Self-tuning run to run optimization of fed-batch processes using unfold-PLS

Unfold Partial-Least Squares (u-PLS) is a modeling method successfully applied to batch-process monitoring and end quality prediction. This method is integrated in a self-tuning optimization algorithm, based on extremum-seeking control. The optimization is driven by the gradient obtained by means of an adaptive u-PLS model. Since this is an empirical model, no first-principles based knowledge of the process is necessary. Heuristic rules are used to constrain the gradient taking into account nonlinearity and unknown causes of variability. Extensions to model the variability in initial conditions, to optimize several performance indices, and to handle inequality constraints are presented. The optimization algorithm is tested on a complex comprehensive simulated-process model for the fed-batch cultivation of Sacharomyces cerevisiae. Results show the performance and versatility of the proposed approach, as well as its robustness to process changes. © 2007 American Institute of Chemical Engineers AIChE J, 2007     

反应器网络多目标综合优化

通过反应系统综合优化获得经济效益好、对环境友好的反应系统是大多化工厂提高全流程整体经济和环境性能的重要手段。反应器网络综合优化方法主要包括可得区法、导数分析法、超结构优化法、目标类法、经验推断法和分布参数法等,然而却很少有文献报道对反应器网络进行多目标综合优化。由于过程中往往存在多个相互冲突的目标函数,所以仅仅依靠单目标对反应器网络进行综合优化已显得不合适。本文采用分布参数法建立多目标优化模型,目标函数为经济最大化和环境影响最小,并采用非支配排序基因算法(NSGA-Ⅱ)进行优化得到Pareto最优解集。     

Water network design with stochastic optimization approach

Water network (called also water allocation) problem has been addressed in more than 200 papers to date – see recent reviews by Je?owski (2010) and Foo (2009). Though various solution methods have been developed they all have some limitations. This paper addresses water usage network with regeneration processes. Multiple contaminants and two types of water using processes are taken into regard. Simultaneous one stage optimization method was developed to synthesize the network. In order to solve complex MINLP formulation we propose to apply meta-heuristic optimization – adaptive random search method.The paper contains detailed solution algorithm. Several examples with specific features are solved to show efficiency and flexibility of the approach.     

Synthesis of the fluid machinery network in a circulating water system

Energy consumption of the fluid machinery network in a circulating water system takes up a large part of energy consumption in the process industry, so optimization on the network will enhance the economic and environmental performance of the industry. In this paper, a synthesis approach is proposed to obtain the optimal network structure. The effective height curves are used as tools to perform energy analysis, so that the potential placement of water turbines and auxiliary pumps can be determined with energy benefit. Then economic optimization is carried out, by the mathematical model with the total cost as the objective function, to identify the branches for water turbines and auxiliary pumps with economic benefit. In this way, the optimal fluid machinery network structure can be obtained. The results of case study indicate that the proposed synthesis approach to optimize the fluid machinery network will obtain more remarkable benefits on economy, compared to optimizing only the water turbine network or pump network. The results under different flowrates of circulating water reveal that using a water turbine to recover power or adding an auxiliary pump to save energy in branches are only suitable to the flowrate in a certain range.     

A global optimal formulation for the water integration in eco-industrial parks considering multiple pollutants

A mathematical programming formulation for the water integration in eco-industrial parks considering streams with several pollutants is presented. The formulation is based on a superstructure that allows the wastewater reuse in the same plant, the water exchange with different plants, and a shared set of interceptors that must be selected to determine the network configuration that satisfies process equipments and environmental constraints. The model formulation considers wastewater with several pollutants, and optimizes the network according to the minimum total annual cost, which includes the costs of fresh water, piping and regeneration. A new discretization approach is also proposed to handle the large set of bilinear terms that appear in the model in order to yield a near global optimal solution. The results obtained in several examples show considerable savings with respect to the solutions of the individual plant integration policy commonly employed for these types of problems.     

人工神经网络结合遗传算法对CFWRP固化制度的优化

聚合物基复合材料的固化制度是影响其性能经济指标的重要因素。它们之间的关系既无先验公式表征,又为非线性,一般是采用“试凑法”探索试验,但耗时长也未必达到优化目的。神经网络法具有超强非线性映射能力,可自动总结出数据之间的函数关系,遗传算法可多点群体搜索,并可不陷入局部最优点。本文以碳纤维缠绕聚合物基复合材料(CFWRP)制成NOL环试件,在试验基础上采用人工神经网络结合遗传算法对固化制度进行优化,得到较好的结果。     

Extending the resource task network for industrial applications

The discrete time resource-task network (RTN) model is a generalized mixed-integer linear programming model used in scheduling optimization problems. This paper presents several extensions to the RTN that have been used at The Dow Chemical Company. One RTN extension allows for more realistic demand fulfillment: customer orders can be filled in their entirety at a distinct time point, rather than over several time periods. Modifications are proposed that allow tasks to interact not just with resources, but also with the bounds on those resources, which allows for an efficient method of modeling storage. The concept of multiple extents is introduced to extend the functionality of a single task and thereby reduce the overall size of the model and improve computation time. An alternative formulation of the RTN is also introduced in spatial rather than temporal coordinates, which allows applicability to a different class of problems such as payload optimization.     

A MATRIX APPROACH FOR OPTIMIZATION OF PIPE NETWORKS IN COOLING WATER SYSTEMS

This article addresses the design problems associated with pipe networks in cooling water systems. The objective is to determine the lowest cost network that can supply the heat exchangers with cooling water at the flow rates previously established in the thermal design. The solution to the problem provides the diameter for each section of pipe in the network together with the corresponding pump alternative. The objective function and constraints are organized in a matrix formulation where the solution consists of a set of linear programming problems. The basic structure of the optimal design problem also extends to the solution for revamp problems. The comparison of the proposed approach to the traditional solution based on economical velocities indicates that the optimization scheme can make pipe network designs less expensive and more reliable for supplying cooling water.     

Improving scenario decomposition algorithms for robust nonlinear model predictive control

This paper deals with the efficient computation of solutions of robust nonlinear model predictive control problems that are formulated using multi-stage stochastic programming via the generation of a scenario tree. Such a formulation makes it possible to consider explicitly the concept of recourse, which is inherent to any receding horizon approach, but it results in large-scale optimization problems. One possibility to solve these problems in an efficient manner is to decompose the large-scale optimization problem into several subproblems that are iteratively modified and repeatedly solved until a solution to the original problem is achieved. In this paper we review the most common methods used for such decomposition and apply them to solve robust nonlinear model predictive control problems in a distributed fashion. We also propose a novel method to reduce the number of iterations of the coordination algorithm needed for the decomposition methods to converge. The performance of the different approaches is evaluated in extensive simulation studies of two nonlinear case studies.     

Integrated scheduling and dynamic optimization of batch processes using state equipment networks

A systematic framework for the integration of short‐term scheduling and dynamic optimization (DO) of batch processes is described. The state equipment network (SEN) is used to represent a process system, where it decomposes the process into two basic kinds of entities: process materials and process units. Mathematical modeling based on the SEN framework invokes both logical disjunctions and operational dynamics; thus the integrated formulation leads to a mixed‐logic dynamic optimization (MLDO) problem. The integrated approach seeks to benefit the overall process performance by incorporating process dynamics into scheduling considerations. The solution procedure of an MLDO problem is also addressed in this article, where MLDO problems are translated into mixed‐integer nonlinear programs using the Big M reformulation and the simultaneous collocation method. Finally, through two case studies, we show advantages of the integrated approach over the conventional recipe‐based scheduling method. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

A Surrogate Integrated Production Modeling Approach to Long-Term Gas-Lift Allocation Optimization

The conventional static gas-lift allocation optimization approaches are not appropriate for long-term gas-lift projects. A good choice for long-term optimization should predict gas-lift performance dynamically as a function of production time and other variables. A good solution approach for problem is a hybrid of surrogate integrated production modeling and genetic algorithm (GA). Hybrid GAs have received significant interest in recent years and are being increasingly used to solve real-world problems. GA incorporates other techniques within its framework to produce a hybrid that reaps the best from the combination. This study discusses a new method known as surrogate integrated production modeling that uses an artificial neural network to predict gas-lift performance based on a database of oil production. Then, a hybrid of the neural network and GA is used for long-term gas-lift allocation optimization in a group of wells under real constraints.     

Simultaneous optimal integration of water utilization and heat exchange networks using holistic mathematical programming

A systematic holistic mathematical programming (HMP) is proposed to formulate a mixed integer nonlinear programming (MINLP) model for one-step optimization of water-allocation and heat exchange network (WAHEN) designs with single- or multi-contaminant water streams. The proposed model formulation and solution strategy are believed to be superior to the available ones in the following aspects. First, a comprehensive representation combining two separate superstructures is adopted to capture the structural characteristics of the integrated WAHEN. Then, a hybrid optimization strategy integrating stochastic and deterministic components is developed for the resulting MINLP model and, also, an interactive iteration method is adopted based on sensitivity analysis to guide the search toward a potential global optimum. Finally, evolutionary strategies and manipulations are executed to enhance WAHEN configurations. Two illustrative examples are presented to demonstrate the validity and advantages of the proposed approach.     

Optimization of refinery hydrogen network based on chance constrained programming

Deterministic optimization approaches have been developed and used in the optimization of hydrogen network in refinery. However, uncertainties may have a large impact on the optimization of hydrogen network. Thus the consideration of uncertainties in optimization approaches is necessary for the optimization of hydrogen network. A novel chance constrained programming (CCP) approach for the optimization of hydrogen network in refinery under uncertainties is proposed. The stochastic properties of the uncertainties are explicitly considered in the problem formulation in which some input and state constraints are to be complied with predefined probability levels. The problem is then transformed to an equivalent deterministic mixed-integer nonlinear programming (MINLP) problem so that it can be solved by a MINLP solver. The solution of the optimization problem provides comprehensive information on the economic benefit under different confidence levels by satisfying process constraints. Based on this approach, an optimal and reliable decision can be made, and a suitable compensation between the profit and the probability of constraints violation can be achieved. The approach proposed in this paper makes better use of resources and can provide significant environmental and economic benefits. Finally, a case study from a refinery in China is presented to illustrate the applicability and efficiency of the developed approach.     

Numerical optimization of proton exchange membrane fuel cell cathodes

A fuel cell gradient-based optimization framework based on adaptive mesh refinement and analytical sensitivities is presented. The proposed approach allows for efficient and reliable multivariable optimization of fuel cell designs. A two-dimensional single-phase cathode electrode model that accounts for voltage losses across the electrolyte and solid phases and water and oxygen concentrations is implemented using an adaptive finite element formulation. Using this model, a multivariable optimization problem is formulated in order to maximize the current density at a given electrode voltage with respect to electrode composition parameters, and the optimization problem is solved using a gradient-based optimization algorithm. In order to solve the optimization problem effectively using gradient-based optimization algorithms, the analytical sensitivity equations of the model with respect to the design variables are obtained. This approach reduces the necessary computational time to obtain the gradients and improves significantly their accuracy when compared to gradients obtained using numerical sensitivities. Optimization results show a substantial increase in the fuel cell performance achieved by increasing platinum loading and reaching a Nafion mass fraction around 20-30 wt.% in the catalyst layer.     

Design and planning of infrastructures for bioethanol and sugar production under demand uncertainty

In this paper, we address the strategic planning of integrated bioethanol–sugar supply chains (SC) under uncertainty in the demand. The design task is formulated as a multi-scenario mixed-integer linear programming (MILP) problem that decides on the capacity expansions of the production and storage facilities of the network over time along with the associated planning decisions (i.e., production rates, sales, etc.). The MILP model seeks to optimize the expected performance of the SC under several financial risk mitigation options. This consideration gives a rise to a multi-objective formulation, whose solution is given by a set of network designs that respond in different ways to the actual realization of the demand (the uncertain parameter). The capabilities of our approach are demonstrated through a case study based on the Argentinean sugarcane industry. Results include the investment strategy for the optimal SC configuration along with an analysis of the effect of demand uncertainty on the economic performance of several biofuels SC structures.     

A hybrid optimization strategy for simultaneous synthesis of heat exchanger network

The heat exchanger network synthesis problem often leads to large-scale non-convex mixed integer nonlinear programming formulations that contain many discrete and continuous variables, as well as nonlinear objective function or nonlinear constraints. In this paper, a novel method consisting of genetic algorithm and particle swarm optimization algorithm is proposed for simultaneous synthesis problem of heat exchanger networks. The simultaneous synthesis problem is solved in the following two levels: in the upper level, the network structures are generated randomly and reproduced using genetic algorithm; and in the lower level, heat load of units and stream-split heat flows are optimized through particle swarm optimization algorithm. The proposed approach is tested on four benchmark problems, and the obtained solutions are compared with those published in previous literature. The results of this study prove that the presented method is effective in obtaining the approximate optimal network with minimum total annual cost as performance index.     

Flexible design‐planning of supply chain networks

Nowadays market competition is essentially associated to supply chain (SC) improvement. Therefore, the locus of value creation has shifted to the chain network. The strategic decision of determining the optimal SC network structure plays a vital role in the later optimization of SC operations. This work focuses on the design and retrofit of SCs. Traditional approaches available in literature addressing this problem usually utilize as departing point a rigid predefined network structure which may restrict the opportunities of adding business value. Instead, a novel flexible formulation approach which translates a recipe representation to the SC environment is proposed to solve the challenging design‐planning problem of SC networks. The resulting mixed integer linear programming model is aimed to achieve the best NPV as key performance metric. The potential of the presented approach is highlighted through illustrative examples of increasing complexity, where results of traditional rigid approaches and those offered by the flexible framework are compared. The implications of exploiting this potential flexibility to improve the SC performance are highlighted and are the subject of our further research work. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

A shortcut method for the preliminary synthesis of process-technology pathways: An optimization approach and application for the conceptual design of integrated biorefineries

Synthesis and screening of technology alternatives is a key process-development activity in the process industries. Recently, this has become particularly important for the conceptual design of biorefineries. This work introduces a shortcut method for the synthesis and screening of integrated biorefineries. A structural representation (referred to as the chemical species/conversion operator) is introduced. It is used to track individual chemicals while allowing for the processing of multiple chemicals in processing technologies. The representation is used to embed potential configurations of interest. An optimization approach is developed to screen and determine optimum network configurations for various technology pathways using simple data. The solution to the optimization formulation provides a quick and effective method for screening and interconnecting the technological pathways and to distributing the flows over the network. Case studies are solved to illustrate the applicability of the proposed approach.     

水系统集成优化方案的博弈分析与评价方法

对水系统集成优化方案的分析和决策需要考虑新鲜水用量、用水系统的柔性和用水网络结构的复杂程度等方面。水网络优化设计方案的确定一般需要在这三者之间进行折中和协调,属于多目标优化问题。为了综合考虑新鲜水消耗量和网络结构复杂程度等指标,并定量分析和确定水网络的优化设计方案,本文提出一种基于博弈分析的水网络优化方案的定量分析方法。以具有中间水道水网络优化设计方案的决策为例,采用本文方法进行了优化设计方案的分析与评价。研究表明：该定量分析和评价用水网络的方法可以合理地评价用水网络的设计方案,该方法可用于定量确定水系统优化问题中的多目标优化方案,可为水系统优化集成方案的确定提供分析依据和指导。     

A property-based optimization of direct recycle networks and wastewater treatment processes

This article presents a mathematical programming approach to optimize direct recycle-reuse networks together with wastewater treatment processes in order to satisfy a given set of environmental regulations. A disjunctive programming formulation is developed to optimize the recycle/reuse of process streams to units and the performance of wastewater treatment units. In addition to composition-based constraints, the formulation also incorporates in-plant property constraints as well as properties impacting the environment toxicity, ThOD, pH, color, and odor. The MINLP model is used to minimize the total annual cost of the system, which includes the cost for the fresh sources, the piping cost for the process integration and the waste stream treatment cost. An example problem is used to show the application of the proposed model. The results show that the simultaneous optimization of a recycle network and waste treatment process yields significant savings with respect to a commonly-used sequential optimization strategy. © 2009 American Institute of Chemical Engineers AIChE J, 2009