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.     

基于免疫机制的多目标蚁群算法用于间歇反应器的约束动态多目标优化

含路径和终端约束的动态多目标优化是过程系统工程的一个重要研究方向,难度较高.传统蚁群算法仅适于离散问题,今采用混合正态分布描述信息素分布,并设计相应的解构造操作,使之拓宽至连续优化问题.通过对目标函数和约束矩阵的非劣捧序,确定解的等级,用以克服传统约束处理方法的局限性.借鉴了免疫系统的浓度概念,将其与解的等级结合,共同确定解的适应度,有助于保持种群的多样性.在更新信息素时将利用外部优解库和种群信息,可加快收敛速度.基于拥挤度距离更新外部优解库可更均匀地逼近Pareto最优解集.由此构建了一种基于免疫机制的多目标蚁群算法(Immune Mechanism based Multi-Objective Ant Colony Algorithm,IM-MOACA),并用于间歇反应器的动态多目标优化问题,效果良好,显示出较强的全局优化性能,能以较快的速度逼近真实的Pareto最优前沿,可为用户进行合理的决策分析提供有效的支持.     

Optimal operation of integrated processing systems: Part II: Closed-loop on-line optimizing control

A method for tracking the economically optimal operating conditions of a chemical process in the presence of constraints is developed. The technique is based on an on-line search rather than a fundamental model. The most profitable operating point is found by fitting a dynamic model of the process based on data obtained from experimental moves on the plant. This model is used to compute gradients of the economic objective and of the constraints so that a direction of economic improvement inside the allowed operating region of the plant is always obtained. Constraint violations during the transients are prevented by a multivariable regulator. A new regulation method (Internal Model Control) is used which permits explicit handling of constraints and which can be made robust against modelling errors. This combined optimization/regulation approach is tested in a demonstrative simulation example and shown to be reliable for following a moving optimum and safely handling complex constraint moves.     

Genetic algorithm development for multi-objective optimization of batch free-radical polymerization reactors

An improved genetic algorithm approach, based on a new ranking strategy, has been proposed to conduct multi-objective optimization of chemical engineering problems. New operators have been introduced to enhance the algorithm performance and reduce the computational effort. A Pareto-set filter operator has been implemented to avoid missing Pareto optimal points during the evolutionary process. A niche operator has been adopted to prevent genetic drift, and an elitism operator, to insure the propagation of the best result of each objective function. A fitness function based on each rank population size and rank level has been used to determine the reproduction ratio. Constraints are handled through a fuzzy penalty function method. The algorithm has been applied to a batch free-radical styrene polymerization process in order to maximize the monomer conversion rate and minimize the concentration of initiator residue in the product. The algorithm proved to be robust, handling satisfactorily multi-modal and multidimensional problems.     

模块环境下的filter-SQP用于过程优化

引言 20世纪70年代中期以来,经过许多学者的努力,SQP法成为求解非线性规划(NLP)问题最有效的方法之一.     

CO2捕集、运输、驱油与封存全流程随机优化

CO₂捕集、运输、驱油与封存（CCUS）是一种缓解温室气体排放的有效手段。在工程实际问题中,由于温度、压力、碳价、电价等随机变量的存在,给CCUS全流程建模与优化带来了很大的困难。为了解决此问题,本文建立了CCUS全流程的工程-经济模型,并以烟气入口流量、管道入口压力、管道直径、泵站数量、注入井入口压力等作为决策变量,质量约束、排放约束、运输约束、存储约束等为约束条件,以CCUS全流程成本为目标函数,提出了一种随机优化期望值模型。并采用基于随机模拟的遗传算法对期望值模型进行求解,通过参数的合理优化配置,提出的优化方法解决了CCUS全流程随机优化问题。研究结果表明,该优化方法能够有效地降低CCUS全流程的成本,为此技术的发展提供了一种参考方案。     

One-stage optimization problem with chance constraints

Generally, the design of chemical processes (CP) is performed with the use of inaccurate mathematical models. Therefore, it is essential to create chemical processes that can satisfy all the design specifications at the operation stage in spite of the changes in internal and external factors. Consequently, the problem of chemical process optimization under uncertainty is of prime importance in chemical engineering. The paper considers one-stage optimization problems with chance constraints. The main issue in solving one-stage optimization problems is calculation of multiple integrals (calculating the expected value of the objective function and probabilities of constraints satisfaction). Here we consider a new approach to solving a one-stage optimization problem which is based on transformation of chance constraints into deterministic ones. A computational experiment has shown the efficiency of this approach.     

Design stage optimization of an industrial low-density polyethylene tubular reactor for multiple objectives using NSGA-II and its jumping gene adaptations

Design stage optimization of an industrial low-density polyethylene (LDPE) tubular reactor is carried out for two simultaneous objectives: maximization of monomer conversion and minimization of normalized side products (methyl, vinyl, and vinylidene groups), both at the reactor end, with end-point constraint on number-average molecular weight (M_n,f) in the product. An inequality constraint is also imposed on reactor temperature to avoid run-away condition in the tubular reactor. The binary-coded elitist non-dominated sorting genetic algorithm (NSGA-II) and its jumping gene (JG) adaptations are used to solve the optimization problem. Both the equality and inequality constraints are handled by penalty functions. Only sub-optimal solutions are obtained when the equality end-point constraint on M_n,f is imposed. But, correct global optimal solutions can be assembled from among the Pareto-optimal sets of several problems involving a softer constraint on M_n,f. A systematic approach of constrained-dominance principle for handling constraints is applied for the first time in the binary-coded NSGA-II-aJG and NSGA-II-JG, and its performance is compared to the penalty function approach. A three-objective optimization problem with the compression power (associated with the compression cost) as the third objective along with the aforementioned two objectives, is also studied. The results of three-objective optimization are compared with two different combinations of two-objective problems.     

Evolutionary algorithms approach to the solution of mixed integer non-linear programming problems

The global optimization of mixed integer non-linear problems (MINLP), constitutes a major area of research in many engineering applications. In this work, a comparison is made between an algorithm based on Simulated Annealing (M-SIMPSA) and two Evolutionary Algorithms: Genetic Algorithms (GAs) and Evolution Strategies (ESs). Results concerning the handling of constraints, through penalty functions, with and without penalty parameter setting, are also reported. Evolutionary Algorithms seem a valid approach to the optimization of non-linear problems. Evolution Strategies emerge as the best algorithm in most of the problems studied.     

混沌搜索方法及其在化工过程优化中的应用

提出利用混沌搜索方法结合精确不可微罚函数求解约束优化问题的新方法 ,并将该方法用于闪蒸过程优化 .结果表明 ,该方法算法简单 ,实现容易 ,求解精度和可靠性较高 ,是解决化工优化问题的有效方法 .     

Parametric optimization with uncertainty on the left hand side of linear programs

Although parametric optimization with uncertainties on the objective function (OF) or on the so-called “right-hand-side” (RHS) of the constraints has been addressed successfully in recent papers, very little work exists on the same with uncertainties on the left-hand-side (LHS) of the constraints or in the coefficients of the constraint matrix. The goal of this work has been to develop a systematic method to solve such parametric optimization problems. This is a very complex problem and we have begun with the simplest of optimization problems, namely the linear programming problem with a single parameter on the LHS. This study reviews the available work on parametric optimization, describes the challenges and issues specific to LHS parametric linear programming (LHS-pLP), and presents a solution algorithm using some classic results from matrix algebra.     

注射模浇口数目和位置的优化设计

给出一种注塑模具浇口位置和数目的优化设计方法.为达到减少塑件翘曲变形和熔接线的目的,以平衡充填和浇口数目最少为优化目标,以最大注射压力为约束条件,将浇口位置坐标作为设计变量,并根据浇口位置在充填数值模拟中对浇口数目和注射流率进行处理,从而可以同时优化浇口数目及其位置,优化求解采用遗传算法.算例表明,提出的优化模型和算法是有效的.     

AN IMPROVED COMPUTATIONAL ALGORITHM FOR SINGULAR CONTROL PROBLEMS IN CHEMICAL REACTION ENGINEERING

A unidirectional method is developed to solve optimal singular control problems with bounded state variables. The computational algorithm utilizes the necessary conditions of optimality and an unidirectional scheme to reduce the iterations required in two-point boundary value problems. The advantage of the method is that it satisfies all the necessary conditions of optimality and results in a considerable reduction in computational effort. Three numerical examples illustrate the use of these algorithms for solving several chemical reaction engineering problems.     

Variational optimization in control and time domains

The study has established, with the help of two typical chemical engineering models, the superiority and versatility of the functional conjugate gradient method in computing optimal control policies for continuous systems. An algorithm named as Difference Method has been developed and tested for optimization in the secondary domain of time. A computationally sound and stable scheme is presented to compute simultaneously optimum duration of time and optimal control policy for a process.     

遗传算法与惩罚函数法在油田开发规划中的应用

遗传算法作为一种通用、高效的优化算法,已应用到工程计算的各个领域。本文提出了应用于油田开发规划中的“遗传算法 惩罚函数法”的通用方法。它非常适合于求解复杂的非线性规划问题。此算法既克服了传统优化算法的不足,得到较为理想的全局最优解,同时也改善了遗传算法的局限性。     

改进的膜计算仿生优化算法及在汽油调和中的应用

为提高膜计算仿生优化算法在求解流程工业复杂优化问题的计算性能,提出一种改进的膜计算仿生优化算法。该算法采用一个新的不确定性提取规则取代改进前的提取规则。4个有约束标准测试函数被用于检验该算法的计算性能,计算结果及对比显示了改进算法在鲁棒性和效率等方面优于改进前算法。改进算法应用于汽油调和优化问题,更高利润的配方及算法的计算效率证实了改进算法的优越性和实用性。     

大规模化工过程优化中的SQP-filter算法

逐次2次规划法(SQP)是目前求解非线性约束问题十分有效的方法,但一般都采用罚函数进行线性搜索,这使得它有了很大的限制性,Roger Fletcher和Sven Leyffer等提出了一种filter SQP优化方法,在充分研究这种方法的基础上,编制了计算程序,将其应用到化工过程优化中,多种计算实例表明,该算法优于传统的SQP法。     

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.     

QUADRATIC PROGRAMMING SOLUTION OF DYNAMIC MATRIX CONTROL (QDMC)

QDMC is an improved version of Shell's Dynamic Matrix Control (DMC) multivariable algorithm which provides a direct and efficient method for handling process constraints. The algorithm utilizes a quadratic program to compute moves on process manipulated variables which keep controlled variables close to their targets while preventing violations of process constraints. Several on-line applications have demonstrated its excellent constraint handling properties, transparent tuning and robustness, while requiring minimal on-line computational load.     

PGS-COM: A hybrid method for constrained non-smooth black-box optimization problems: Brief review,novel algorithm and comparative evaluation

In the areas of chemical processes and energy systems, the relevance of black-box optimization problems is growing because they arise not only in the optimization of processes with modular/sequential simulation codes but also when decomposing complex optimization problems into bilevel programs. The objective function is typically discontinuous, non-differentiable, not defined in some points, noisy, and subject to linear and nonlinear relaxable and unrelaxable constraints. In this work, after briefly reviewing the main available direct-search methods applicable to this class of problems, we propose a new hybrid algorithm, referred to as PGS-COM, which combines the positive features of Constrained Particle Swarm, Generating Set Search, and Complex. The remarkable performance and reliability of PGS-COM are assessed and compared with those of eleven main alternative methods on twenty five test problems as well as two challenging process engineering applications related to the optimization of a heat recovery steam cycle and a styrene production process.