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.     

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.     

EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES

The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented.     

Modeling and optimization methods of integrated production planning for steel plate mill with flexible customization

With diversified requirements and varying manufacturing environments, the optimal production planning for a steelmill becomes more flexible and complicated. The flexibility provides operators with auxiliary requirements through an implementable integrated production planning. In this paper, a mixed-integer nonlinear programming (MINLP) model is proposed for the optimal planning that incorporates various manufacturing constraints and flexibility in a steel plate mill. Furthermore, two solution strategies are developed to overcome theweakness in solving the MINLP problem directly. The first one is to transformthe original MINLP formulation to an approximate mixed integer linear programming using a classic linearization method. The second one is to decompose the originalmodel using a branch-and-bound based iterative method. Computational experiments on various instances are presented in terms of the effectiveness and applicability. The result shows that the second method performs better in computational efforts and solution accuracy.     

Global optimization for scheduling refinery crude oil operations

In this work we present an outer-approximation algorithm to obtain the global optimum of a nonconvex mixed-integer nonlinear programming (MINLP) model that is used to represent the scheduling of crude oil movement at the front-end of a petroleum refinery. The model relies on a continuous time representation making use of transfer events. The proposed algorithm focuses on effectively solving a mixed-integer linear programming (MILP) relaxation of the nonconvex MINLP to obtain a rigorous lower bound (LB) on the global optimum. Cutting planes derived by spatially decomposing the network are added to the MILP relaxation of the original nonconvex MINLP in order to reduce the solution time for the MILP relaxation. The solution of this relaxation is used as a heuristic to obtain a feasible solution to the MINLP which serves as an upper bound (UB). The lower and upper bounds are made to converge to within a specified tolerance in the proposed outer-approximation algorithm. On applying the proposed technique to test examples, significant savings are realized in the computational effort required to obtain provably global optimal solutions.     

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.     

Homotopy continuation methods for computer-aided process design

Homotopy continuation methods have been used by the authors and others to solve difficult chemical engineering flowsheeting and design problems involving the solution of simultaneous nonlinear equations. Such methods can fail when: (1) the homotopy path, which one follows from the solution of a simple problem to the solution of the original (difficult) problem, returns to a second solution of the simple problem; (2) the homotopy path strikes an interior boundary of the domain of definition of the original (vector-valued) function; and (3) the homotopy path goes off to infinity. For the first two modes of failure, the use of an affine homotopy is discussed here as a possible remedy. Failure due to an unbounded homotopy path is the subject of current research.     

用于热集成精馏序列综合的改进模拟退火算法

提出一个用于多组分热集成精馏系统综合问题的改进模拟退火算法.将优化问题表示为混合整数非线性规划（MINLP）问题,将算法设计同研究问题的特征相结合,运用本文方法可在同一退火策略下实现流程结构和操作参数的同步优化,并能达到计算精度和计算速度的更好均衡.通过对大规模算例（产品数≥10）的计算表明,该方法对求解此类问题非常有效.     

Optimization of process synthesis and design problems: A modified differential evolution approach

A large number of process synthesis and design problems in chemical engineering can be modeled as mixed integer nonlinear programming (MINLP) problems. They involve continuous (floating point) and integer variables. A common feature of this class of mathematical problems is the potential existence of non-convexities due to the particular form of the objective function and/or the set of constraints. Due to their combinatorial nature, these problems are considered to be difficult. In recent years, evolutionary algorithms (EAs) are gaining popularity for finding the optimal solution of nonlinear multimodal problems encountered in many engineering disciplines. In the present study, a novel modified differential evolution [Angira, R., Babu, B.V., 2005a. Optimization of non-linear chemical processes using modified differential evolution (MDE). Proceedings of the Second Indian International Conference on Artificial Intelligence (IICAI-05), Pune, India, December 20-22, pp. 911-923. Also available at 〈http://discovery.bits-pilani.ac.in/discipline/chemical/bvb/publications.html〉], one of the evolutionary algorithms, is used for solving process synthesis and design problems. To illustrate the applicability and efficiency of modified differential evolution (MDE), seven test problems on process synthesis and design have been solved. These problems arise from the area of chemical engineering, and represent difficult nonconvex optimization problems, with continuous and discrete variables. The performance of MDE is compared with that of Genetic Algorithm, Evolution Strategy, and MINLP-Simplex Simulated Annealing (M-SIMPSA).     

MINLP synthesis of reactor networks in overall process schemes based on a concept of time-dependent economic regions

The design and optimization of reactor networks using the conventional concept of attainable region is based on technological (conversion, selectivity, etc.), rather than, economical criteria (cost, profit, etc.). The solution from the economical point of view when the operating and investment costs cannot be neglected may not be optimal, not even in regard to the structure. In order to circumvent this deficiency, the conventional Concentration Attainable Region (CAR) is transformed into an Economic Region (ER) using economic optimization criteria. A novel concept for ER construction is proposed for multi-D problems. One-parametric NLP or MINLP optimizations with reactor volume as a varying parameter are performed to construct trajectories in the ER. In this way the ER is aided by mathematical programming for 3D or more D problems in order to handle dimensions higher than 2 as degrees of freedom for the economic objective function. ER is attainable (EAR) only when the economic objective function is linear. The more the objective function is discontinuous, discrete, nonlinear and non-convex and the more its cost coefficients vary with time, the less the principles of AR can be applied to ER. However, economically optimal reactor systems always lie at the borders of ERs. Two important insights have been gained during the construction of different time-dependent ERs, which have been used in upgrading the MINLP approach to the synthesis of reactor networks in overall process schemes: (i) A reactor network superstructure has been reestablished based on economical optimization criteria and the principles of ER. (ii) Over a longer period, the performing of a stochastic multi-period MINLP synthesis is recommended, in order to consider the time variability and uncertainties of economic parameters. A special multi-period strategy is proposed to upgrade the efficiency of the MINLP synthesis.     

Differential Geometry Based Continuation Algorithms for Separation Process Applications

Abstract

Nonlinear representation of equilibrium phenomena in azeotropic distillation, extractive distillation and liquid extraction has been shown to result in simulations that have as many as three concentration and temperature profiles that meet the same process specifications. Continuation algorithms are the only assured technique of indicating this multiplicity and solving these highly nonlinear problems. Unfortunately, the robustness of solution is accompanied by increased computation. New procedures that increase the efficiency of these algorithms are documented in this paper.

Local differential geometry is exploited during the continuation procedure to provide a more accurate prediction of the solution trajectory. A rigorous method is documented for accurate prediction of the unit tangent, principal unit normal, and the curvature of the solution path. The resulting computational procedure is significantly more efficient than other continuation methods. It is shown that the effects of increased accuracy of prediction are threefold. The number of a) continuation steps, b)newton corrections to return to the solution path, and c)trajectory prediction failures are all reduced.     

全局优化搜索新算法--列队竞争算法(Ⅰ)解非线性和混合整数非线性规划问题

提出了一种称为列队竞争算法(LCA)的群体搜索算法,该算法在进化过程中始终保持着独立并行进化的家族,通过家族内部的生存竞争和家族间的地位竞争这两种不同的竞争方式,使群体快速进化到最优或接近最优的区域.根据家族的目标函数值大小排列成一个列队,按列队中家族地位的不同分配不同的搜索空间,使局部搜索与全局搜索达到均衡,同时,应用逐步收缩搜索空间技术加速收敛速度.数值计算表明,列队竞争算法的搜索效率优于遗传算法和模拟退火法等算法.     

全局优化搜索新算法——列队竞争算法(Ⅰ) 解非线性和混合整数非线性规划问题

提出了一种称为列队竞争算法(LCA)的群体搜索算法,该算法在进化过程中始终保持着独立并行进化的家族,通过家族内部的生存竞争和家族间的地位竞争这两种不同的竞争方式,使群体快速进化到最优或接近最优的区域.根据家族的目标函数值大小排列成一个列队,按列队中家族地位的不同分配不同的搜索空间,使局部搜索与全局搜索达到均衡,同时,应用逐步收缩搜索空间技术加速收敛速度.数值计算表明,列队竞争算法的搜索效率优于遗传算法和模拟退火法等算法.     

Solving Multi‐objective MILP Problems in Process Synthesis using the Multi‐Criteria Branch and Bound Algorithm

The paper briefly describes the problem of process synthesis in the area of chemical engineering, and suggests its formulation as a Multi‐Objective Programming problem. Process synthesis optimization is usually modeled as Mixed Integer Linear Programming (MILP) or Mixed Integer Non‐Linear Programming (MINLP) with an economic objective function. We claim that incorporating more criteria (e.g., environmental criteria) in this kind of combinatorial optimization problem offers the decision makers the opportunity to refine their final decision by examining more than one solution (a set of efficient or Pareto optimal solutions instead of one optimal solution). For solving the multi‐objective process synthesis problem, an improved version of the Multi‐Criteria Branch and Bound (MCBB) algorithm, which has been developed by the same authors, is used. MCBB is a vector maximization algorithm capable of deriving all efficient points (supported and unsupported), for small and medium sized Multi‐Objective MILP problems. The application of MCBB in two examples from process synthesis is also presented.     

Solving mixed integer nonlinear programming problems with line-up competition algorithm

Line-up competition algorithm (LCA), a global optimization algorithm proposed recently, is applied to the solution of mixed integer nonlinear programming (MINLP) problems. Through using alternative schemes to handle integer variables, the algorithm reported previously for solving NLP problems can be extended expediently to the solution of MINLP problems. The performance of the LCA is tested with several non-convex MINLP problems published in the literature, including the optimal design of multi-product batch chemical processes and the location-allocation problem. Testing shows that the LCA algorithm is efficient and robust in the solution of MINLP problems.     

A Modular Mixed‐Integer Non‐Linear Programming Algorithm for Synthesis of Chemical Processes

A modular approach to the formulation and a solution of mixed‐integer non‐linear programming (MINLP) problems are presented, which reduce the size of MINLP and the computational expenses effectively. The method decomposes the synthesis task into three hierarchical levels—the superstructure, the structure, and the modules, with the layer of modules being the most critical to the problem solution. The strategy has been implemented in a simulation environment in which the variables of interest are defined as implicit functions of the optimization variables. The implicit relationships are handled using a data‐oriented process simulation technique (DOPS) that significantly simplify the simulation. The method has been effectively applied to two case studies, one from literature for the synthesis of hydrodesalkylation, and another from industrial process manufacturing methylene diphenylene diisocyanates.     

Optimal design and planning of heap leaching process. Application to copper oxide leaching

Although the process of heap leaching is an established technology for treating minerals, such as copper, gold, silver, uranium and saltpeter, as well as remediating soil, no studies to date have investigated process optimization. This work presents a methodology for the design and planning of heap leaching systems to optimize the process. This methodology consists of the creation of a superstructure that represents a set of alternatives to search for the optimal solution; from this superstructure, a mixed integer nonlinear programming (MINLP) model was generated, and a BARON-GAMS solver was used to find the optimal solution. This method was applied to the extraction of copper from systems with one, two and three heaps, and the effects of copper price, ore grade and other variables were analyzed for each system. From the results, it can be concluded that this methodology can be used to optimize heap leaching processes, including planning and design issues.     

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。     

多流股换热器网络综合方法在原油预热系统中的应用

以原油常减压蒸馏装置原油预热网络为研究对象,进行了多流股换热器网络的实例综合. 基于超结构物理模型建立了改进的多流股换热器网络综合数学模型,提出将该网络综合问题由混合整数非线性规划问题转化为简单的非线性规划问题的求解策略,并利用改进的遗传/模拟退火新算法进行了原油预热网络的综合. 与Hextran软件的综合结果以及现场换热网络的对比表明,本模型和求解策略可以应用于工业规模的多流股换热器网络综合,有可能取得较好的经济效益.     

Optimal storage design for a multi-product plant: A non-convex MINLP formulation

We discuss a tank design problem for a multi product plant, in which the optimal cycle time and the optimal campaign size are unknown. A mixed-integer nonlinear programming (MINLP) formulation is presented, where non-convexities are due to the tank investment cost, storage cost, campaign setup cost and variable production rates. The objective of the optimization model is to minimize the sum of the production cost per ton per product produced. A continuous-time mathematical programming formulation is proposed and several extensions are discussed. The model is implemented in GAMS and computational results are reported for the two global MINLP solver BARON and LINDOGlobal as well as several nonlinear solvers available in GAMS.