Domain reduction for Benders decomposition based global optimization

While domain reduction has been successfully applied in branch-and-bound based global optimization over the last two decades, it has not been systematically studied for decomposition based global optimization, which is usually more efficient for problems with decomposable structures. This paper discusses integration of domain reduction in Benders decomposition based global optimization, specifically, generalized Benders decomposition (GBD) and nonconvex generalized Benders decomposition (NGBD). Revised GBD and NGBD frameworks are proposed to incorporate bound contraction operations or/and range reduction calculations, which can reduce the variable bounds and therefore improve the convergence rate and expedite the solution of nonconvex subproblems. Novel customized bound contraction problems are proposed for GBD and NGBD, and they are easier to solve than the classical bound contraction problems because they are defined on reduced variable spaces. The benefits of the proposed methods are demonstrated through a gas production operation problem and a power distribution system design problem.     

两群微粒群算法及其在油品调和优化中的应用

针对复杂的非线性约束优化问题,提出了一种含变异算子的两群微粒群算法。算法构造了两个粒子群,分别设置了不同的搜索速度上限,并设计了粒子群间的协调机制和变异算子,使算法的寻优能力得到增强。针对油品调和配方优化进行了实例仿真,研究结果表明所提出的算法能获得较理想的调和配方,在满足调和利润最大的同时能保证对调和指标的卡边,使调和成品油的指标富余量大大降低。     

Logarithm-transform piecewise linearization method for the optimization of fasoline blending processes

Gasoline blending is a key process in a petroleum refinery, as it can yield 60%–70% of a typical refinery's total revenue. This process not only exhibits non-convex nonlinear blending behavior due to the complicated blend mechanism of various component feedstocks with different quality properties, but also involves global optimum searching among numerous blending recipes. Since blend products are required to meet a series of quality requirements and highly-sensitive to the proportion changes of blending feedstocks, global optimization methods for NLP problems are often difficult to be applied because of heavy computational burdens. Thus, piecewise linearization methods are naturally proposed to provide an approximate global optimum solution by adding binary variables into the models and converting the original NLP problems into MILP ones. In this paper, Logarithmtransform piecewise linearization(LTPL) method, an improved piecewise linearization, is proposed. In this method a logarithm transform is applied to convert multi-variable multi-degree constraints into a series of single-variable constraints. As a result, the number of 0–1 variables is greatly reduced. In the final part of this paper, an industrial case study is conducted to demonstrate the effectiveness of LTPL method. In principle, this method would be useful for blending problems with complicated empirical or theoretical models.     

A global optimization method based on multi-unit extremum-seeking for scalar nonlinear systems

Finding the global optimum of a nonlinear function is a challenging task that could involve a large number of functional evaluations. In this paper, an algorithm that uses tools from the domain of extremum-seeking is shown to provide an efficient deterministic method for global optimization. Extremum-seeking schemes typically find the local optimum by controlling the gradient to zero. In this paper, the multi-unit framework is used, where the gradient is estimated by finite difference for a given offset between the inputs. The gradient is pushed to zero by an integral controller. It is shown that if the offset is reduced to zero, the system can be made to converge to the global optimum of nonlinear continuous static, scalar maps. The result is extended to constrained problems where a switching control strategy is employed. Several illustrative examples are presented and the proposed method is compared with other methods of global optimization.     

汽油调合调度优化

采用连续时间建模方法,建立了一种新的汽油非线性调合和调度集成优化的混合整数非线性规划（MINLP）模型,克服了当前在油品调合调度中采用线性调合模型或者将非线性调合过程和调度分开优化的缺陷。针对建立MINLP模型的特点,将原MINLP问题转化为求解一系列的混合整数线性规划（MILP）模型,避免了直接求解MINLP模型的复杂性。最后以某大型炼油企业为例,验证了模型和算法的实用性。     

Cutting planes for improved global logic-based outer-approximation for the synthesis of process networks

In this work, we present an improved global logic-based outer-approximation method (GLBOA) for the solution of nonconvex generalized disjunctive programs (GDP). The GLBOA allows the solution of nonconvex GDP models, and is particularly useful for optimizing the synthesis of process networks, which yields MINLP models that can be highly nonconvex. However, in many cases the NLP that results from fixing the discrete decisions is much simpler to solve than the original problem. The proposed method exploits this property. Two enhancements to the basic GLBOA are presented. The first enhancement seeks to obtain feasible solutions faster by dividing the basic algorithm into two stages. The first stage seeks to find feasible solutions faster by restricting the solution time of the problems and diversifying the search. The second stage guarantees the convergence by solving the original algorithm. The second enhancement seeks to tighten the lower bound of the algorithm by the use of cutting planes. The proposed method for obtaining cutting planes, the main contribution of this work, is a separation problem based on the convex hull of the feasible region of a subset of the constraints. Results and comparison with other global solvers show that the enhancements improve the performance of the algorithm, and that it is more effective in the tested problems at finding near optimal solutions compared to general-purpose global solvers.     

A global optimization method for model selection in chemical reactions networks

Model inference is a challenging problem in the analysis of chemical reactions networks. In order to empirically test which, out of a catalogue of proposed kinetic models, is governing a network of chemical reactions, the user can compare the empirical data obtained in one experiment against the theoretical values suggested by the models under consideration. It is thus fundamental to make an adequate choice of the decision variables (e.g. initial concentrations of the different species in the tank) in order to have maximal separation between sets of concentrations provided by the theoretical models, making then easier to identify which of the theoretical models yields data closest to those obtained empirically under identical conditions.In this paper we illustrate how global optimization techniques can be successfully used to address the problem of model separation, as a basis for model selection. Some examples illustrate the usefulness of our approach.     

A global optimization algorithm for nonconvex generalized disjunctive programming and applications to process systems

A global optimization algorithm for nonconvex Generalized Disjunctive Programming (GDP) problems is proposed in this paper. By making use of convex underestimating functions for bilinear, linear fractional and concave separable functions in the continuous variables, the convex hull of each nonlinear disjunction is constructed. The relaxed convex GDP problem is then solved in the first level of a two-level branch and bound algorithm, in which a discrete branch and bound search is performed on the disjunctions to predict lower bounds. In the second level, a spatial branch and bound method is used to solve nonconvex NLP problems for updating the upper bound. The proposed algorithm exploits the convex hull relaxation for the discrete search, and the fact that the spatial branch and bound is restricted to fixed discrete variables in order to predict tight lower bounds. Application of the proposed algorithm to several example problems is shown, as well as a comparison with other algorithms.     

Integrated gasoline blending and order delivery operations: Part I. short‐term scheduling and global optimization for single and multi‐period operations

Gasoline is one of the most valuable products in an oil refinery and can account for as much as 60–70% of total profit. Optimal integrated scheduling of gasoline blending and order delivery operations can significantly increase profit by avoiding ship demurrage, improving customer satisfaction, minimizing quality give‐aways, reducing costly transitions and slop generation, exploiting low‐quality cuts, and reducing inventory costs. In this article, we first introduce a new unit‐specific event‐based continuous‐time formulation for the integrated treatment of recipes, blending, and scheduling of gasoline blending and order delivery operations. Many operational features are included such as nonidentical parallel blenders, constant blending rate, minimum blend length and amount, blender transition times, multipurpose product tanks, changeovers, and piecewise constant profiles for blend component qualities and feed rates. To address the nonconvexities arising from forcing constant blending rates during a run, we propose a hybrid global optimization approach incorporating a schedule adjustment procedure, iteratively via a mixed‐integer programming and nonlinear programming scheme, and a rigorous deterministic global optimization approach. The computational results demonstrate that our proposed formulation does improve the mixed‐integer linear programming relaxation of Li and Karimi, Ind. Eng. Chem. Res., 2011, 50, 9156–9174. All examples are solved to be 1%‐global optimality with modest computational effort. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2043–2070, 2016     

基于Matlab/VB混合编程的动力配煤优化系统设计

应用Matlab与VB编程工具相结合的手段开发了动力配煤优化模型软件系统。通过ActiveX机制实现Matlab与VB数据通信,利用VB编写配煤优化系统主界面,利用Matlab遗传算法工具箱设计配煤优化数学模型,从而实现在VB中调用Matlab。2个软件优点的结合,有效提高了程序的设计效率。     

A new optimization model and a customized solution method for natural gas production network design and operation

This article proposes to tackle integrated design and operation of natural gas production networks under uncertainty, using a new two‐stage stochastic programming model, a novel reformulation strategy, and a customized global optimization method. The new model addresses material balances for multiple key gas components, pressure flow relationships in gas wells and pipelines, and compressor performance. This model is a large‐scale nonconvex mixed‐integer nonlinear programming problem that cannot be practically solved by existing global optimization solvers or decomposition‐based optimization methods. With the new reformulation strategy, the reformulated model has a better decomposable structure, and then a new decomposition‐based global optimization method is developed for efficient global optimization. In the case study of an industrial naturals production system, it is shown that the proposed modeling and optimization methods enable efficient solution, and the proposed optimization method is faster than a state‐of‐the‐art decomposition method by at least an order of magnitude. © 2016 American Institute of Chemical Engineers AIChE J, 63: 933–948, 2017     

Optimization of short-time gasoline blending scheduling problem with a DNA based hybrid genetic algorithm

Gasoline blending is a key process in the petroleum refinery industry posed as a nonlinear optimization problem with heavily nonlinear constraints. This paper presents a DNA based hybrid genetic algorithm (DNA-HGA) to optimize such nonlinear optimization problems. In the proposed algorithm, potential solutions are represented with nucleotide bases. Based on the complementary properties of nucleotide bases, operators inspired by DNA are applied to improve the global searching ability of GA for efficiently locating the feasible domains. After the feasible region is obtained, the sequential quadratic programming (SQP) is implemented to improve the solution. The hybrid approach is tested on a set of constrained nonlinear optimization problems taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm. The recipes of a short-time gasoline blending problem are optimized by the hybrid algorithm, and the comparison results show that the profit of the products is largely improved while achieving more satisfactory quality indicators in both certainty and uncertainty environment.     

Dynamic optimization for gas blending in pipeline networks with gas interchangeability control

The increasing penetration of unconventional gas and liquefied natural gas poses an operational challenge on existing regional gas networks for gas quality problems. A new dynamic model for natural gas pipeline network with multiple supplies is presented with a special emphasis on gas interchangeability control. Wobbe index serves as gas interchangeability indicator and is calculated by equations derived from rigorous composition-based partial differential equations. Disjunctive formulation is applied to represent different modes of gas blending due to gas reversal, and the disjunctive model is then reformulated as a nonsmooth model with min/max and absolute value functions, which is solved by a gradient-based nonlinear program solver after smooth approximation. Moreover, a heuristic algorithm is proposed to tune the penalty parameters in order to focus on different penalty terms while keeping the model well-conditioned. The developed model and strategy are first tested with a small pipeline network model and then extended to a large model. The results show that the model can effectively manage gas interchangeability issues in pipeline networks within reasonable CPU time.     

考虑碳排放因素的汽油调合在线优化

针对国家“双碳”战略目标要求,以炼化企业汽油调合在线优化为研究对象,分析了国Ⅵ汽油新标准下被控属性更多、更严、调合效率要求更高等特点,以及由此带来的调合组分油调整导致调合成品汽油携带碳排放量的变化情况。考虑到传统的汽油调合在线优化一般只考虑调合成本、质量卡边等目标,首先建立了非线性的汽油调合辛烷值、蒸气压和馏程等软测量模型,然后构建了基于调合效应的汽油调合优化模型,优化目标中引入调合成品油二氧化碳排放最低化目标,开发了一种融合携带碳排放特征的汽油调合优化模型。为满足在线调合优化需求,优化模型中考虑了实际累积调合过程,将调合工艺过程中储罐汽油属性合格转化成调合头属性区间合格,利用调合头处优化的属性补偿已调合体积和罐底油的属性偏差。仿真结果表明,设计的考虑碳排放因素汽油累积调合优化技术能很好地满足汽油调合在线优化需求,为国Ⅵ标准和碳交易背景下汽油调合工艺设计及在线优化控制提供了技术支撑。     

基于无简仓的实时优化配煤系统研究

针对煤质差造成火电厂燃煤与锅炉设计煤质严重偏离,运行不稳等问题,分析了燃料管理落后环节和不适应因素,结合燃煤电厂燃料配煤和管理现状,提出了火电厂燃料无筒仓的实时优化配煤、燃料智能化管理系统构建的总体设计,给出燃料从计划、入厂、入炉、结算的精准计划管理的实时配煤解决方案.结果表明,采用无筒仓的实时优化配煤系统经过前置预处理沟,基于热值和硫含量的精确定位,配合在线监测、控制系统,对给煤进行调整混配,可实现燃料均匀混配,使燃煤粒度小于10mm,硫含量、热值均满足锅炉设计煤要求,保证锅炉稳定燃烧及污染物有效控制.多渠道分离输送装置及无筒仓封闭式储煤混配控制系统、燃料混配的智能化管理系统的构建在保证正常生产条件下,最大限度地降低生产成本和煤耗,提高了资金利用率,实现电厂燃料智能化管理.     

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems

In this paper we present a strategy to improve the relaxation for the global optimization of non-convex MINLPs. The main idea consists in recognizing that each constraint or set of constraints has a meaning that comes from the physical interpretation of the problem. When these constraints are relaxed part of this meaning is lost. Adding redundant constraints that recover that physical meaning strengthens the relaxation. We propose a methodology to find such redundant constraints based on engineering knowledge and physical insight.     

New MINLP formulation for the multiperiod pooling problem

The modeling of blending tank operations in petroleum refineries for the most profitable production of liquid fuels in a context of time‐varying supply and demand is addressed. A new mixed‐integer nonlinear programming formulation is proposed that using individual flows and split fractions as key model variables leads to a different set of nonconvex bilinear terms compared with the original work of Kolodziej et al. These are better handled by decomposition algorithms that divide the problem into integer and nonlinear components as well as by commercial solvers. In fact, BARON and GloMIQO can solve to global optimality all problems resulting from the new formulation and test problems from the literature. A tailored global optimization algorithm working with a tight mixed‐integer linear relaxation from multiparametric disaggregation achieves a similar performance. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3728–3738, 2015     

A discretization-based approach for the optimization of the multiperiod blend scheduling problem

In this paper, we introduce a new generalized multiperiod scheduling version of the pooling problem to represent time varying blending systems. A general nonconvex MINLP formulation of the problem is presented. The primary difficulties in solving this optimization problem are the presence of bilinear terms, as well as binary decision variables required to impose operational constraints. An illustrative example is presented to provide unique insight into the difficulties faced by conventional MINLP approaches to this problem, specifically in finding feasible solutions. Based on recent work, a new radix-based discretization scheme is developed with which the problem can be reformulated approximately as an MILP, which is incorporated in a heuristic procedure and in two rigorous global optimization methods, and requires much less computational time than existing global optimization solvers. Detailed computational results of each approach are presented on a set of examples, including a comparison with other global optimization solvers.     

Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method

This paper presents a new method for multiphase equilibria calculation by direct minimization of the Gibbs free energy of multicomponent systems. The methods for multiphase equilibria calculation based on the equality of chemical potentials cannot guarantee the convergence to the correct solution since the problem is non-convex (with several local minima), and they can find only one for a given initial guess. The global optimization methods currently available are generally very expensive. A global optimization method called Tunneling, able to escape from local minima and saddle points is used here, and has shown to be able to find efficiently the global solution for all the hypothetical and real problems tested. The Tunneling method has two phases. In phase one, a local bounded optimization method is used to minimize the objective function. In phase two (tunnelization), either global optimality is ascertained, or a feasible initial estimate for a new minimization is generated. For the minimization step, a limited-memory quasi-Newton method is used. The calculation of multiphase equilibria is organized in a stepwise manner, combining phase stability analysis by minimization of the tangent plane distance function with phase splitting calculations. The problems addressed here are the vapor–liquid and liquid–liquid two-phase equilibria, three-phase vapor–liquid–liquid equilibria, and three-phase vapor–liquid–solid equilibria, for a variety of representative systems. The examples show the robustness of the proposed method even in the most difficult situations. The Tunneling method is found to be more efficient than other global optimization methods. The results showed the efficiency and reliability of the novel method for solving the multiphase equilibria and the global stability problems. Although we have used here a cubic equation of state model for Gibbs free energy, any other approach can be used, as the method is model independent.