Optimal design of chemical processes with chance constraints

Generally, chemical processes (CP) are designed with the use of inaccurate mathematical models. Therefore, it is important to create a chemical process that guarantees satisfaction of all design specifications either exactly or with some probability. The paper considers the issue of chemical process optimization when at the operation stage the design specification should be met with some probability and the control variables can be changed. We have developed a common approach for solving the broad class of optimization problems with normally distributed uncertain parameters. This class includes the one-stage and two-stage optimization problems with chance constraints. This approach is based on approximate transformation of chance constraints into deterministic ones.     

Design of Chemical Engineering Systems with Chance Constraints

In the design of chemical process under uncertainty in initial information, an important problem is to determine a structure in which the control system will guarantee that all constraints are satisfied despite variations in internal and external factors at the operation stage. A method has been proposed for solving onestage optimization problems with chance constraints in the design of optimal flexible chemical processes. The developed approach makes it possible to avoid multidimensional integration in each of the iterations of problem solving, thus reducing the computational effort. The efficiency of the proposed approach is illustrated by model examples.     

Two-stage optimization problem with chance constraints

In general, chemical processes (CP) are designed with the use of inaccurate mathematical models. Therefore, it is important to create a chemical process that guarantees satisfaction of all design specifications either exactly or with some probability. The paper considers the issue of chemical process optimization when at the operation stage the design specification should be met with some probability and the control variables can be changed. We developed a new formulation of the two-stage optimization problem (TSOP) with chance constraints. On the basis of this formulation and approximate transformation of chance constraints into deterministic ones the iteration method of solving the TSOP with chance constraints is devised.     

Optimization problem with normally distributed uncertain parameters

The issue of chemical process optimization when at the operation stage the design specification should be met with some probability and the control variables can be changed has been considered. A common approach for solving the broad class of optimization problems with normally distributed uncertain parameters were developed. This class includes the one‐stage and two‐stage optimization problems with chance constraints. This approach is based on approximate transformation of chance constraints into deterministic ones. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2471–2484, 2013     

Optimal robust optimization approximation for chance constrained optimization problem

Chance constraints are useful for modeling solution reliability in optimization under uncertainty. In general, solving chance constrained optimization problems is challenging and the existing methods for solving a chance constrained optimization problem largely rely on solving an approximation problem. Among the various approximation methods, robust optimization can provide safe and tractable analytical approximation. In this paper, we address the question of what is the optimal (least conservative) robust optimization approximation for the chance constrained optimization problems. A novel algorithm is proposed to find the smallest possible uncertainty set size that leads to the optimal robust optimization approximation. The proposed method first identifies the maximum set size that leads to feasible robust optimization problems and then identifies the best set size that leads to the desired probability of constraint satisfaction. Effectiveness of the proposed algorithm is demonstrated through a portfolio optimization problem, a production planning and a process scheduling problem.     

An efficient constraint handling method with integrated differential evolution for numerical and engineering optimization

Constrained optimization problems are very important as they are encountered in many engineering applications. Equality constraints in them are challenging to handle due to tiny feasible region. Additionally, global optimization is required for finding global optimum when the objective function and constraints are nonlinear. Stochastic global optimization methods can handle non-differentiable and multi-modal objective functions. In this paper, a new constraint handling method for use with such methods is proposed for solving equality and/or inequality constrained problems. It incorporates adaptive relaxation of constraints and the feasibility approach for selection. The recent integrated differential evolution (IDE) with the proposed constraint handling technique is tested for solving benchmark problems with constraints, and then applied to many chemical engineering application problems with equality and inequality constraints. The results show that the proposed constraint handling method with IDE (C-IDE) is reliable and efficient for solving constrained optimization problems, even with equality constraints.     

Integrated design of power- and resource-saving chemical processes and process control systems: Strategy,methods, and application

A strategy for the integrated design of power-and resource-saving chemical processes and the systems controlling their operating conditions with uncertain input data on physicochemical and process parameters is formulated. A multistep iterative procedure for solving integrated design problems is developed. The procedure includes the generation of alternative chemical processes meeting the “rigid” and/or “soft” flexibility constraints and the choice of operating (control) actions, the synthesis of alternative systems for the automatic control of the operating conditions of the chemical process and the choice of the best control system, the pairwise comparison of feasible automated integrated systems consisting of the chemical engineering process and its control system and the choice of the best integrated system using the criterion based on the power and resource savings and control quality by solving one-and/or two-stage stochastic optimization problems with rigid and/or soft constraints. An example integrated design of the flexible continuous synthesis of azo pigments with an automatic-control system for stabilizing the optimal static conditions is discussed.     

Multistage adaptive optimization using hybrid scenario and decision rule formulation

Scenario-based stochastic programming and linear decision rule (LDR)-based robust optimization are prevalent methods for solving multistage adaptive optimization (MSAP) problems. In practical applications such as capacity expansion planning of chemical processes, often multiple sources of uncertainty affect the problem which introduces challenges to traditional stochastic optimization methods. While a large number of uncertain parameters exist in the problem, using scenario-based method results in very large problem size and the solution becomes computationally expensive. In addition, when the constraints include multiplication of uncertain parameters and adaptive variables, the constraints are not linear with respect to uncertain parameters when the LDR method is used. In order to address these challenges, we propose two different hybrid methods where scenario and decision rule methods are combined to solve the MSAP problem. The article demonstrates the computational performance of the proposed hybrid methods using two chemical process planning examples.     

A multiobjective approach to design chemical plants with robust dynamic operability characteristics

In chemical plants, operability problems arise mainly due to poor process designs, inaccurate models and/or the control system designs that are unable to cope with process uncertainties. In this paper, a process design methodology is presented that addresses the issue of improving dynamic operability in the present of process uncertainty through appropriate design modifications. The multiobjective nature of the design problem is carefully exploited in the subsequent formulations and a nonlinear programming approach is taken for the simultaneous treatment of both steady-state and dynamic constraints.

Scope—Today, a chemical engineer faces the challenge of designing chemical plants that can operate safely, smoothly and profitably within a dynamic process environment. For a typical chemical plant, major contributions to such an environment originate from external disturbances such as variations in the feedstock quality, different product specifications and/or internal disturbances like catalyst poisoning and heat-exchanger fouling. To guarantee a flexible operation despite such upsets, traditionally, the procedure was either to oversize the equipment or to place large storage tanks between the processing units. Proposed design methods attempted to find optimal operating regimes for chemical plants while compensating for process uncertainty through empirical overdesign factors.

Studies concerned with the interplay between the process design and operation aspects have appeared recently [1, 2] and focused on achieving better controllability upon modifying the plant design, without explicitly considering process uncertainty. Nevertheless, maintaining satisfactory dynamic operability in an environment of uncertainty remained as a pressing issue and the need was raised quite frequently for a rigorous treatment of the topic [3].

The development of new analytical tools [4, 5] made it possible to consider dynamic operability at the process design stage and modify the plant design accordingly. In this paper, a methodology is presented, that systematically guides the designer towards process designs with better dynamic operability and economics, The problem is formulated within a multiobjective optimization framework and makes extensive use of singular-value decomposition and nonlinear semi-infinite programming techniques.

Conclusions and Significance—A multiobjective optimization problem is proposed for designing chemical processes with better dynamic operability characteristics. Robustness indices are used as the indicators of dynamic operability and placed as constraints within the optimization scheme. A semi-infinite nonlinear programming problem results due to the frequency-dependent nature of such constraints. A discretization procedure is suggested to handle the infinite number of constraints and an ellipsoid algorithm allows an interactive solution of the process design problem. A process consisting of three CSTRs is treated as an example, illustrating the potential of the methodology in solving design-related operability problems.     

Chance constrained optimization of process systems under uncertainty: I. Strict monotonicity

An approach for chance constrained programming of large-scale nonlinear dynamic systems is presented. The stochastic property of the uncertainties is explicitly considered in the problem formulation in which some input and state constraints are to be complied with predefined probability levels. The method considers a nonlinear relation between the uncertain input and the constrained variables. It also involves efficient algorithms so as to compute the probabilities and, simultaneously, the gradients through integration by collocation in finite elements. The formulation of single or joint probability limits incorporates the issue of feasibility and the contemplation of trade-off between robustness and profitability regarding the objective function values. The approach is relevant to all cases when uncertainty can be described by any kind of joint correlated multivariate distribution function. Thus, chance constrained programming is a promising technique in solving optimization problems under uncertainty in system engineering. The potential and the efficiency of the presented systematic methodology, which assumes a strict monotonic relationship between the uncertain input and the uncertain constrained output, are illustrated with application to a reactive batch distillation processes under uncertainty.     

Steady‐state process optimization with guaranteed robust stability under parametric uncertainty

Interest in chemical processes that perform well in dynamic environments has led to the development of design methodologies that account for operational aspects of processes, including flexibility, operability, and controllability. In this article, we address the problem of identifying process designs that optimize an economic objective function and are guaranteed to be stable under parametric uncertainties. The underlying mathematical problem is difficult to solve as it involves infinitely many constraints, nonconvexities and multiple local optima. We develop a methodology that embeds robust stability constraints to steady‐state process optimization formulations without any a priori bifurcation analysis. We propose a successive row and column generation algorithm to solve the resulting generalized semi‐infinite programming problem to global optimality. The proposed methodology allows modeling different levels of robustness, handles uncertainty regions without overestimating them, and works for both unique and multiple steady states. We apply the proposed approach to a number of steady‐state optimization problems and obtain the least conservative solutions that guarantee robust stability. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

A global optimization algorithm (GOP) for certain classes of nonconvex NLPs—II. Application of theory and test problems

In Part I (Floudas and Visweswaran, Computers chem. Engng 14, 1397, 1990), a deterministic global optimization approach was proposed for solving certain classes of nonconvex optimization problems. An algorithm, GOP, was presented for the rigorous solution of the problem through a series of primal and relaxed dual problems until the upper and lower bounds from these problems converged to an -global optimum. In this paper, theoretical results are presented for several classes of mathematical programming problems that include: (i) the general quadratic programming problem; (ii) quadratic programming problems with quadratic constraints; (iii) pooling and blending problems; and (iv) unconstrained and constrained optimization problems with polynomial terms in the objective function and/or constraints. For each class, a few examples are presented illustrating the approach.     

采用同步策略的化工动态优化求解(英文)

An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control variables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at element knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies. The second technique is to make the mesh refinement more feasible and reliable by introducing length constraints and guideline in designing appropriate element length boundaries, so that the proposed approach becomes more efficient in adjusting elements to track optimal control profile breakpoints and ensure accurate state and control profiles. Four classic benchmarks of dynamic optimization problems are used as illustrations, and the proposed approach is compared with literature reports. The research results reveal that the proposed approach is preferable in improving the solution accuracy of chemical dynamic optimization problem.     

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.     

Nichtlineare stochastische Optimierung unter Unsicherheiten

Nonlinear Stochastic Optimization under Uncertainty Robust decision making under uncertainty is considered to be of fundamental importance in numerous disciplines and application areas. In dynamic chemical processes in particular there are parameters which are usually uncertain, but may have a large impact on equipment decisions, plant operability, and economic analysis. Thus the consideration of the stochastic property of the uncertainties in the optimization approach is necessary for robust process design and operation. As a part of it, efficient chance constrained programming has become an important field of research in process systems engineering. A new approach is presented and applied for stochastic optimization problems of batch distillation with a detailed dynamic process model.     

Optimization of chemical technology processes under probabilistic constraints

In designing technical systems in conditions of partial ambiguity of the initial physical, chemical, and economic information, it is important to determine a construction whose control system would guarantee implementation of all the constraints (precisely or with some probability) despite a change in the internal and external factors during the operating stage. The article is devoted to one of such problems and its solution, namely, the single-stage problem with probabilistic constraints. The approach to solving problems of this kind, based on a transformation of probabilistic constraints into determinate ones, has been suggested.     

New approaches to the integrated synthesis of flexible automated chemical engineering systems

The problems of optimizing the design and operational (control) variables during the integrated design of flexible automated complexes of chemical engineering process (CEP)—automated control systems (ACS) under conditions of the uncertainty of physicochemical, engineering, and economic initial data have been formalized. The selection of the best available version of a flexible automated complex is performed by means of the pairwise comparison of alternative versions of automated complexes using criteria that take into account both the quality of the manufactured products and the characteristics of energy and resource saving, on one hand, and the quality of transient processes in the ACS, on the other hand. A two-stage problem of stoichastic optimization of flexible automated complexes with hard and soft constraints has been stated, and a new approach to its solution has been proposed. An example of the integrated design of a flexible continuous process of azo pigments synthesis and a system of the optimum stabilization of its conditions in the presence of an interval uncertainty of the kinetic coefficients of the chemical reaction and individual engineering variables has been shown.     

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.     

全局优化搜索新算法──列队竞争算法(Ⅱ)解网络综合问题

本文给出了列队竞争算法解组合优化问题的框架和确定变异领域的两条原则 .对管路网络综合问题和换热网络综合问题确定了相应的变异领域 ,用列队竞争算法分别解这两个网络综合问题 ,所得到的最优解优于文献报道的结果 .     

Steady-state optimization of chemical processes with guaranteed robust stability and controllability under parametric uncertainty and disturbances

A new methodology is proposed for the steady-state optimal design of chemical processes under parametric uncertainty and disturbances. The methodology allows the integration of uniform constraints for robust controllability and stability in an optimization problem by using the Routh–Hurwitz test and zero dynamics based method. The underlying mathematical problem is difficult to solve because it involves infinite stability and controllability constraints. We developed an algorithm where an infinite number of constraints can be implemented as several relaxation problems that are solved iteratively. Additionally, the dynamic simulation results under parametric uncertainty and disturbances are also used to estimate the bound of the state perturbations rather than assumptions based on experience, which may lead to overly conservative or non-implementable design. To illustrate the methodology, three different examples are presented and robustly stable and controllable designs are obtained.