化工过程系统综合问题新的模块化求解策略和算法

针对过程系统综合问题中求解混合整数非线性规划（MINLP）问题传统解法的不足提出了在[JP+1]模块化环境中过程系统综合问题新的求解策略,同时提出相对应的算法.实例证明了该策略的正确性和新算法的有效性.     

Automated reformulation of disjunctive constraints in MINLP optimization

In this paper, a general method for handling disjunctive constraints in a MINLP optimization problem is presented. This method automates the reformulation of an, in a abstract modeling language given, optimization problem into a mathematical problem that is solvable with existing optimization tools. This implementation can use common MILP solvers for linear problems and nonlinear methods for quasi-convex optimization problems. It also includes the possibility to use the logics in the system and solve the system logically using subproblems.     

An adaptive discretization MINLP algorithm for optimal synthesis of decentralized energy supply systems

Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to meet time-varying energy demands, e.g., heating, cooling, and electricity. The synthesis problem of DESS addresses combining various types of energy conversion units, choosing their sizing and operations to maximize an objective function, e.g., the net present value. In practice, investment costs and part-load performances are nonlinear. Thus, this optimization problem can be modeled as a nonconvex mixed-integer nonlinear programming (MINLP) problem. We present an adaptive discretization algorithm to solve such synthesis problems containing an iterative interaction between mixed-integer linear programs (MIPs) and nonlinear programs (NLPs). The proposed algorithm outperforms state-of-the-art MINLP solvers as well as linearization approaches with regard to solution quality and computation times on a test set obtained from real industrial data, which we made available online.     

An improved piecewise outer-approximation algorithm for the global optimization of MINLP models involving concave and bilinear terms

In this paper a new version of the Outer Approximation for Global Optimization Algorithm by Bergamini et al. [Bergamini, M.L., Aguirre, P., & Grossmann, I.E. (2005a). Logic based outer approximation for global optimization of synthesis of process networks. Computers and Chemical Engineering 29, 1914] is proposed, in order to speed up the convergence in nonconvex MINLP models that involve bilinear and concave terms. Bounding problems are constructed replacing these nonconvex terms by piecewise linear underestimators. These problems, which correspond to mixed-integer linear programs, are solved to generate approximate solutions with improved objective value. When no further feasible solution can be found, this guarantees that the upper bound cannot be improved in the nonconvex problem, thus providing a termination criterion. The new algorithm is applied to five different synthesis problems in the areas of water networks, heat exchanger networks and distillation sequences. The results show a significant reduction in the computational cost compared with the previous version of the algorithm.     

过程系统能量集成同步最优综合法

将换热网络超结构混合整数非线性规划多目标同步最优综合方法进一步扩展到与过程系统的联合优化,提出了改进的过程热集成同步综合方法,并以反应分离过程与换热网络能量集成为例,建立了同步优化超结构模型,采用混合整数非线性规划的遗传算法求解,可同时得到热集成系统最优的流程结构和操作条件。     

An MILP-MINLP decomposition method for the global optimization of a source based model of the multiperiod blending problem

The multiperiod blending problem involves binary variables and bilinear terms, yielding a nonconvex MINLP. In this work we present two major contributions for the global solution of the problem. The first one is an alternative formulation of the problem. This formulation makes use of redundant constraints that improve the MILP relaxation of the MINLP. The second contribution is an algorithm that decomposes the MINLP model into two levels. The first level, or master problem, is an MILP relaxation of the original MINLP. The second level, or subproblem, is a smaller MINLP in which some of the binary variables of the original problem are fixed. The results show that the new formulation can be solved faster than alternative models, and that the decomposition method can solve the problems faster than state of the art general purpose solvers.     

换热器网络同步最优综合方法──改进的MINLP转运模型法

针对现有的换热器网络最优综合方法的局限性，采用分级超结构转运模型和物流吸、放热潜力的概念，提出了非等温混合线性约束的换热器网络同步最优综合混合整数非线性规划（MINLP）的改进模型．该模型不仅可以对公用工程费用、换热面积、换热设备台数及物流的匹配选择进行多目标同步优化，而且在线性约束的条件下消除了等温混合的不合理假设，只需求解一次MINLP问题就可得到包括分流情况在内的最优网络结构．算例表明，该模型优于以往的几种同步优化模型．     

Integrated multi‐echelon supply chain design with inventories under uncertainty: MINLP models,computational strategies

We address in this article a problem that is of significance to the chemical industry, namely, the optimal design of a multi‐echelon supply chain and the associated inventory systems in the presence of uncertain customer demands. By using the guaranteed service approach to model the multi‐echelon stochastic inventory system, we develop an optimization model to simultaneously determine the transportation, inventory, and network structure of a multi‐echelon supply chain. The model is an MINLP with a nonconvex objective function including bilinear, trilinear, and square root terms. By exploiting the properties of the basic model, we reformulate this problem as a separable concave minimization program. A spatial decomposition algorithm based on the integration of Lagrangean relaxation and piecewise linear approximation is proposed to obtain near global optimal solutions with reasonable computational expense. Examples for specialty chemicals and industrial gas supply chains with up to 15 plants, 100 potential distribution centers, and 200 markets are presented. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

生态工业园区的MINLP模型

生态工业园区的设计和管理需要建立在定量分析的基础上，目前仍然是一个薄弱环节. 本文提出了一个引入逻辑表达式的生态工业园区模型，可以通过对一个混合整数非线性规划(MINLP)问题进行求解来获得有价值的参考信息. 模型可以分为成员模型和连接模型两部分，成员模型作为积木，通过连接模型搭建成不同拓扑结构的生态工业园区方案. 开发的生态工业园区模型具有良好的扩展性、可修改性、可重用性，可以作为生态工业园区决策系统的核心模型. 以山东枣庄市南工业区为对象进行了案例分析. 模型用非线性优化软件LINGO求解.     

Flexible mass transfer model for water minimization in batch plants

This paper presents the least constrained mass transfer mathematical formulation for freshwater minimization in multipurpose batch chemical processes with central reusable water storage. The mathematical formulation is an extension of the model developed by Majozi [T. Majozi, Wastewater minimization using central reusable water storage in batch processes, Computers and Chemical Engineering Journal 29 (7) (2005) 1631–1646]. In the latter model four scenarios were considered with various limitations or constraints. In the scenario presented in this paper only the mass load is fixed, whilst both the quantity of water used in a particular operation and outlet concentration are allowed to vary. In essence, fixing the mass load is more representative of the practical case. A solution procedure for the resultant nonconvex mixed integer nonlinear programming (MINLP) model is also presented. The solution procedure first involves reformulating the MINLP into a relaxed linear model (MILP). The MILP is first solved, the solution of which forms a feasible starting solution for the MINLP. Presented are two illustrative examples.     

Optimal design of reverse-osmosis networks for wastewater treatment

An optimization study of reverse-osmosis networks (RON) for wastewater treatment has been carried out by describing the system as a nonconvex mixed-integer nonlinear problem (MINLP). A mixed-integer linear problem (MILP) is derived from the original nonlinear problem by the convex relaxation of the nonconvex terms in the MINLP to provide bounds for the global optimum. The MILP model is solved iteratively to supply different initial guesses for the nonconvex MINLP model. It is found that such a procedure is effective in finding local optimum solutions in reasonable time and overcoming possible convergence difficulties associated with MINLP local search methods. Examples of water desalination and wastewater treatment from the pulp and paper industry are considered as case studies to illustrate the proposed solution strategy.     

Computational strategies for improved MINLP algorithms

In order to improve the efficiency for solving MINLP problems, we present in this paper three computational strategies. These include multiple-generation cuts, hybrid methods and partial surrogate cuts for the Outer Approximation and Generalized Benders Decomposition. The properties and convergence of the strategies are analyzed. Based on the proposed strategies, five new MINLP algorithms are developed, and their implementation is discussed. Results of numerical experiments for benchmark MINLP problems are reported to demonstrate the efficiency of the proposed methods.     

A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs

This paper presents an algorithm for the solution of nonconvex mixed integer nonlinear programming (MINLP) problems involving general constraints and objective functions. The algorithm employs a symbolic reformulation step that brings the original MINLP problem to an equivalent standard form for which a convex relaxation can be constructed. The reformulated problem is then solved using a spatial branch-and-bound algorithm which branches on both integer and continuous variables. Issues relating to the efficient implementation of this algorithm and its parallelisation are also discussed. The algorithm has been incorporated within the gPROMS process modelling environment and tested on several MINLP problems arising from process engineering applications.     

混合整数非线性规划与化学工程系统最优化计设——(Ⅰ)一个用于工程系统最优设计的混合整数非线性规划方法

化学工程系统最优化设计问题一般可被直接描述为混合整数非线性规划问题.本文着重导出一个求解上述问题的混合整数非线性规划方法.推导中,分解、投影等概念的引入使此方法易于实施.本文举例对算法进行了验证,并表明此方法是适于化学工程系统最优化设计的有效工具.     

混合整数非线性规划法求解多组分复杂体系相平衡问题

基于Gibbs自由能最小化原理,提出一种求解多组分复杂体系相平衡问题的混合整数非线性规划(MlNLP)方法.通过建立MlNLP模型,将相平衡计算问题转化为有约束的双层最优化问题,内层用来计算给定相组合结构下的平衡组成,外层则是搜索最优的相组合结构,整个求解过程通过遗传算法来实现.所建立的方法只需要求解最小化问题,就可以同时给出多相平衡时存在的相数、相态及各相组成.以苯-乙氰-水和甲醇合成两个体系的相平衡计算为例,结果表明该方法是可行和有效的.     

MINLP optimization of mechanical draft counter flow wet-cooling towers

In this paper, the problem of the optimal design of mechanical draft counter flow cooling towers that meets a set of specified constraints is formulated as a mixed-integer nonlinear programming (MINLP) problem. The Merkel's method is used to specify the characteristic dimensions of cooling towers, together with empirical correlations for the loss and overall mass transfer coefficients in the packing region of the tower. Water-to-air mass ratio, water mass flow rate, water inlet and outlet temperatures, operational temperature approach, type of packing, type of draft, height and area of the tower packing, total pressure drop of air flow, power consumption of the fan, and water consumption provide the set of optimization variables. The MINLP problem is formulated so as to minimize the total annual cost of the cooling tower. The performance of the proposed procedure is shown with the solution of six examples.     

Exergy as an objective function to MINLP problems in process synthesis

The optimal layout of a chemical plant is determined by both economic and environmental aspects. The mathematical approach to this problem is given by representing the process through a superstructure, including any foreseeable process topology. It is described by integer variables, whereas real variables arise from the unit models and the thermodynamic calculations. By including process constraints and an objective function, a Mixed Integer Nonlinear Programming (MINLP) optimization problem is postulated. In this paper MINLP algorithms are combined with a technique for the exergy analysis of chemical processes for the preliminary screening of process alternatives. The exergy analysis as a screening technique is advantageous due to a significantly smaller amount of required data and computing time, compared with true optimization, including cost estimation at an earlier stage of process synthesis and analysis. Thus, a broader solution space can be examined. The subsequent cost analysis has then only to be focused on a reduced set of parameters.     

Comparison of certain MINLP algorithms when applied to a model structure determination and parameter estimation problem

The maximum likelihood method is frequently used in parameter estimation. If the structure of the model is unknown, the maximization of the likelihood function can be replaced by minimizing an information criterion. One criterion that allows this to be done is Akaike’s information criterion (AIC). Minimizing the AIC is a mixed integer non-linear programming (MINLP) problem. In this paper, three different MINLP algorithms are compared in the solution of a simultaneous model structure determination and parameter estimation problem by minimizing the AIC criterion. The problem considered appears in quantitative Fourier transformed infra red (FTIR) spectroscopy where concentration estimates of certain gas components are to be obtained from measured absorbances at different wave numbers. The resulting problem is a large MINLP problem containing several hundreds, or even thousands, of variables including a huge number of possible model structures. It is, however, found that the studied algorithms solve the considered problem in quite a small number of iterations and a reasonable CPU-time.     

SIMOP: Application to global MINLP stochastic optimization

SIMOP (SIMulation for OPtimization) is an application that automatically creates FORTRAN simulation models for the stochastic optimizers MSGA and MSIMPSA. This paper presents the next step in SIMOP's development timeline, namely its expansion to cope with mixer-integer nonlinear problems (MINLP). From the perspective of MINLP formulations' relevance to the Chemical Engineering field, an introduction to SIMOP's MINLP modeling features is given. Its application is addressed by three case studies. The best results match those previously obtained with MSGA and MSIMPSA when non-automatically coded MINLP simulations where employed, thus validating the present approach. The introduction of discrete variables benefits the performance of both stochastic optimizers, contrary to what should a priori be expected, since a MINLP formulation promotes an accurate search on lower and upper bounds for several continuous variables.     

改进的自适应模拟退火算法及其在过程综合中的应用

为有效解决化工过程综合中的MINLP问题，针对连续变量的模拟退火算法搜索慢的缺点，提出了一种改进的自适应模拟退火算法（Adaptive Simulated Algorithms,ASA)，采取自适应调整温度和搜索步长两种策略，大大加快搜索速度，提高最优解的质量。实算结果充分体现了所提出算法的优点，并很好地应用于化工过程综合问题。