data‐driven multistage adaptive robust optimization framework for planning and scheduling under uncertainty

A novel data‐driven approach for optimization under uncertainty based on multistage adaptive robust optimization (ARO) and nonparametric kernel density M‐estimation is proposed. Different from conventional robust optimization methods, the proposed framework incorporates distributional information to avoid over‐conservatism. Robust kernel density estimation with Hampel loss function is employed to extract probability distributions from uncertainty data via a kernelized iteratively reweighted least squares algorithm. A data‐driven uncertainty set is proposed, where bounds of uncertain parameters are defined by quantile functions, to organically integrate the multistage ARO framework with uncertainty data. Based on this uncertainty set, we further develop an exact robust counterpart in its general form for solving the resulting data‐driven multistage ARO problem. To illustrate the applicability of the proposed framework, two typical applications in process operations are presented: The first one is on strategic planning of process networks, and the other one on short‐term scheduling of multipurpose batch processes. The proposed approach returns 23.9% higher net present value and 31.5% more profits than the conventional robust optimization method in planning and scheduling applications, respectively. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4343–4369, 2017