基于输入输出线性化的连续系统非线性模型预测控制

非线性约束预测控制关键是求得可行性优化解. 输入输出反馈线性化是非线性控制一种常用的方法, 其系统的初始线性输入约束转化成非线性基于状态的约束, 因而无法采用常规的二次规划(QP)求解优化问题. 针对连续状态空间模型系统, 本文提出迭代二次规划方法来寻求非线性优化解. 为了保证算法的收敛性, 系统加入另外一种迭代算法来保证其在整个预测时域上能得到可行解. 仿真控制结果表明了该方法的有效性.     

求解约束优化问题的动态邻域粒子群算法*

粒子群算法(PSO)求解约束优化问题存在较严重的早熟收敛现象,为了有效抑制早熟收敛,提出了基于改进的约束自适应方法的动态邻域粒子群算法(IPSO)。算法采用动态邻域策略提高算法的全局搜索能力,设计了一种改进的自适应约束处理方法,根据迭代代数线性增加搜索偏向系数,在早期偏向于搜索可行解,在后期偏向于搜索最优解,并引入序列二次规划增强算法的局部搜索能力。通过基准测试函数实验对比分析,表明该算法对于约束优化问题具有较好的全局收敛性。     

求解一类凸优化问题的区间迭代算法

研究了一类非线性带约束的凸优化问题的求解.利用Kuhn-Tucker条件将凸优化问题等价地转化为多变元非线性方程组的求解问题.基于区间算术的包含原理及改进的Krawczyk区间迭代算法,提出一个求解凸优化问题的区间算法.对于目标函数和约束函数可微的凸优化,所提算法具有全局寻优的特性.在数值实验方面,与遗传算法、模式搜索法、模拟退火法及数学软件内置的求解器进行了比较,结果表明所提算法就此类凸优化问题能找到较多且误差较小的全局最优点.     

改进果蝇算法在净化除钴过程锌粉量优化设定中的应用

本文提出一种基于细菌迁徙的自适应果蝇算法(CAFOABM),用于求解净化除钴过程锌粉添加量优化设定问题.首先从净化除钴的反应机理出发,通过引入除钴率建立锌粉添加量与氧化还原电位值、出口钴离子浓度间带约束的非线性优化设定模型;为了避免果蝇算法在迭代寻优过程中出现停滞现象,CAFOABM引入多种群并行搜索策略和改进搜索算子对搜索状态的转移规则进行改进;并采用区分可行解与不可行解法进行约束处理,保留一定比例的不可行解个体,有效避免了有用解信息的丢失.实际生产数据验证结果表明,CAFOABM算法优化设定的锌粉添加量与人工操作的经验数据相比减少7.83%,出口钴离子浓度满足实际生产要求且趋于平稳.     

求解含非线性参数的QoS路由的启发式算法

具有非线性参数的QoS路由分为含有非线性约束条件的QoS路由和含有非线性优化目标的QoS路由两类，它们都是NP问题．提出了两种启发式算法求解这两类QOS路由优化问题问题．对第一类问题，求解去掉非线性约束条件后的优化问题．如果找到的解满足非线性约束条件，则该解是最优解；否则在优化问题中添加一个新的线性约束，将已得到的解去掉，反复下去就可得到最终解．对第二类问题，将非线性优化目标换为约束条件中的线性参数，求解此优化模型，如果有解，则记录此时对应的非线性目标值．而后增加一个新的线性约束，去掉刚才得到的解，比较两次得到的非线性目标值，保留最小值．如果得到的解不满足该线性参数的约束条件，则算法结束；否则继续迭代．证明了两种算法的收敛性，并且时间复杂性为近似多项式时间．计算实例表明了算法的有效性．     

择优学习多个体差分算法求解约束优化问题

提出一种择优学习的多个体差分算法用于求解约束优化问题,目的是用来提高差分算法的搜索能力。首先,将择优学习策略应用到混合变异算子中,使其快速搜索到可行解区域,然后使用克隆策略加大对最优解区域的搜索力度,增强局部搜索能力。通过对CEC2006经典Benchmark函数测试,实验结果表明本算法在求解效率和精度上都取得了较好的结果。     

基于种群个体可行性的约束优化进化算法

提出一种新的求解约束优化问题的进化算法.该算法在处理约束时不引入惩罚因子,使约束处理问题简单化.基于种群中个体的可行性,分别采用3种不同的交叉方式和混合变异机制用于指导算法快速搜索过程.为了求解位于边界附近的全局最优解,引入一种不可行解保存和替换机制,允许一定比例的最好不可行解进入下一代种群.标准测试问题的实验结果表明了该算法的可行性和有效性.     

非线性过程自优化控制的快速算法

针对非线性过程的自优化控制问题,提出了一种求取被控变量的快速算法.不同于线性过程的自优化控制,本文方法基于系统的非线性模型,并且最小化全局平均损失.为快速求解得到的非凸非线性规划问题,作者对其进行了简化.讨论了被控变量解空间的相关特性,阐述了引入的正交酉约束的合理性,并进一步提出了求解次优被控变量的解析法.对一个数值算例和蒸发过程的研究结果表明,提出的快速算法是便捷的、有效的.     

求解非线性约束问题的混合粒子群优化算法

将处理约束问题的乘子法与改进的粒子群算法相结合,提出了一种求解非线性约束问题的混合粒子群算法。此算法兼顾了粒子群优化算法和乘子法的优点,对迭代过程中出现的不可行粒子,利用乘子法处理后产生可行粒子,然后用改进的粒子群算法来搜索其最优解,这样不仅减小了粒子群算法在寻优过程中陷入局部极小的概率,而且提高了搜索精度。数值试验结果表明提出的新算法具有搜索精度更高、稳定性更强、鲁棒性更好等特点。     

求解多背包问题的人工鱼群算法

多背包问题是出现在现实世界中许多领域的一个NP-hard组合优化问题。提出一种基于人工鱼觅食,追尾、聚群等行为的求解多背包问题的优化算法。针对多约束导致大量非可行解的产生而使算法性能劣化的问题,采用基于启发式规则的调整算子,使人工鱼始终在可行解域中寻优。数值实验结果表明,提出的算法能够快速搜索到最优解。算法对其他有约束组合优化问题也具有应用价值。     

结合序列线性规划法的混合遗传算法

通过将遗传算法与改进的序列线性规划法相结合，形成混合遗传算法．当迭代点没有发生交叉和变异时，将目标函数和约束条件在迭代点处线性化，为使迭代点邻域仍然满足约束条件，加入软约束项，用线性规划方法进行寻优．该方法具有全局收敛性，不要求迭代点一定为可行点．仿真结果验证了此法的有效性和合理性．     

基于梯度投影法与随机优化算法的约束优化方法

针对带有线性等式和不等式约束的无确定函数形式的约束优化问题,提出一种利用梯度投影法与遗传算法、同时扰动随机逼近等随机算法相结合的优化方法。该方法利用遗传算法进行全局搜索,利用同时扰动随机逼近算法进行局部搜索,算法在每次进化时根据线性约束计算父个体处的梯度投影方向,以产生新个体,从而能够严格保证新个体满足全部约束条件。将上述约束优化算法应用于典型约束优化问题,其仿真结果表明了所提出算法的可行性和收敛性。     

Mathematical Model and Solution Method of Optimization Problem of Placement of Rectangles and Circles Taking into Account Special Constraints

A mathematical model of the problem is constructed. A feasible region and peculiarities of the problem are investigated. Extremum of a linear objective function is searched at extreme points. To solve the problem a solution method based on a combination of the branch-and-bound algorithm and the reduced gradient method is utilized. A search tree for sorting all the extreme points of the feasible region is constructed. A stepwise passage from one extreme point to another towards decreasing the objective function is given. Appropriate software has been developed. To illustrate results of calculations the examples are given.     

An interior point cutting plane heuristic for mixed integer programming

We explore the use of interior point methods in finding feasible solutions to mixed integer programming. As integer solutions are typically in the interior, we use the analytic center cutting plane method to search for integer feasible points within the interior of the feasible set. The algorithm searches along two line segments that connect the weighted analytic center and two extreme points of the linear programming relaxation. Candidate points are rounded and tested for feasibility. Cuts aimed to improve the objective function and restore feasibility are then added to displace the weighted analytic center until a feasible integer solution is found. The algorithm is composed of three phases. In the first, points along the two line segments are rounded gradually to find integer feasible solutions. Then in an attempt to improve the quality of the solutions, the cut related to the bound constraint is updated and a new weighted analytic center is found. Upon failing to find a feasible integer solution, a second phase is started where cuts related to the violated feasibility constraints are added. As a last resort, the algorithm solves a minimum distance problem in a third phase. The heuristic is tested on a set of problems from MIPLIB and CORAL. The algorithm finds good quality feasible solutions in the first two phases and never requires the third phase.     

A feasible direction algorithm for general nonlinear semidefinite programming

This paper deals with nonlinear smooth optimization problems with equality and inequality constraints, as well as semidefinite constraints on nonlinear symmetric matrix-valued functions. A new semidefinite programming algorithm that takes advantage of the structure of the matrix constraints is presented. This one is relevant in applications where the matrices have a favorable structure, as in the case when finite element models are employed. FDIPA_GSDP is then obtained by integration of this new method with the well known Feasible Direction Interior Point Algorithm for nonlinear smooth optimization, FDIPA. FDIPA_GSDP makes iterations in the primal and dual variables to solve the first order optimality conditions. Given an initial feasible point with respect to the inequality constraints, FDIPA_GSDP generates a feasible descent sequence, converging to a local solution of the problem. At each iteration a feasible descent direction is computed by merely solving two linear systems with the same matrix. A line search along this direction looks for a new feasible point with a lower objective. Global convergence to stationary points is proved. Some structural optimization test problems were solved very efficiently, without need of parameters tuning.     

Extension of a hybrid Genetic Algorithm for nonlinear programming problems with equality and inequality constraints

As an extension of the hybrid Genetic Algorithm-HGA proposed by Tang et al. (Comput. Math. Appl. 36 (1998) 11), this paper focuses on the critical techniques in the application of the GA to nonlinear programming (NLP) problems with equality and inequality constraints. Taking into account the equality constraints and embedding the information of infeasible points/chromosomes into the evaluation function, an extended fuzzy-based methodology and three new evaluation functions are proposed to formulate and evaluate the infeasible chromosomes. The extended version of concepts of dominated semi-feasible direction (DSFD), feasibility degree (FD₁) of semi-feasible direction, feasibility degree (FD₂) of infeasible points ‘belonging to’ feasible domain are introduced. Combining the new evaluation functions and weighted gradient direction search into the Genetic Algorithm, an extended hybrid Genetic Algorithm (EHGA) is developed to solve nonlinear programming (NLP) problems with equality and inequality constraints. Simulation shows that this new algorithm is efficient.Scope and purposeNon-linear Programming (NLP) problems with equality and inequality constraints is an important type of constrained optimization problems. Genetic Algorithm (GA) is one of the well known evolutionary computation techniques. In the application of GA to NLP problems, chromosomes randomly generated at the beginning and/or generated by genetic operators during the evolutionary process usually violate the constraints, resulting in infeasible chromosomes. Therefore, the handling of system constraints, particularly the nonlinear equation constraints, and the measurement and evaluation of infeasible chromosomes, are major concerns in GA. Penalty strategy in the construction of fitness function is commonly used to evaluate the infeasible chromosomes in some traditional AG methods. However, this approach essentially narrows down the search space by eliminating all infeasible chromosomes from the evolutionary process, and it may reduce the chances of finding better candidates for the global optimization. In particular, it absolutely ignores the information carried by the infeasible chromosomes itself. Therefore, formulating the infeasible chromosomes by embedding the relevant information into the evaluation function are important when applying GA to NLP.As an extension of the Hybrid Genetic Algorithm-HGA proposed by Tang et al. (1998), this paper focuses on the critical techniques in the application of GA to NLP problems with equality and inequality constraints. Taking into account the equality constraints and embedding the information of infeasible chromosomes into the evaluation function, an extended fuzzy-based methodology and three new evaluation functions are designed to formulate and evaluate the infeasible chromosomes. By introducing an extended version of the concepts of dominated semi-feasible direction (DSFD), feasibility degree (FD₁) of semi-feasible direction, feasibility degree (FD₂) of infeasible points ‘belonging to’ feasible domain, an extended hybrid Genetic Algorithm (EHGA) is developed for solving NLP problems with equality and inequality constraints.     

ASCIM—an accelerated constrained simplex technique

In many design studies similar optimization problems have to be solved. In these problems a non-linear objective,function, defined in terms of a small number of variables, has to be minimized subject to the additional requirement that the variables must satisfy non-linear and/or linear inequality constrainss. There are still relatively few algorithms that claim to solve this type of problem, especially when analytical expression for the first derivatives of the function and constraints are not available.In the author's experience, these derivatives are rarely available and not always continuous over all the feasible region and the algorithm described here is initially a combination of the simplex technique with the ideas of projection and hemstitching. A switch to quadratic hillclimbing techniques is made when the computer senses that the region of the minimum has been achieved, thus enabling rapid ultimate convergence to be obtained.     

Linear programming with fuzzy coefficients in constraints

This paper presents a new method for solving linear programming problems with fuzzy coefficients in constraints. It is shown that such problems can be reduced to a linear semi-infinite programming problem. The relations between optimal solutions and extreme points of the linear semi-infinite program are established. A cutting plane algorithm is introduced with a convergence proof, and a numerical example is included to illustrate the solution procedure.     

考虑复杂需求特性的多级煤炭供应链网络优化

由于不同燃煤设备与装置对煤质的要求存在差异,需要将不同类别、品质的煤进行配煤加工,以满足客户差异化需求并减少环境污染。考虑到这一复杂产品需求特性,结合配煤加工与流量平衡等特有约束,建立了新的四级煤炭供应链网络混合整数规划模型,以确定网络中的矿井、物流转运中心与配煤加工中心的数量、位置及规模,并分配各条网络路径上的合理煤炭流量。鉴于问题的NP-hard特性,设计了一种遗传算法,对染色体采用了新的编码结构,并结合贪婪启发式算法生成初始种群,提高了求解效率。大规模实验算例表明,该算法的求解质量明显优于混合遗传算法与模拟退火算法;同时,随着算例规模的增大,与LINGO软件相比,算法在计算时间方面的优势越来越显著。     

基于微粒群优化算法的间歇过程迭代学习

在实际的间歇过程优化控制中面临着模型参数不确定性的问题,并且基于梯度的优化控制技术在处理具有多个局部极值的目标函数时,往往会陷入局部极值点.针对该问题,提出一种基于微粒群优化算法的间歇过程产品质量迭代学习策略.结合间歇过程产品质量控制问题的特点和各种约束条件,利用微粒群优化算法在非线性问题求解及大尺度空间搜索上的优势,...