Optimization of an operating domestic wastewater treatment plant using elitist non-dominated sorting genetic algorithm

Multi-objective optimization of an operating domestic wastewater treatment plant is carried out using binary coded elitist non-dominated sorting genetic algorithm. Activated sludge model with extended aeration is used for optimization. For optimal plant operation, two different optimization problems are formulated and solved. The first optimization problem involves single-objective function to estimate kinetic parameters in activated sludge model using available plant data by minimizing the weighted sum-of-square errors between computed and plant values. The second optimization problem involves single-, two- and three-objective functions for efficient plant monitoring. In second category problem, objective functions are based on plant performance criteria (i.e., maximizing the influent flow rate of wastewater and minimizing the exit effluent concentration) and economic criteria (i.e., minimizing the plant operating cost). The important decision variables are: mean cell-residence time, mixed liquor suspended solid concentration in the reactor and underflow sludge concentration. Unique solution is obtained for the single-objective function optimization problem whereas a set of non-dominated solutions are obtained for the multi-objective optimization problems. A set of optimal operating conditions are proposed based on the present optimization study, which enhances the plant performance without affecting the discharge effluent quality. Finally, sensitivity analyses of the model results to the kinetic parameters and the kinetic parameters to the GA parameters are carried out to know the sensitivity of the obtained results with changes in the input parameter space.     

一种新的DNA遗传算法及其在参数估计中的应用

化工过程的参数估计是十分棘手的问题,为此常将这类问题转化为非线性优化问题来解决。遗传算法是一种适应性强的全局搜索方法,常被用于解决非线性系统的参数估计问题。但其局部搜索能力较差,易早熟。针对遗传算法的缺点,提出了一种新的DNA遗传算法。该方法使用碱基对个体进行四进制编码,受DNA分子操作启发设计了新的交叉和变异算子。两个经典测试函数的计算结果表明,该算法的搜索能力相对于其他两种算法有了明显提高。使用该算法来估计重油热解三集总模型中的参数,结果表明所建模型拟合精度高。     

基于遗传算法和粒子群优化算法的电力系统无功优化

从数学的角度分析,电力系统无功优化是一个多变量、多约束、非连续性的混合非线性规划问题,因此,优化过程十分复杂.以减少有功网损为目标函数建立电力系统无功优化计算的数学模型,基于遗传算法和粒子群优化算法,提出一种新颖的混合策略来求解无功优化问题.IEEE 6和IEEE 14节点系统的仿真计算结果表明:与单一的遗传算法或粒子群优化算法相比,该混合策略在优化效果方面具有明显的优势.     

Optimization of a large scale industrial reactor by genetic algorithms

The present work aims to employ genetic algorithms (GAs) to optimize an industrial chemical process, characterized by being difficult to be optimized by conventional methods. The considered chemical process is the three phase catalytic slurry reactor in which the reaction of the hydrogenation of o-cresol producing 2-methyl-cyclohexanol occurs. In order to describe the dynamic behavior of the multivariable process, a non-linear mathematical model is used. Due to the high dimensionality and non-linearity of the model, a rigorous one, the solution of the optimization problem through conventional algorithms does not always lead to convergence. This fact justifies the use of an evolutionary method, based on the GAs, to deal with this process. In this way, in order to optimize the process, the GA code is coupled with the rigorous model of the reactor. The aim of the optimization through GAs is the searching of the process inputs that maximizes the productivity of 2-methyl-cyclohexanol subject to the environmental constraint of conversion. Many simulations are conducted in order to find the maximization of the objective function without violating the constraint. The results show that the GAs are used successfully in the process optimization. The selection of the most important GA parameters making use of a factorial design approach by fractional factorial design is proposed. A factorial design approach by a central composite design is also proposed in order to determine the best values of the GA parameters that lead to the optimal solution of the optimization problem.     

Off-line optimization and control for real time integration of a three-phase hydrogenation catalytic reactor

In order to develop and test the integration procedure, in this paper a real time process integration involving the optimization and control of the process is presented, in this case, with the two-layer approach. The used optimization algorithms were Levenberg–Marquardt and SQP that solve a non-linear least square problem subject to bounds on the variables. The two-layer approach is a hierarchical control structure where an optimization layer calculates the set points and manipulated variables to the advanced controller, which is based on the dynamic matrix control with constraints (QDMC). The non-isothermal dynamic model of the three-phase slurry catalytic reactor with appropriate solution procedure was utilized in this work (Vasco de Toledo, E. C., Santana, P. L., Maciel, M. R. W., & Maciel Filho, R. (2001). Dynamic modeling of a three-phase catalytic slurry reactor. Chemical Engineering Science, 56, 6055–6061). The model consists on mass and heat balance equations for the catalyst particles as well as for the bulk phases of gas and liquid. The model was used to describe the dynamic behavior of hydrogenation reaction of o-cresol to obtain 2-methil-cyclohexanol, in the presence of a catalyst Ni/SiO₂.     

应用遗传算法求解多相化学反应体系的相稳定性及平衡组成

基于吉布斯自由能最小法原理,研究用遗传算法求解复杂化学体系的平衡问题。将相数和相态未知体系的平衡计算问题分解为两步最优化问题:假定相态数目下的吉布斯自由能最小化问题和相稳定性判据问题。通过序贯加入新相和用遗传算法交替求解两个最优化子问题,可得到最终体系的相数、相态和平衡组成。对合成甲醇和酯化反应两个多相复杂体系进行了的计算,结果验证了本研究方法的有效性。     

Optimization of short-time gasoline blending scheduling problem with a DNA based hybrid genetic algorithm

Gasoline blending is a key process in the petroleum refinery industry posed as a nonlinear optimization problem with heavily nonlinear constraints. This paper presents a DNA based hybrid genetic algorithm (DNA-HGA) to optimize such nonlinear optimization problems. In the proposed algorithm, potential solutions are represented with nucleotide bases. Based on the complementary properties of nucleotide bases, operators inspired by DNA are applied to improve the global searching ability of GA for efficiently locating the feasible domains. After the feasible region is obtained, the sequential quadratic programming (SQP) is implemented to improve the solution. The hybrid approach is tested on a set of constrained nonlinear optimization problems taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm. The recipes of a short-time gasoline blending problem are optimized by the hybrid algorithm, and the comparison results show that the profit of the products is largely improved while achieving more satisfactory quality indicators in both certainty and uncertainty environment.     

并行多家族遗传算法解多目标优化问题

提出了一种并行多家族遗传算法,采用主从节点分布式的计算策略,并应用分解协调的思想,对Pareto前沿进行分段,将计算任务分配到局域网上的多台计算机上完成,以减少计算时间。将所提出的方法用于两个化工实际问题的求解,得到的Pareto前沿的分布均匀性和全面性均优于单个遗传算法算得的结果。解决了遗传算法与流程模拟器结合解化工过程多目标优化问题时计算耗时太长的难题。     

Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm

Many optimal control problems are characterized by their multiple performance measures that are often noncommensurable and competing with each other. The presence of multiple objectives in a problem usually give rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Evolutionary algorithms have been recognized to be well suited for multi-objective optimization because of their capability to evolve a set of nondominated solutions distributed along the Pareto front. This has led to the development of many evolutionary multi-objective optimization algorithms among which Nondominated Sorting Genetic Algorithm (NSGA and its enhanced version NSGA-II) has been found effective in solving a wide variety of problems. Recently, we reported a genetic algorithm based technique for solving dynamic single-objective optimization problems, with single as well as multiple control variables, that appear in fed-batch bioreactor applications. The purpose of this study is to extend this methodology for solution of multi-objective optimal control problems under the framework of NSGA-II. The applicability of the technique is illustrated by solving two optimal control problems, taken from literature, which have usually been solved by several methods as single-objective dynamic optimization problems.     

迭代遗传算法及其用于生物反应器补料优化

针对化工动态优化的数值求解问题,提出将迭代思想与遗传操作相结合,构建迭代遗传算法.算法首先对时间区间和控制搜索域实施离散化,进而应用遗传操作搜索离散问题的最优控制策略.逐步收缩搜索域并迭代以消减离散化带来的偏差,不断改善寻优结果,增强算法的稳健性.实例测试表明该算法简便、可行、高效,已成功地应用于Lee-Ramirez生物反应器补料流率的优化,运算结果优于文献值,显示了迭代遗传算法的优越性.迭代遗传算法尤其适用于系统的梯度信息不可得的情况.     

基于群体智能算法的换热网络同步最优综合

换热网络同步综合方法一般需要建立复杂的混合整数非线性数学规划模型,该模型具有非凸、非线、不连续的特点,属于最难求解的一类NP-hard问题,应用传统的优化算法很难确定其全局最优解,尤其是对大规模换热网络综合问题,甚至无法在合理时间内接近全局最优的局部最优解。针对换热网络同步综合问题,提出基于群体智能算法的分层优化策略,外层采用离散粒子群算法与遗传算法相结合的混合群体智能算法优化换热网络结构,内层在结构变量给定条件下利用改进粒子群算法优化冷热物流分流比与换热负荷。两个典型算例研究证明了该方法能以较高的效率和稳定性得到较好的优化结果。     

A hybrid approach to global optimization using a clustering algorithm in a genetic search framework

The concern of this work is global optimization using genetic algorithms (GAs). In this work we propose a synergy between the cluster analysis technique, popular in classical stochastic global optimization, and the GA to accomplish global optimization. This synergy minimizes redundant searches around local optima and enhances the capability of the GA to explore new areas in the search space. The proposed methodology demonstrates superior performance when compared with the simple GA on benchmark cases. We also report our solution of the optimal pumps configuration synthesis problem.     

Multi-objective optimization of fuel oil blending using the jumping gene adaptation of genetic algorithm

Production and marketing of heavy fuel oil (HFO) are an easy, effective and economical way to dispose off certain very heavy refinery streams such as short residue (SR, available from the bottom of vacuum distillation units) and clarified liquid oil (CLO, available from the bottom of the main fractionators of fluidized-bed catalytic crackers). Certain lighter streams such as heavy cycle oil (HCO), light cycle oil (LCO) and kerosene, are added to the heavy residual stock to improve its quality in terms of fluidity, combustibility, etc., to be marketed as fuel oil. The present study aims at optimization of the fuel oil blending process to maximize profit, minimize quality give-away, maximize production, minimize use of lighter products such as LCO and kerosene, and maximize the calorific value, etc. Several multi-objective optimization problems have been formulated comprising of two and three-objective functions and solved using the elitist non-dominated sorting genetic algorithm (NSGA-II). This evolutionary technique produces a set of non-dominating (equally good) Pareto optimal solutions from which the operator can choose the one that is most suitable (preferred point). Also, a fixed-length macro–macro mutation operator, inspired by jumping genes in natural genetics, has been used with NSGA-II to solve this problem. This modified algorithm leads to a significant reduction in the computational effort. Indeed, this adaptation can be of immense use in reducing the computational effort for other problems in chemical engineering.     

一种基于偏好的多目标遗传算法在动态模型参数辨识中的应用

针对多目标优化问题,提出了PNSGA算法(preference-based non-dominated sorting genetic algorithm),是一种NSGA Ⅱ的改进算法,结合Pareto支配和偏好信息定义了新的优于关系;把偏好信息加入快速非支配排序中,引导搜索方向,更方便决策者选择;并进一步分析了加入偏好对拥挤度机制的影响.实验证明该算法能较好地解决动态模型参数辨识的问题,有利于决策者做出决策.     

A novel 3-layer mixed cultural evolutionary optimization framework for optimal operation of syngas production in a Texaco coal-water slurry gasifier☆

Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP (Error Back Propagation) neural networks. To solve this model, a new 3-layer cultural evolving algorithm framework which has a population space, a medium space and a belief space is firstly conceived. Standard differential evolution algorithm (DE), genetic algorithm (GA), and parti-cle swarm optimization algorithm (PSO) are embedded in this framework to build 3-layer mixed cultural DE/GA/PSO (3LM-CDE, 3LM-CGA, and 3LM-CPSO) algorithms. The accuracy and efficiency of the proposed hybrid algo-rithms are firstly tested in 20 benchmark nonlinear constrained functions. Then, the operational optimization model for syngas production in a Texaco coal-water slurry gasifier of a real-world chemical plant is solved effective-ly. The simulation results are encouraging that the 3-layer cultural algorithm evolving framework suggests ways in which the performance of DE, GA, PSO and other population-based evolutionary algorithms (EAs) can be improved, and the optimal operational parameters based on 3LM-CDE algorithm of the syngas production in the Texaco coal-water slurry gasifier shows outstanding computing results than actual industry use and other algorithms.     

Mathematical modeling and optimization of gas transport through carbon molecular sieve membrane and determining the model parameters using genetic algorithm

Permeation of N₂, CH₄, O₂ and CO₂ molecules through a carbon molecular sieve (CMS) was studied over a wide range of pressures using the transport mechanism. For proper utilization of carbon molecular sieve membrane in gas separation processes, prediction of behavior and recognition of proper gas transport mechanism as well as finding effective permeation parameters are necessary. A mathematical model of the gas transfer through a CMS membrane was developed using genetic algorithm (GA). Numerous types of mechanisms have been proposed so far for gas transport through capillaries, namely: Knudsen, slip and viscous flow. Moreover, surface flow usually occurs in parallel with other transport mechanisms such as Knudsen or viscous flow. The experimental data of gas permeation in CMS membranes and an appropriate genetic algorithm-based optimization method were used to establish the transport parameters. A GA, an optimization procedure based on the theory of evolution, was compared with non-linear regression for the ability of these two algorithms to fit the coefficients of Poultry growth models. It was found that GA approach could be more capable to define the parameters of permeation equation than non-linear regression. The model in most cases showed a good agreement between the predicted and measured values of the permeability.     

Using fuzzy logic to tune an evolutionary algorithm for dynamic optimization of chemical processes

Dynamic optimization of chemical processes can be carried out with evolutionary algorithms that involve many parameters. These parameters need to be given appropriate values for the algorithms to perform efficiently. This paper proposes parameter setting methods based on factorial experimentation and fuzzy logic, aimed at balancing convergence speed, robustness (consistent performance for each problem) and versatility (applicability to many different problems). The methods were tested on an existing dynamic optimisation method with at least nine tuneable parameters. The test problem set turned out to be quite demanding due to one particular problem behaving in opposite direction to the rest with respect to the most influential factor, population size. It is probable that no single tuning would be possible that will satisfy all problems. However, for the other problems, the Fuzzy Logic tuning method proposed in this paper proves to be a very promising approach.     

基于知识改进的文化算法及其在化工动态优化中的应用

针对化工以及生化过程的动态优化问题,提出了一种基于改进知识引导的文化算法。该算法首先对控制搜索域与时间域分别进行了等分和离散化,利用"软约束"思想编码控制序列,采用"种群产生"-"控制域进化"-"种群寻优"迭代过程实现对控制序列的逐步寻优;其次在种群空间采用遗传算法,在信度空间采用差分算法,并将进化过程中的已有种群信息设计为3种知识,通过分析知识、提取知识、管理知识来指导进化过程。由于引入了文化进化理念和机制,大大提高了动态优化问题的搜索效率。通过3种典型化工动态优化问题的仿真实例,表明该算法具有较好的寻优效率以及更好的优化结果,验证了该算法在解决具有非线性动态约束问题的有效性。     

Novel genetic algorithm for short-term scheduling of sequence dependent changeovers in multiproduct polymer plants

Polymer plants generally operate to produce different grades of product from the same reactor. Such systems commonly require short-term scheduling to meet market demand. One important requirement in continuous-time scheduling of such systems is to satisfy a variety of constraints, including identifying feasible sequences of the predecessor and successor jobs to effectively handle changeovers. In this study, a new genetic algorithm (GA) is proposed to solve such job sequencing problems. The proposed GA uses real-coded chromosome to represent job orders and their sequences in the schedule. The novelty is that the representation ensures that all constraints are satisfied a priori, except the sequence constraint which is handled by penalizing violations. Three important problems relevant to polymer industry are solved to obtain optimal schedules. The first deals with the sequencing constraint between individual product orders, the second with sequencing constraint between groups of product orders, while the third incorporates batching with scheduling.