Reliable Modeling and Optimization for Chemical Engineering Applications: Interval Analysis Approach

In many applications of interest in chemical engineering it is necessary to deal with nonlinear models of complex physical phenomena, on scales ranging from the macroscopic to the molecular. Frequently these are problems that require solving a nonlinear equation system and/or finding the global optimum of a nonconvex function. Thus, the reliability with which these computations can be done is often an important issue. Interval analysis provides tools with which these reliability issues can be addressed, allowing such problems to be solved with complete certainty. This paper will focus on three types of applications: 1) parameter estimation in the modeling of phase equilibrium, including the implications of using locally vs. globally optimal parameters in subsequent computations; 2) nonlinear dynamics, in particular the location of equilibrium states and bifurcations of equilibria in ecosystem models used to assess the risk associated with the introduction of new chemicals int the environment; 3) molecular modeling, with focus on transition state analysis of the diffusion of a sorbate molecule in a zeolite.Author to whom all correspondence should be addressed.     

An Evolutionary Algorithm for Global Optimization Based on Level-Set Evolution and Latin Squares

In this paper, the level-set evolution is exploited in the design of a novel evolutionary algorithm (EA) for global optimization. An application of Latin squares leads to a new and effective crossover operator. This crossover operator can generate a set of uniformly scattered offspring around their parents, has the ability to search locally, and can explore the search space efficiently. To compute a globally optimal solution, the level set of the objective function is successively evolved by crossover and mutation operators so that it gradually approaches the globally optimal solution set. As a result, the level set can be efficiently improved. Based on these skills, a new EA is developed to solve a global optimization problem by successively evolving the level set of the objective function such that it becomes smaller and smaller until all of its points are optimal solutions. Furthermore, we can prove that the proposed algorithm converges to a global optimizer with probability one. Numerical simulations are conducted for 20 standard test functions. The performance of the proposed algorithm is compared with that of eight EAs that have been published recently and the Monte Carlo implementation of the mean-value-level-set method. The results indicate that the proposed algorithm is effective and efficient.     

On optimally combining pieces of information, with application to estimating 3-d complex-object position from range data

New asymptotic methods are introduced that permit computationally simple Bayesian recognition and parameter estimation for many large data sets described by a combination of algebraic, geometric, and probabilistic models. The techniques introduced permit controlled decomposition of a large problem into small problems for separate parallel processing where maximum likelihood estimation or Bayesian estimation or recognition can be realized locally. These results can be combined to arrive at globally optimum estimation or recognition. The approach is applied to the maximum likelihood estimation of 3-D complex-object position. To this end, the surface of an object is modeled as a collection of patches of primitive quadrics, i.e., planar, cylindrical, and spherical patches, possibly augmented by boundary segments. The primitive surface-patch models are specified by geometric parameters, reflecting location, orientation, and dimension information. The object-position estimation is based on sets of range data points, each set associated with an object primitive. Probability density functions are introduced that model the generation of range measurement points. This entails the formulation of a noise mechanism in three-space accounting for inaccuracies in the 3-D measurements and possibly for inaccuracies in the 3-D modeling. We develop the necessary techniques for optimal local parameter estimation and primitive boundary or surface type recognition for each small patch of data, and then optimal combining of these inaccurate locally derived parameter estimates in order to arrive at roughly globally optimum object-position estimation.     

Global parameter optimization for biokinetic modeling of simple batch experiments

Environmental process modeling is challenged by the lack of high quality data, stochastic variations, and nonlinear behavior. Conventionally, parameter optimization is based on stochastic sampling techniques to deal with the nonlinear behavior of the proposed models. Despite widespread use, such tools cannot guarantee globally optimal parameter estimates. It can be especially difficult in practice to differentiate between lack of algorithm convergence, convergence to a non-global local optimum, and model structure deficits. For this reason, we use a deterministic global optimization algorithm for kinetic model identification and demonstrate it with a model describing a typical batch experiment. A combination of interval arithmetic, reformulations, and relaxations allows globally optimal identification of all (six) model parameters. In addition, the results suggest that further improvements may be obtained by modification of the optimization problem or by proof of the hypothesized pseudo-convex nature of the problem suggested by our results.     

基于遗传模拟退火算法的移动机器人路径规划

针对移动机器人路径规划的难题,运用了一种基于遗传模拟退火算法的移动机器人最优路径规划方法,对移动机器人的路径规划进行了设计,采用了栅格法对环境进行建模.为了提高路径规划的效率,采用了一种改进的避障算法来生成初始种群.将遗传算法与模拟退火算法相结合形成遗传模拟退火算法,新算法具有较强的全局和局部搜索能力.仿真实验结果证明算法相对于基本遗传算法的收敛速度、搜索质量和最优解输出概率方面有了明显的提高.     

Optimal design of continuous time irrational filter with a set of fractional order gammatone components via norm relaxed sequential quadratic programming approach

This paper proposes a continuous time irrational filter structure via a set of the fractional order Gammatone components instead of via a set of integer order Gammatone components. The filter design problem is formulated as a nonsmooth and nonconvex infinite constrained optimization problem. The nonsmooth function is approximated by a smooth operator. The domain of the constraint functions is sampled into a set of finite discrete points so the infinite constrained optimization problem is approximated by a finite constrained optimization problem. To find a near globally optimal solution, the norm relaxed sequential quadratic programming approach is applied to find the locally optimal solutions of this nonconvex optimization problem. The current or the previous locally optimal solutions are kicked out by adding the random vectors to them. The locally optimal solutions with the lower objective functional values are retained and the locally optimal solutions with the higher objective functional values are discarded. By iterating the above procedures, a near globally optimal solution is found. The designed filter is applied to perform the denoising. It is found that the signal to noise ratio of the designed filter is higher than those of the filters designed by the conventional gradient descent approach and the genetic algorithm method, while the required computational power of our proposed method is lower than those of the conventional gradient descent approach and the genetic algorithm method. Also, the signal to noise ratio of the filter with the fractional order Gammatone components is higher than those of the filter with the integer order Gammatone components and the conventional rational infinite impulse response filters.     

A New Algorithm and System for the Characterization of Handwriting Strokes with Delta-Lognormal Parameters

In this paper, we present a new analytical method for estimating the parameters of delta-lognormal functions and characterizing handwriting strokes. According to the kinematic theory of rapid human movements, these parameters contain information on both the motor commands and the timing properties of a neuromuscular system. The new algorithm, called XZERO, exploits relationships between the zero crossings of the first and second time derivatives of a lognormal function and its four basic parameters. The methodology is described and then evaluated under various testing conditions. The new tool allows a greater variety of stroke patterns to be processed automatically. Furthermore, for the first time, the extraction accuracy is quantified empirically, taking advantage of the exponential relationships that link the dispersion of the extraction errors with its signal-to-noise ratio. A new extraction system which combines this algorithm with two other previously published methods is also described and evaluated. This system provides researchers involved in various domains of pattern analysis and artificial intelligence with new tools for the basic study of single strokes as primitives for understanding rapid human movements.     

Field of Particle Filters for Image Inpainting

We present a novel algorithm for solving the image inpainting problem based on a field of locally interacting particle filters. Image inpainting, also known as image completion, is concerned with the problem of filling image regions with new visually plausible data. In order to avoid the difficulty of solving the problem globally for the region to be inpainted, we introduce a field of local particle filters. The states of the particle filters are image patches. Global consistency is enforced by a Markov random field image model which connects neighbouring particle filters. The benefit of using locally interacting particle filters is that several competing hypotheses on inpainting solutions are kept active, allowing the method to provide globally consistent solutions on problems where other local methods may fail. We provide examples of applications of the developed method.     

含区间参数多目标系统的微粒群优化算法

参数不确定优化问题是实践中经常遇到的复杂优化问题, 现有方法多针对单目标函数的情况. 本文利用微粒群优化算法解决含区间参数多目标优化问题, 提出一种基于概率支配的多目标微粒群优化算法. 该算法通过定义概率支配关系, 比较所得解的优劣; 基于 σ 区间值, 选择微粒的全局极值点, 并给出新的微粒个体极值点及外部储备集的更新策略. 与传统多目标微粒群优化算法比较, 仿真结果表明本文所提算法的有效性.     

A Novel Chaotic Neural Network With the Ability to Characterize Local Features and Its Application

To provide an ability to characterize local features for the chaotic neural network (CNN), Gauss wavelet is used for the self-feedback of the CNN with the dilation parameter acting as the bifurcation parameter. The exponentially decaying dilation parameter and the chaotically varying translation parameter not only govern the wavelet self-feedback transform but also enable the CNN to generate complex dynamics behavior preventing the network from being trapped in the local minima. Analysis of the energy function of the CNN indicates that the local characterization ability of the proposed CNN is effectively provided by the wavelet self-feedback in the manner of inverse wavelet transform and that the proposed CNN can achieve asymptotical stability. The experimental results on traveling salesman problem (TSP) suggest that the proposed CNN has a higher average success rate for obtaining globally optimal or near-optimal solutions.     

基于斐波那契树优化算法的切削参数多方案优化方法

针对切削参数优化问题,以生产成本最小化为优化目标,基于斐波那契法最优化原理与黄金分割法,提出斐波那契树优化算法(FTO)进行优化求解.该算法通过全局探索与局部寻优交替进行,达到快速收敛到全局最优解的目的,避免陷入局部最优;通过设置距离参数保留多个有价值的全局最优解和局部最优解,可以一次性得到多个全局最优的优化设计方案.8个典型多峰函数的测试结果表明,FTO算法具有较强的全局寻优能力和较高的寻优精度.利用FTO算法对切削参数进行优化,仿真结果表明,所提出算法能够找到多个满足约束条件的切削参数优化结果.采用多方案优化方法不仅能一次性得到多个生产成本最低的最优解,还能给出切削参数的优化组合取值.多方案优化方法使优化算法应用于工程优化问题具有现实意义.     

Modeling and control of high-throughput screening systems in a max-plus algebraic setting

In this paper, we present a max-plus algebraic modeling and control approach for cyclically operated high-throughput screening plants. In previous work an algorithm has been developed to determine the globally optimal solution of the cyclic scheduling problem. The obtained optimal schedule is modeled in a max-plus algebraic framework. The max-plus algebraic model can then be used to generate appropriate control actions to handle unexpected deviations from the predetermined cyclic operation during runtime.     

Propelling a torque controlled baton to a maximum height

Recent applications of optimal control theory to the analysis of human and animal locomotion have resulted in optimal control problems that are too complex for analytic solution. Furthermore, these problems involve unusual constraints and dynamics. In order to provide a clearer understanding of the problems involved, the much simpler but related problem of causing a baton to "jump" maximally has been completely solved via elementary methods. The solution is given in feedback form. The state space divides into several regions according to the form of the optimal control. There exist regions where many controls are globally optimal, regions where a locally optimal control and a globally optimal control both exist, and regions where a unique globally optimal control exists. Finally, some relations between these results and experimental observations in both human and animal jumping are discussed.     

Computation of nonconservative stability perturbation bounds forsystems with nonlinearly correlated uncertainties

Consideration is given to the problem of robust stability analysis of linear dynamic systems with uncertain physical parameters entering as polynomials in the state equation matrices. A method is proposed giving necessary and sufficient conditions for computing the uncertain system stability margin in parameter space, which provides a measure of maximal parameter perturbations preserving stability of the perturbed system around a known, stable, nominal system. A globally convergent optimization algorithm that enables solutions to the problem to be obtained is presented. Using the polynomial structure of the problem, the algorithm generates a convergent sequence of interval estimates of the global extremum. These intervals provide a measure of the accuracy of the approximating solution achieved at each step of the iterative procedure. Some numerical examples are reported, showing attractive features of the algorithm from the point of view of computational burden and convergence behavior     

改进遗传算法在装配操作优化中的应用

针对复杂车身连接关系和多装配顺序,改进后的装配模型不仅描述了零件间的装配优先关系,而且还包含了可以用于公差分析的装配连接特征信息.在此基础上,根据迂回遗传算法对零件间的装配操作进行优化,以提高优化效率及求解范围.最后,通过某车身侧围装配案例说明了该算法的有效性.     

The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore

First-order necessary conditions for quadratically optimal reduced-order modeling of linear time-invariant systems are derived in the form of a pair of modified Lyapunov equations coupled by an oblique projection which determines the optimal reduced-order model. This form of the necessary conditions considerably simplifies previous results of Wilson [1] and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of Moore [2]. The possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation-type algorithm is proposed for computing these local extrema. A component-cost analysis of the model-error criterion similar to the approach of Skelton [3] is utilized at each iteration to direct the algorithm to the global minimum.     

动态环境下机器人多目标路径规划蚂蚁算法

研究了一种新颖的动态复杂不确定环境下的机器人多目标路径规划蚂蚁算法。该方法首先根据蚂蚁觅食行为对多个目标点的组合进行优化,规划出一条最优的全局导航路径。在此基础上,机器人按照规划好的目标点访问顺序根据多蚂蚁协作局部路径算法完成局部路径的搜索。机器人每前进一步都实时地进行动态障碍物运动轨迹预测以及碰撞预测,并重新进行避碰局部路径规划。仿真结果表明,即使在障碍物非常复杂的地理环境,用该算法也能使机器人沿一条全局优化的路径安全避碰的遍历各个目标点,效果十分令人满意。     

Neural clustering networks based on global optimisation of prototypes in metric spaces

The utilisation of clustering algorithms based on the optimisation of prototypes in neural networks is demonstrated for unsupervised learning. Stimulated by common clustering methods of this type (learning vector quantisation [LVQ, GLVQ] and K-means) a globally operating algorithm was developed to cope with known shortcomings of existing tools. This algorithm and K-means (for the common methods) were applied to the problem of clustering EEG patterns being pre-processed. It can be shown that the algorithm based on global random optimisation may find an optimal solution repeatedly, whereas K-means provides different sub-optimal solutions with respect to the quality measure defined as objective function. The results are presented. The performance of the algorithms is discussed.     

Satellite image classification using genetically guided fuzzy clustering with spatial information

Land‐cover classification of satellite images is an important task in analysis of remote sensing imagery. Segmentation is one of the widely used techniques in this regard. One of the important approaches for segmentation of an image is by clustering the pixels in the spectral domain, where pixels that share some common spectral property are put in the same group, or cluster. However, such spectral clustering completely ignores the spatial information contained in the pixels, which is often an important consideration for good segmentation of images. Moreover, the clustering algorithms often provide locally optimal solutions. In this paper, we propose to perform image segmentation by a genetically guided unsupervised fuzzy clustering technique where some spatial information of the pixels is incorporated. Two ways of incorporating spatial information are suggested. The characteristic of this technique is that it is able to determine automatically the appropriate number of clusters without making any assumptions regarding the dataset, while attempting to provide globally near‐optimal solutions. In order to evolve the appropriate number of clusters, the chromosome encoding scheme is enhanced to incorporate the don't care symbol (#). Real‐coded genetic algorithm with appropriately defined operators is used. A cluster validity index is used as a measure of the fitness value of the chromosomes. Results, both quantitative and qualitative, are demonstrated for several images, including a satellite image of a part of the city of Mumbai.     

一种基于改进支持向量机的入侵检测方法研究

提出基于粒子群优化（Particle Swarm Optimization,PSO）算法和支持向量机（Support Vector Machines,SVM）的入侵检测方法,为优化SVM性能,使用PSO的全局搜索特性寻找SVM的最优参数[C]和[σ];为避免PSO算法陷入局部最优,引入变异操作,找到最优参数组合后进行基于PSO_SVM入侵检测算法的训练和检测,解决了入侵检测系统准确度难题。仿真实验表明该方法的检测率为92.8%,误报率为6.911 9%,漏报率为9.708 7%,对KDDCUP竞赛的最佳结果有一定程度的提高,实验结果验证了该算法的有效性和可行性。