Mixed integer polynomial programming

The mixed integer polynomial programming problem is reformulated as a multi-parametric programming problem by relaxing integer variables as continuous variables and then treating them as parameters. The optimality conditions for the resulting parametric programming problem are given by a set of simultaneous parametric polynomial equations which are solved analytically to give the parametric optimal solution as a function of the relaxed integer variables. Evaluation of the parametric optimal solution for integer variables fixed at their integer values followed by screening of the evaluated solutions gives the optimal solutions.     

Continuous-time scheduling formulation for multipurpose batch plants

Short-term scheduling of batch processes is a complex combinatorial problem with remarkable impact on the total revenue of chemical plants. It consists of the optimal allocation of limited resources to tasks over time in order to manufacture final products following given batch recipes. This article addresses the short-term scheduling of multipurpose batch plants, using a mixed integer linear programming formulation based on the state-task network representation. It employs both single-grid and multi-grid continuous-time representations, derived from generalized disjunctive programming. In comparison to other multigrid scheduling models in the literature, the proposed multi-grid model uses no big-M constraints and leads to more compact mathematical models with strong linear relaxations, which often results in shorter computational times. The single-grid counterpart of the formulation is not as favorable, as it leads to weaker linear relaxations than the multi-grid approach and is not capable of handling changeover time constraints.     

Explicit model predictive control of hybrid systems and multiparametric mixed integer polynomial programming

Hybrid systems are dynamical systems characterized by the simultaneous presence of discrete and continuous variables. Model‐based control of such systems is computationally demanding. To this effect, explicit controllers which provide control inputs as a set of functions of the state variables have been derived, using multiparametric programming mainly for the linear systems. Hybrid polynomial systems are considered resulting in a Mixed Integer Polynomial Programming problem. Treating the initial state of the system as a set of bounded parameters, the problem is reformulated as a multiparametric Mixed Integer Polynomial optimization (mp‐MIPOPT) problem. A novel algorithm for mp‐MIPOPT problems is proposed and the exact explicit control law for polynomial hybrid systems is computed. The key idea is the computation of the analytical solution of the optimality conditions while the binary variables are treated as relaxed parameters. Finally, using symbolic calculations exact nonconvex critical regions are computed. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 3441–3460, 2016     

换热网络的同步综合设计

提出了换热网络的一种新的转运模型,以并串模式和非等温混合过程描述换热网络的热力学和经济性的总要求,不使用挟点分离、最小单元数等启发式规则,并允许交叉换热和不同物流间的膜传热系数与温差合理匹配.这一模型与优化模型相结合,自动产生换热网络,确定相应的最优公用工程费用、换热面积、换热器台数与冷热流间的匹配,其可行域由一集线性约束确定,鲁棒性很好,易于求解.该方法克服了换热网络的各种分步骤综合方法的缺陷(包括挟点技术、双温差法及相关数学规划方法).与文献上其它同步优化方法比较,具有模型简单、规模小、可算性强、初始化简易、计算结果可靠的优点.通过对文献中广泛使用的例题的检验,结果优于现有的其它方法.     

一种约束一般模型控制新方法

在引入近似预测模型的基础上 ,应用基于二次规划的滚动优化算法 ,处理被控量、操作量及其变化速率的线性约束 .将此优化算法与经典的一般模型控制 (GMC)方法相结合 ,给出了一种基于二次规划的约束一般模型控制新方法 .     

Emission characteristics of PAHs, benzene and phenol group hydrocarbons in O2/RFG waste incineration processes

This study applies the oxygen/recycled flue gas (O₂/RFG) combustion technology for waste incineration in a laboratory-scale fluidized bed incinerator to investigate the effects of different RFG percentages and O₂ concentrations on the emission characteristics of organic pollutants (PAHs, phenol and benzene hydrocarbons). Experimental results show that most PAHs with high-ring structures were present in solid-phase and most low-ring PAHs were present in gas-phase. The major compounds of benzene and phenol hydrocarbons were benzene, toluene, trichlorobenzene and 2,4-dinitrophenol, phenol, dichlorophenol, respectively. As the O₂ concentration in feed gas was increased from 21% to 40%, the emissions of solid- and gas-phase PAHs and phenol compounds were decreased but not for benzene compounds. Increasing RFG percentages would decrease the emissions of gas-phase PAHs, benzene and phenol compounds, but increased those of solid-phase pollutants. The best operating conditions of such O₂/RFG combustion system to reduce the emissions of PAHs and phenol compounds were 40% O₂, 35% RFG, and that for benzene compounds was 21% O₂, 75% RFG. Comparing with conventional air combustion system, the best diminution efficiencies of PAHs, benzene and phenol compounds at such O₂/RFG conditions were 59.54%, 70.97% and 52.60%, respectively. With proper feed gas compositions and RFG percentages, the combustion efficiency and destruction efficiency of organic pollutants can be improved by this O₂/RFG combustion technology.     

Systematic modeling of discrete‐continuous optimization models through generalized disjunctive programming

Discrete‐continuous optimization problems are commonly modeled in algebraic form as mixed‐integer linear or nonlinear programming models. Since these models can be formulated in different ways, leading either to solvable or nonsolvable problems, there is a need for a systematic modeling framework that provides a fundamental understanding on the nature of these models. This work presents a modeling framework, generalized disjunctive programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions. An overview is provided of major research results that have emerged in this area. Basic concepts are emphasized as well as the major classes of formulations that can be derived. These are illustrated with a number of examples in the area of process systems engineering. As will be shown, GDP provides a structured way for systematically deriving mixed‐integer optimization models that exhibit strong continuous relaxations, which often translates into shorter computational times. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3276–3295, 2013     

Sample‐based approaches to decision making problems under uncertainty

Decision making under uncertainty is becoming more important in process industries as optimisation is applied to novel applications as well as plant‐wide and enterprise optimisation. Among the standard stochastic optimisation techniques are stochastic programming and dynamic programming. It is difficult to use these techniques for practical applications due to unwieldy computational requirements, arising from a large number of uncertain parameters and state variables, respectively. In this paper, we present sample‐based techniques for ameliorating the computational difficulties. Application studies involving catalyst design and real‐time optimisation point to the promising potentials of the sample‐based techniques. © 2011 Canadian Society for Chemical Engineering     

A comparative assessment of linearization methods for bilinear models

In this article, optimization problems with bilinear constraints involving one discrete variable are studied. Several industrial problems present bilinear non-convex constraints which are difficult to solve to global optimality. For this purpose models must be reformulated what in general terms increases the problem size. This article proposes two disjunctive transformation techniques which are compared to other approaches presented in the literature. An analysis is made comparing qualitative and quantitative characteristics of the methods employed. In order to implement proposed transformations, three industrial cases are studied: trim-loss in a paper mill, cutting stock in the production of carton board boxes and the purchase, inventory and delivery optimization problem. All of them are reformulated and solved using the strategies included in the paper. Several instances of each problem are evaluated and their results are analyzed comparing performance of the different methods.     

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。     

混杂系统基于参数规划的状态反馈预测控制

In this article, state feedback predictive controller for hybrid system via parametric programming is proposed. First, mixed logic dynamic （MLD） modeling mechanism for hybrid system is analyzed, which has a distinguished advantage to deal with the logic rules and constraints of a plant. Model predictive control algorithm with moving horizon state estimator （MHE） is presented. The estimator is adopted to estimate the current state of the plant with process disturbance and measurement noise, and the state estimated are utilized in the predictive controller for both regulation and tracking problems of the hybrid system based on MLD model. Off-line parametric programming is adopted and then on-line mixed integer programming problem can be treated as the parameter programming with estimated state as the parameters. A three tank system is used for computer simulation, results show that the proposed MHE based predictive control via parametric programming is effective for hybrid system with model/olant mismatch, and has a potential for the engineering applications.     

Multi-objective optimization with convex quadratic cost functions: A multi-parametric programming approach

In this note we present an approximate algorithm for the explicit calculation of the Pareto front for multi-objective optimization problems featuring convex quadratic cost functions and linear constraints based on multi-parametric programming and employing a set of suitable overestimators with tunable suboptimality. A numerical example as well as a small computational study highlight the features of the novel algorithm.     

A planning model for multiple blending schemes☆

The key of production planning of refineries is to determine the production planning of units and blending schemes of blends in each period of the plan horizon, since they affect the effective utilization of components of refineries and hence profits. The optimization is difficult, because of many complicated product production–consumption relation-ships in production processes, which are closely related to the running modes of the units. Additional y, the blending products, such as gasoline and diesel, may use multiple blending schemes for their production that increase the complexity of the problem. This paper models the production planning problem as a mixed integer nonlinear programming. Computational experiments for a refinery show the effectiveness of the model. The optimal results give the effective utilization of the self-produced components and increase of the profit.     

New algorithm for the flexibility index problem of quadratic systems

A new flexibility index algorithm for systems under uncertainty and represented by quadratic inequalities is presented. Inspired by the outer‐approximation algorithm for convex mixed‐integer nonlinear programming, a similar iterative strategy is developed. The subproblem, which is a nonlinear program, is constructed by fixing the vertex directions since this class of systems is proved to have a vertex solution if the entries on the diagonal of the Hessian matrix are non‐negative. By overestimating the nonlinear constraints, a linear min–max problem is formulated. By dualizing the inner maximization problem, and introducing new variables and constraints, the master problem is reformulated as a mixed‐integer linear program. By iteratively solving the subproblem and master problem, the algorithm can be guaranteed to converge to the flexibility index. Numerical examples including a heat exchanger network, a process network, and a unit commitment problem are presented to illustrate the computational efficiency of the algorithm. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2486–2499, 2018     

A reformulated nonlinear model to solve the facility layout problem

The facility layout problem is fundamental during the plant design. The solution of this problem has required strategies that become in numerical challenges. One of them is the exact method, which finds optimal distributions for facility layout, as demonstrated in the linear and disjunctive models. Both models are distinguished by a high quantity of nonoverlapping constraints. In contrast, a nonlinear model was formulated with low number of constraints, but it has been solved by genetic algorithms. Herein, that model is reformulated to a MINLP (mixed integer nonlinear programing) problem. The solution was possible using a visual interface linked to GAMS (General Algebraic Modeling System). Three case studies were solved to compare them. The reformulated model reached feasible solutions, and its computational time and binary variables were lower than those of the others. This suggests that the reformulated model can be extended to solve topics about process safety.     

通过模型为基础的溶液选择来调控药品化合物的形貌

In this paper we present a strategy for tuning the crystal morphology of pharmaceutical compounds by the appropriate choice of solvent via an optimization model. A three-stage approach involving a pre-design stage, a product design stage and a post-design experimental verification stage is presented. The pre-design stage addresses the tormulation of the property constraint tor crystal morphology. This involves crystallization experiments aria development of property models and constraints for morphology. In the design stage various property requirements for the solvent along with crystal morphology are considered and the product design problem is formulated as a mixed integer nonlinear programming model.The design stage provides an optimal solvent/list of candidate solvents. Similar to the pre-design stage, in the post design experimental verification stage, the morphology of the crystals （precipitated from the designed solvent） is verified through crystallization experiments followed by product characterization via scanni＇ng electron microscopy, powder X-ray diffraction imaging and Fourier transform spectra analysis.     

通过模型为基础的溶液选择来调控药品化合物的形貌

In this paper we present a strategy for tuning the crystal morphology of pharmaceutical compounds by the appropriate choice of solvent via an optimization model. A three-stage approach involving a pre-design stage, a product design stage and a post-design experimental verification stage is presented. The pre-design stage addresses the formulation of the property constraint for crystal morphology. This involves crystallization experiments and development of property models and constraints for morphology. In the design stage various property requirements for the solvent along with crystal morphology are considered and the product design problem is formulated as a mixed integer nonlinear programming model. The design stage provides an optimal solvent/list of candidate solvents. Similar to the pre-design stage, in the post design experimental verification stage, the morphology of the crystals (precipitated from the designed solvent) is verified through crystallization experiments followed by productcharacterization via scanning electron microscopy, powder X-ray diffraction imaging and Fourier transform spectra analysis.     

Oxygenated transportation fuels. Evaluation of properties and emission performance in light-duty vehicles in Mexico

Recently a “Biofuels Promotion and Development Law” was approved in Mexico that requires increasing volumes of renewable to blend into the transportation fuel pool, much of which is likely to be ethanol. Emissions data under the three different driving conditions of the United States FTP-75 certification cycle were obtained for regulated, toxic and carbonyl compounds using recent model year vehicles representing 61% of the typical fleet available in Mexico. Ozone-forming potential and specific reactivity of tailpipe and evaporative emissions were also calculated. Comparison were performed using the traditional methyl-tertiary butyl ether employed in Mexico with an ethanol fuel at the same level of oxygen content, taking into account the current fuel specifications and the stream stocks available at the Mexican refineries. The results suggest that the contribution of cold start to regulated emissions range from 37% to 40% whiles those of toxic from 40% to 47% in both fuels. Results also indicate an increase in the rates of evaporative emissions of higher Specific Reactivy with the ethanol fuel. Estimation of the percent reduction of pollutants using the Complex Model of the USA Environmental Protection Agency suggests that volatile organic compounds will exceeds the limits imposed by the model if vapour pressure of the ethanol gasoline is not properly adjusted.     

Gasoline displacement and NOx reduction in an SI engine by aqueous alcohol injection

Substitution of bio-fuels for fossil fuels in gasoline engines is conventionally achieved by premixing ethanol and gasoline before use. The drawbacks are the high purity ethanol (>95%) required for mixing to prevent phase separation and the invariable fraction of ethanol throughout the drive cycle. In this study, an independently controlled set of aqueous alcohols injectors were installed at the manifold alongside the gasoline injectors. Aqueous alcohols with high water content can be injected as a substitutional fuel for gasoline. The fraction of ethanol can be controlled to achieve best engine performance and emissions. Engine tests showed that, at highway driving condition, the engine compensated for the aqueous alcohol and reduced gasoline flowrate. However, at high-load running, the ECU (Engine Control Unit) no longer reads the feedback signals to reduce gasoline supply and the engine burned at fuel-rich conditions; both the engine performance and emissions deteriorated.     

Analysis of main gaseous emissions of heavy duty gas turbines burning several syngas fuels

This work presents the development of a simple analytical model of performance for heavy duty gas turbine combustors and its use for the analysis of main emissions for a set of syngas fuels. This set of syngas fuels has been selected as a wide representation of different compositions of syngas fuels, from fossil or vegetal origins. Their combustion processes have been modelled as a set of chemical reactors in serial and a detailed kinetic model, simulating a conventional diffusion flame combustor. In each slice, the thermodynamics and the kinetics have been modelled using perfect stirred reactor models. The combustor model has been validated with the GE MS7001F gas turbine experimental data. From this validation the model applicability range has been established for combustor outlet temperatures above 1200 K. Finally the combustor model has been applied to the comparison of different syngas fuels emissions in three new generation gas turbines.