Robust Optimal Operation of Two‐Chamber Microbial Fuel Cell System Under Uncertainty: A Stochastic Simulation Based Multi‐Objective Genetic Algorithm Approach

This investigation is performed to study the optimal operation decision of two‐chamber microbial fuel cell (MFC) system under uncertainty. To gain insight into the mechanism of uncertainty propagation, a Quasi‐Monte Carlo method‐based stochastic analysis is conducted not only to elucidate the effect of each uncertain parameter on the variability of power density output, but also to illustrate the interactive effects of the all uncertain parameters on the performance of MFC. Moreover, a systematic stochastic simulation‐based multi‐objective genetic algorithm framework is proposed to identify a set of Pareto‐optimal robust operation strategies, which is helpful to provide an imperative insight into the relationship between the mean and standard deviation of output power density. The results indicate that (1) the coefficient of variance (COV) value of output power density has a linear relationship with the COV value of each uncertainty parameter as well as all interactive parameters; and (2) a significant performance improvement with respect to both mean and standard deviation of power density is observed by implementing the multi‐objective robust optimization. These results thus validate that the proposed uncertainty analysis and robust optimization framework provide a promising tool for robust optimal design and operation of fuel cell systems under uncertainty.     

Stochastic pooling problem for natural gas production network design and operation under uncertainty

Product quality and uncertainty are two important issues in the design and operation of natural gas production networks. This paper presents a stochastic pooling problem optimization formulation to address these two issues, where the qualities of the flows in the system are described with a pooling model and the uncertainty in the system is handled with a multi‐scenario, two‐stage stochastic recourse approach. In addition, multi‐objective problems are handled via a hierarchical optimization approach. The advantages of the proposed formulation are demonstrated with case studies involving an example system based on Haverly's pooling problem and a real industrial system. The stochastic pooling problem is a potentially large‐scale nonconvex Mixed‐Integer Nonlinear Program (MINLP), and a rigorous decomposition method developed recently is used to solve this problem. A computational study demonstrates the advantage of the decomposition method over a state‐of‐the‐art branch‐and‐reduce global optimizer, BARON. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Process Analysis and Multi‐Objective Optimization of Ionic Liquid‐Containing Acetonitrile Process to Produce 1,3‐Butadiene

Using ionic liquid (IL) [C₂MIM][PF₆] as an additive could remarkably improve the performance of the acetonitrile (CAN) process, which is the most widely used distillation process to produce 1,3‐butadiene (1,3‐BT). In this work, a rigorous simulation of a new IL process to produce 1,3‐BT was carried out to evaluate the performance of IL additive on an industrial scale, using UNIFAC as the global thermodynamic model. Based on the simulation models, some key operation parameters, such as solvent ratio and reflux ratio, were determined by sensitivity analysis. Furthermore, a multi‐objective optimization was proposed and performed considering both the energy consumption and environmental impact (green degree) of the new process. A nonlinear mathematical model was established to express this multi‐objective optimization problem, which includes six decision variables and involves maximizing the green degree of the process, the purity and the recovery of 1,3‐BT, and minimizing the energy consumption of the process. The optimization results showed that the energy consumption of the IL‐containing process could be reduced by 22 % and that its green degree could be improved by 9.2 %.     

Fuzzy Optimization of Extractive Fermentation Processes Including Cell Recycle for Lactic Acid Production

In this study, a bioprocess optimization problem was considered for a multiple‐stage extractive fermentation, including cell recycling, to produce lactic acid. The aim of the optimization problem is to obtain the maximum overall productivity, conversion and yield simultaneously, so that the optimization problem is formulated as a multi‐objective optimization procedure. The fuzzy goal attainment method was introduced to the multi‐objective optimization problem in order to obtain a trade‐off solution. The approach was also employed to determine the optimal design for two simplified continuous fermentation processes. From the computational results, the overall productivity for the fermentation processes including cell recycling, enabled a higher dilution rate so that the overall productivity was ca. thirteen‐fold higher than that of the continuous fermentation process without cell recycling.     

Multi‐stage adjustable robust optimization for process scheduling under uncertainty

Variations in parameters such as processing times, yields, and availability of materials and utilities can have a detrimental effect in the optimality and/or feasibility of an otherwise “optimal” production schedule. In this article, we propose a multi‐stage adjustable robust optimization approach to alleviate the risk from such operational uncertainties during scheduling decisions. We derive a novel robust counterpart of a deterministic scheduling model, and we show how to obey the observability and non‐anticipativity restrictions that are necessary for the resulting solution policy to be implementable in practice. We also develop decision‐dependent uncertainty sets to model the endogenous uncertainty that is inherently present in process scheduling applications. A computational study reveals that, given a chosen level of robustness, adjusting decisions to past parameter realizations leads to significant improvements, both in terms of worst‐case objective as well as objective in expectation, compared to the traditional robust scheduling approaches. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1646–1667, 2016     

Theoretical and computational comparison of continuous‐time process scheduling models for adjustable robust optimization

Coping with uncertainty in system parameters is a prominent hurdle when scheduling multi‐purpose batch plants. In this context, our previously introduced multi‐stage adjustable robust optimization (ARO) framework has been shown to obtain more profitable solutions, while maintaining the same level of immunity against risk, as compared to traditional robust optimization approaches. This paper investigates the amenability of existing deterministic continuous‐time scheduling models to serve as the basis of this ARO framework. A comprehensive computational study is conducted that compares the numerical tractability of various models across a suite of literature benchmark instances and a wide range of uncertainty sets. This study also provides, for the first time in the open literature, robust optimal solutions to process scheduling instances that involve uncertainty in production yields. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3055–3070, 2018     

Integration of Design and Control: A Robust Control Approach Using MPC

This paper presents a new method to integrate process control with process design. The process design is based on steady‐state costs, .i.e., capital and operating costs. Control is incorporated into the design in terms of a variability cost. This term is calculated based on the non‐linear process model, represented here as a nominal linear model supplemented with model parameter uncertainty. Robust control tools are then used within the approach to assess closed‐loop robust stability and to calculate closed‐loop variability. The integrated method results in a non‐linear constrained optimization problem with an objective function that consists of the sum of the steady costs and the variability cost. Optimization using the traditional sequential approach and the new integrated method was applied to design a multi‐component distillation column using a Model Predictive Control (MPC) algorithm. The optimization results show that the integrated method can lead to significant cost savings when compared to the traditional sequential approach. In addition, an RGA analysis was performed to study the effects of process interactions on the optimization results.     

Multi‐Objective Optimization of Interior Ballistic Performance Using NSGA‐II

This paper investigates an interior ballistic design with equal and unequal web thicknesses of seven‐perforation propellant grains using optimization methods. In order to reveal the influence of the web thickness of the propellant grains on the overall interior ballistic performance, burning seven‐perforation propellant grains with both equal and unequal web thickness is modeled. A currently popular evolution algorithm (EA) is used to compare two charge shapes, and to seek which one could achieve the optimal ballistic performance. Complete optimization of the interior ballistic performance is a complex process in view of the conflicting objectives to be achieved and a solution to such problems is sought by converting them into a single composite objective and using many tedious measurements. In this paper, a true multi‐objective optimization of the interior ballistic charging design is carried out by considering three objectives simultaneously. The non‐dominated sorting genetic algorithm version II (NSGA‐II) is used to solve this multi‐objective optimization problem (MOP). In order to check its implementation, both the conventional optimization algorithm‐hill climbing method (HCM) and NSGA‐II are used to solve the same single objective problem. The NSGA‐II used to capture the full Pareto‐optimal front is capable of identifying the trade‐off among the conflicting objectives thereby providing alternative useful designs for a designer. Furthermore, for seven‐perforation propellant grains, the results of using equal web thickness are compared with those of unequal web thickness, and it is shown that the two charge shapes produce no distinct difference in the interior ballistic performance.     

Impact of Fuel Cell Power Plants on Multi‐objective Optimal Operation Management of Distribution Network

This paper presents an interactive fuzzy satisfying method based on hybrid modified honey bee mating optimization and differential evolution (MHBMO‐DE) to solve the multi‐objective optimal operation management (MOOM) problem, which can be affected by fuel cell power plants (FCPPs). The objective functions are to minimize total electrical energy losses, total electrical energy cost, total pollutant emission produced by sources, and deviation of bus voltages. A new interactive fuzzy satisfying method is presented to solve the multi‐objective problem by assuming that the decision‐maker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions. Then, by considering the current solution, the DM acts on this solution by updating the reference membership values until the satisfying solution for the DM can be obtained. The MOOM problem is modeled as a mixed integer nonlinear programming problem. Evolutionary methods are used to solve this problem because of their independence from type of the objective function and constraints. Recently researchers have presented a new evolutionary method called honey bee mating optimization (HBMO) algorithm. Original HBMO often converges to local optima, in order to overcome this shortcoming, we propose a new method that improves the mating process and also, combines the modified HBMO with DE algorithm. Numerical results for a distribution test system have been presented to illustrate the performance and applicability of the proposed method.     

Risk management for a global supply chain planning under uncertainty: Models and algorithms

In this article, we consider the risk management for mid‐term planning of a global multi‐product chemical supply chain under demand and freight rate uncertainty. A two‐stage stochastic linear programming approach is proposed within a multi‐period planning model that takes into account the production and inventory levels, transportation modes, times of shipments, and customer service levels. To investigate the potential improvement by using stochastic programming, we describe a simulation framework that relies on a rolling horizon approach. The studies suggest that at least 5% savings in the total real cost can be achieved compared with the deterministic case. In addition, an algorithm based on the multi‐cut L‐shaped method is proposed to effectively solve the resulting large scale industrial size problems. We also introduce risk management models by incorporating risk measures into the stochastic programming model, and multi‐objective optimization schemes are implemented to establish the tradeoffs between cost and risk. To demonstrate the effectiveness of the proposed stochastic models and decomposition algorithms, a case study of a realistic global chemical supply chain problem is presented. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Optimization strategy of the multihole products weld lines based on the multi‐objective evaluation system and kriging surrogate model

The plastic multihole products are widely used in Household Appliance and Automobile industry. The densely distributed weld lines resulting from the multiaperture structure seriously damage the surface appearance and mechanical properties of the products. However, there are relatively few studies on the optimization of weld lines of the plastic multihole products. Therefore, a multihole plate was taken as an example to exploit an optimization strategy for this kind of defects. The multi‐objective evaluation system was established to assess bonding quality of weld lines based on Numerical Simulation. And a multi‐objective optimization methodology was presented to efficiently optimize the process parameters. First, back propagation neural networks and Kriging method were combined to build the surrogate models based on the experiments arranged by Latin hypercube sampling. Second, a systematic test strategy was proposed to ensure high accuracy of the surrogate model. Then, the pareto optimal solution was obtained by integrating the surrogate model and Non‐dominated Sorting Genetic Algorithm II. Finally, the simulated and practical confirmation experiments indicate that bonding quality of weld lines can be effectively characterized and significantly improved by the multi‐objective evaluation system and the multi‐objective optimization methodology, respectively. POLYM. ENG. SCI., 59:781–790, 2019. © 2018 Society of Plastics Engineers     

Multi‐Objective Optimization of Pseudo‐Dynamic Operation of Naphtha Pyrolysis by a Surrogate Model

A simple pseudo‐dynamic surrogate model is developed in the framework of the state space model with the feed‐forward neural network to replace the complex free radical pyrolysis model. The surrogate model is then applied to investigate the multi‐objective optimization of two key performance objectives with distinct contradiction: the mean yields of key products and the day mean profits. The ?‐constraint method is employed to solve the multi‐objective optimization problem, which provides a broad range of operation conditions depicting tradeoffs of both key objectives. The Pareto‐optimal frontier is successfully obtained and five selected cases on the frontier are discussed, suggesting that flexible operations can be performed based on industrial demands.     

A Comparative Study of Fuzzy Techniques to Handle Uncertainty: An Industrial Grinding Process

Fuzzy‐based approaches like fuzzy chance constrained programming (FCCP) and fuzzy expected value model (FEVM) have been applied to a multi‐objective optimization problem of the industrial grinding process to carry out the uncertainty analysis. Results are compared with respect to the power of risk averseness adopted in the approaches used. The extent of constraint satisfaction due to the presence of uncertain parameters can be accommodated assuming credibility of constraint satisfaction under the FCCP framework whereas the robust set of parameters in the FEVM approach is determined by considering the expectation terms for objectives and constraints. Nonlinear relation of uncertain parameters has been handled by adopting simulation‐based approaches while computing the credibility. These approaches are very generic and can be applied for the study of parametric sensitivity for any process model in a novel manner.     

Optimization‐Based Nonlinear Centralized Controller Tuning of Liquid‐Liquid Extraction Processes

Abstract

The control problem of an agitated contactor is considered in this work. A Scheibel extraction column is modeled using the non‐equilibrium backflow mixing cell model. Model dynamic analysis shows that this process is highly nonlinear, thus the control problem solution of such a system needs to tackle the process nonlinearity efficiently. The control problem of this process is solved by developing a multivariable nonlinear control system implemented in MATLAB?. In this control methodology, a new controller tuning method is adopted, in which the time‐domain control parameter‐tuning problem is solved as a constrained optimization problem. A MIMO (multi‐input multi‐output) PI controller structure is used in this strategy. The centralized controller uses a 2×2 transfer function and accounts for loops interaction. The controller parameters are tuned using an optimization‐based algorithm with constraints imposed on the process variables reference trajectories. Incremental tuning procedure is performed until the extractor output variables transient response satisfies a preset uncertainty which bounds around the reference trajectory. A decentralized model‐based IMC (internal model control) control strategy is compared with the newly developed centralized MIMO PI control one. Stability and robustness tests are applied to the two algorithms. The performance of the MIMO PI controller is found to be superior to that of the conventional IMC controller in terms of stability, robustness, loops interaction handling, and step‐change tracking characteristics.     

Probabilistic Multiobjective Operation Management of MicroGrids With Hydrogen Storage and Polymer Exchange Fuel Cell Power Plants

This paper models and solves the operation management problem of MicroGrids (MGs) including cost and emissions minimization under uncertain environment. The proposed model emphasizes on fuel cells (FCs) as a prime mover of combined heat and power (CHP) systems. An electro‐chemical model of the proton exchange membrane fuel cell (PEMFC) is used and linked to the daily operating cost and emissions of the MGs. A reformer is considered to produce hydrogen for PEMFCs. Moreover, in high thermal load intervals, in order to make the MG more efficient, a part of produced hydrogen is stored in a hydrogen tank. The stored hydrogen can be reused by PEMFCs to generate electricity or be sold to other hydrogen consumers. A probabilistic optimization algorithm is devised which consists of 2m + 1 point estimate method to handle the uncertainty in input random variables (IRVs) and a multi‐objective Self‐adaptive Bee Swarm Optimization (SBSO) algorithm to minimize the cost and emissions simultaneously. Several techniques are proposed in the SBSO algorithm to make it a powerful black‐box optimization tool. The efficiency of the proposed approach is verified on a typical grid‐connected MG with several distributed energy sources.     

Dividing Wall Distillation Columns: Optimization and Control Properties

The optimal design of dividing wall columns is a non‐linear and multivariable problem, and the objective function used as optimization criterion is generally non‐convex with several local optimums. Considering this fact, in this paper, we studied the design of dividing wall columns using as a design tool, a multi‐objective genetic algorithm with restrictions, written in Matlab^TM and using the process simulator Aspen Plus^TM for the evaluation of the objective function. Numerical performance of this method has been tested in the design of columns with one or two dividing walls and with several mixtures to test the effect of the relative volatilities of the feed mixtures on energy consumption, second law efficiency, total annual cost, and theoretical control properties. In general, the numerical performance shows that this method appears to be robust and suitable for the design of sequences with dividing walls.     

Design under uncertainty using parallel multiperiod dynamic optimization

A technique for optimizing dynamic systems under uncertainty using a parallel programming implementation is developed in this article. A multiple‐shooting discretization scheme is applied, whereby each shooting interval is solved using an error‐controlled differential equation solver. In addition, the uncertain parameter space is discretized, resulting in a multiperiod optimization formulation. Each shooting interval and period (scenario) realization is completely independent, thus a major focus of this article is on demonstrating potential computational performance improvement when the embedded dynamic model solution of the multiperiod algorithm is implemented in parallel. We assess our parallel multiperiod and multiple‐shooting‐based dynamic optimization algorithm on two case studies involving integrated plant and control system design, where the objective is to simultaneously determine the size of the process equipment and the control system tuning parameters that minimize cost, subject to uncertainty in the disturbance inputs. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3151–3168, 2014     

An optimization framework to combine operable space maximization with design of experiments

The introduction of Quality by Design in the pharmaceutical industry stimulates practitioners to better understand the relationship of materials, processes and products. One way to achieve this is through the use of targeted experimentation. In this study, an optimization framework to design experiments that effectively leverage parameterized process models is presented to maximize the space covered in the output variables while also obtaining an orthogonal bracketing study in the process input factors. The framework considers both multi‐objective and bilevel optimization methods for relating the two maximization objectives. Results are presented for two case studies—a spray coating process and a continuously stirred reactor cascade—demonstrating the ability to generate and identify efficient designs with fit‐for‐purpose trade‐offs between bracketed orthogonality in the input factors and volume explored in the process output space. The proposed approach allows a more complete understanding of the process to emerge from a small set of experiments. © 2018 The Authors. AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers. AIChE J, 64: 3944–3957, 2018     

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.