PSO求解带法向约束的B样条曲线逼近问题

若是B样条拟合曲线的节点向量与控制顶点均为变量,则该问题变为一个带约束的多维多变量高度非线性的优化问题,反求方程系统的方法已经难以求得最优解.针对该类问题,提出一种带有法向约束的粒子群优化算法(PSO)求解曲线逼近问题的方法,首先将带有法向约束的非线性最优化问题以罚函数的方法转化为无约束的最优化问题,建立一个与数据点和法向同时相关且比较合适的适应度函数(误差函数),然后以PSO调节节点向量,并使用最小二乘法求解在该节点向量下的最优拟合曲线,通过判断适应度函数值的优劣循环迭代,直到达到终止条件或者产生令人满意(误差容忍值)的拟合曲线为止.将文中算法产生的拟合曲线通过实验数据的对比与说明,突出了该方法的优越性,表明其用于解决带法向约束的逼近问题切实可行.     

基于遗传算法的B样条曲线拟合改进算法

B样条曲线拟合应用于绘制离散数据点的变化趋势,一般采用数据逼近或者迭代的方法得到,是图像处理和逆向工程中的重要内容。针对待拟合曲线存在多峰值、尖点、间断等问题,提出一种基于遗传算法的B样条曲线拟合算法。首先利用惩罚函数将带约束的曲线优化问题转换为无约束问题,然后利用改进的遗传算法来选择合适的适应度函数,再结合模拟退火算法自适应调整节点的数量和位置,在寻优的过程中找到最优的节点向量,持续迭代直到产生最终的优良重建曲线为止。实验结果表明,该算法有效地提高了精度并加快了收敛速度。     

基于相对差商与GA的离散变量结构优化研究

针对离散变量结构优化设计中存在的NP问题,提出了相对差商-遗传算法混合优化设计思想,建立了混合优化教学模型.在隔代映射遗传算法的基础上引入自适应策略,使得IP_GA中的交叉、变异概率根据适应度大小自动调节,提高了收敛速度及解的质量.比较结果表明,该方法在处理目标函数与约束函数具有单调变化性质的离散变量优化问题时,具有很好的可行性.     

基于改进遗传算法的电力系统无功优化的研究

电力系统无功优化问题是一个多变量、多约束的混合非线性规划问题,其操作变量既有连续变量又有离散变量,其优化过程比较复杂。遗传算法是模拟生物在自然环境中的遗传和进化过程而形成的一种自适应的全局优化搜索算法,可用于解决含有离散变量的复杂优化问题。本文选用遗传算法求解电力系统无功优化问题,并对基本遗传算法的编码、初始种群、适应度函数和交叉、变异策略等进行改进,使用本文提出的改进算法对IEEE1 4节点进行无功优化计算,结果证明本文模型和算法的实用性、可靠性和优越性。     

基于改进GA-PSO的可重构测试资源匹配方法

为提高测点信号与可重构测试资源匹配效率,建立了基于STD标准的测点信号与可重构测试资源的数学描述模型.针对可重构测试资源的特点,结合工程实际提出了基于Sigmoid函数的匹配函数,以资源可靠性、配置文件大小及配置时间因子作为罚函数,利用匹配函数构造出遗传算法的适应度函数.为解决遗传算法搜索速度较慢的问题,改进了遗传算法的选择算子和交叉算子,将粒子群算法应用到遗传算法中,解决了遗传算法在算法后期迭代效率低下的问题,最后通过实例验证了算法的有效性.     

多目标优化设计在杀螺剂配方研究中的应用

针对某生物杀螺剂制作中多目标约束问题,提出了一种应用Pareto遗传算法来解决问题的优化方法。建立了用于多目标优化的适应度函数,使用排列选择方法将带约束的多目标问题转换为无约束优化问题;并根据计算中的收敛情况引入了适当的移民算子,改善了遗传算法的进化性能,得到了Pareto最优解集,成功地解决了该生物杀螺剂的最优配方问题。     

基于DNA遗传优化的正交小波常模盲均衡算法

在上行多用户中继网络中,针对中继协作波束成形与多天线基站联合优化的问题,本文提出了两种不同的但是具有一定相关性的设计方法。在第一种方法中,考虑在接收端SINR约束的情况下,使中继节点总功率最小化;在第二种方法中,研究在中继节点满足一定功率约束的情况下,使接收端SINR最大化。研究发现,基站线性接收器的最优权值矩阵决定于中继节点加权向量,进而可将多变量优化的复杂问题转化为单一变量优化问题。原问题进而可转化为半正定规划问题,可以用内点法方便的解决。仿真结果表明,与通过迭代运用凸优化求多向量的方法相比,该方法性能更优。     

基于混沌遗传的Ad Hoc网络组播路由算法?

针对移动Ad Hoc网络(MANETS)的QoS组播路由优化问题,提出一种基于混沌遗传的组播路由算法。利用混沌变量的遍历性特点对遗传算法的适应度函数进行优化,避免遗传算法出现早熟现象。仿真实验结果表明,该算法具有较好的收敛性和稳定性,能解决多QoS约束下MANETS的组播路由问题。     

带法向约束的隐式B样条曲线重构PIA方法EI北大核心CSCD

为使隐式曲线能够更好地拟合散乱数据点及其几何特征,提出一种带法向约束的隐式曲线重构渐进迭代(progressive and iterative approximation,PIA)方法.首先,基于隐式B样条函数提出有效的曲线拟合模型;其次,通过加入偏移数据点来消除额外零水平集,同时加入法向项来控制曲线的法向误差;最后,经多次优化迭代得到高精度的拟合曲线.在配置为2.6 GHz英特尔处理器,内存为16 GB的电脑上采用MATLAB实现编程.经多条不同形态封闭曲线拟合的实验结果表明,与隐式PIA(implicit PIA,I-PIA)方法和T样条曲线重构方法相比,从数据点精度和法向误差以及收敛速度3个评价指标进行评估,该方法能够在保证数据点精度的前提下,有效地降低法向误差,并具有更快的收敛速度.此外,实例结果也表明该方法具备鲁棒性.     

基于服务的异质作战实体协同优化研究

针对作战仿真中异质作战实体协同分配模型存在的信息交互及协同效能低的问题,建立了一种基于服务的作战实体协同分配模型.通过服务调用机制解决异质作战实体任务分配时的信息交互和共享,以基于能力向量的效用函数为适应度函数,应用遗传算法优化初始任务分配方案;以航空协同反潜为背景进行了仿真实例验证,仿真结果表明,优化后的任务分配模型在基本相近的时间内,能有效提高任务分配方案的效能,使得分配方案更逼近全局最优.     

Target shape design optimization by evolving B-splines with cooperative coevolution

With high reputation in handling non-linear and multi-model problems with little prior knowledge, evolutionary algorithms (EAs) have successfully been applied to design optimization problems as robust optimizers. Since real-world design optimization is often computationally expensive, target shape design optimization problems (TSDOPs) have been frequently used as efficient miniature model to check algorithmic performance for general shape design. There are at least three important issues in developing EAs for TSDOPs, i.e., design representation, fitness evaluation and evolution paradigm. Existing work has mainly focused on the first two issues, in which (1) an adaptive encoding scheme with B-spline has been proposed as a representation, and (2) a symmetric Hausdorff distance based metric has been used as a fitness function. But for the third issue, off-the-shelf EAs were used directly to evolve B-spline control points and/or knot vector. In this paper, we first demonstrate why it is unreasonable to evolve the control points and knot vector simultaneously. And then a new coevolutionary paradigm is proposed to evolve the control points and knot vector of B-spline separately in a cooperative manner. In the new paradigm, an initial population is generated for both the control points, and the knot vector. The two populations are evolved mostly separately in a round-robin fashion, with only cooperation at the fitness evaluation phase. The new paradigm has at least two significant advantages over conventional EAs. Firstly, it provides a platform to evolve both the control points and knot vector reasonably. Secondly, it reduces the difficulty of TSDOPs by decomposing the objective vector into two smaller subcomponents (i.e., control points and knot vector). To evaluate the efficacy of the proposed coevolutionary paradigm, an algorithm named CMA-ES-CC was formulated. Experimental studies were conducted based on two target shapes. The comparison with six other EAs suggests that the proposed cooperative coevolution paradigm is very effective for TSDOPs.     

一种新的基于参考曲线的 B 样条曲线延拓算法

针对计算机辅助几何设计(CAGD)中 B 样条曲线延拓问题提出了一种新的算法, 可以使延拓后的曲线和给定的参考曲线形状尽量相似。首先通过统一待延拓曲线和参考曲线的 节点矢量来确定延拓后曲线的节点矢量;然后,利用 B 样条端点松弛算法确定延拓后曲线中和 原曲线对应的控制顶点;最后,通过优化方法确定新增加的控制顶点,优化的目标是经仿射变 换后的参考曲线和延拓后的曲线对应控制顶点之间距离的平方和最小。提出了一种两步法求解 该优化问题,先通过优化方法确定仿射变换,然后利用该仿射变换计算新增加的控制顶点。为 了使延拓后的曲线光顺性较好,通过引入光顺项对该算法进行了进一步的改进。实验结果表明, 该算法得到的延拓曲线和参考曲线形状具有一定的相似性,算法具有很好的实用性和灵活性。     

Lofted B-spline surface interpolation by linearly constrained energy minimization

This paper proposes a new approach for lofted B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. The approach first finds a common knot vector consisting of fewer knots that contain enough degrees of freedom to guarantee the existence of a B-spline curve interpolating each contour. Then, it computes from the contours a set of compatible B-spline curves defined on the knot vector by adopting B-spline curve interpolation based on linearly constrained energy minimization. Finally, it generates a B-spline surface interpolating the curves via B-spline surface lofting. As the energy functional is quadratic, the energy minimization problem leads to that of solving a linear system. The proposed approach is efficient in computation and can realize more efficient data reduction than previous approaches while providing visually pleasing B-spline surfaces. Moreover, the approach works well on measured data with noise. Some experimental results demonstrate its usefulness and quality.     

Evolutionary trajectory planning for an industrial robot

This paper presents a novel general method for computing optimal motions of an industrial robot manipulator (AdeptOne XL robot) in the presence of fixed and oscillating obstacles. The optimization model considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacle avoidance. The problem has 6 objective functions, 88 variables, and 21 constraints. Two evolutionary algorithms, namely, elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE), have been used for the optimization. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best solution tradeoffs. Two multi-objective performance measures, namely solution spread measure and ratio of non-dominated individuals, are used to evaluate the Pareto optimal fronts. Two multi-objective performance measures, namely, optimizer overhead and algorithm effort, are used to find the computational effort of the optimization algorithm. The trajectories are defined by B-spline functions. The results obtained from NSGA-II and MODE are compared and analyzed.     

Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation

One of the key problems in using B-splines successfully to approximate an object contour is to determine good knots. In this paper, the knots of a parametric B-spline curve were treated as variables, and the initial location of every knot was generated using the Monte Carlo method in its solution domain. The best km knot vectors among the initial candidates were searched according to the fitness. Based on the initial parameters estimated by an improved k-means algorithm, the Gaussian Mixture Model (GMM) for every knot was built according to the best km knot vectors. Then, the new generation of the population was generated according to the Gaussian mixture probabilistic models. An iterative procedure repeating these steps was carried out until a termination criterion was met. The GMM-based continuous optimization algorithm could determine the appropriate location of knots automatically. A set of experiments was then implemented to evaluate the performance of the new algorithm. The results show that the proposed method achieves better approximation accuracy than methods based on artificial immune system, genetic algorithm or squared distance minimization (SDM).     

一种分级竞争紧致遗传算法的研究

根据随机游动理论,研究了二进制编码的紧致遗传算法中概率向量的进化特性,提出了一种分级竞争模式紧致遗传算法(GCGA),该算法加大参与竞争的两个个体的适应度的差距,目的在于使概率向量有效进化。在数值函数优化问题中进行仿真实验,结果表明,分级竞争模式紧致遗传算法收敛速度更快,全局寻优能力也得到提高。     

Iteration and optimization scheme for the reconstruction of 3D surfaces based on non-uniform rational B-splines

Curve or surface reconstruction is a challenging problem in the fields of engineering design, virtual reality, film making and data visualization. Non-uniform rational B-spline (NURBS) fitting has been applied to curve and surface reconstruction for many years because it is a flexible method and can be used to build many complex mathematical models, unlike certain other methods. To apply NURBS fitting, there are two major difficult sub-problems that must be solved: (1) the determination of a knot vector and (2) the computation of weights and the parameterization of data points. These two problems are quite challenging and determine the effectiveness of the overall NURBS fit. In this study, we propose a new method, which is a combination of a hybrid optimization algorithm and an iterative scheme (with the acronym HOAAI), to address these difficulties. The novelties of our proposed method are the following: (1) it introduces a projected optimization algorithm for optimizing the weights and the parameterization of the data points, (2) it provides an iterative scheme to determine the knot vectors, which is based on the calculated point parameterization, and (3) it proposes the boundary-determined parameterization and the partition-based parameterization for unorganized points. We conduct numerical experiments to measure the performance of the proposed HOAAI with six test problems, including a complicated curve, twisted and singular surfaces, unorganized data points and, most importantly, real measured data points from the Mashan Pumped Storage Power Station in China. The simulation results show that the proposed HOAAI is very fast, effective and robust against noise. Furthermore, a comparison with other approaches indicates that the HOAAI is competitive in terms of both accuracy and runtime costs.     

Constrained efficient global optimization with support vector machines

This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). While the objective function is approximated using Kriging, as in the original EGO formulation, the boundary of the feasible domain is approximated explicitly as a function of the design variables using an SVM. Because SVM is a classification approach and does not involve response approximations, this approach alleviates issues due to discontinuous or binary responses. More importantly, several constraints, even correlated, can be represented using one unique SVM, thus considerably simplifying constrained problems. In order to account for constraints, this paper introduces an SVM-based ??probability of feasibility?? using a new Probabilistic SVM model. The proposed optimization scheme is constituted of two levels. In a first stage, a global search for the optimal solution is performed based on the ??expected improvement?? of the objective function and the probability of feasibility. In a second stage, the SVM boundary is locally refined using an adaptive sampling scheme. An unconstrained and a constrained formulation of the optimization problem are presented and compared. Several analytical examples are used to test the formulations. In particular, a problem with 99 constraints and an aeroelasticity problem with binary output are presented. Overall, the results indicate that the constrained formulation is more robust and efficient.     

Reducing control points in lofted B-spline surface interpolation using common knot vector determination

A new algorithm for reducing control points in lofted surface interpolation to rows of data points is presented in this paper. The key step of surface lofting is to obtain a set of compatible B-spline curves interpolating each row. Given a set of points and their parameterization, a necessary and sufficient condition is proposed to determine the existence of interpolating B-spline curves defined on a given knot vector. Based on this condition, we first properly construct a common knot vector that guarantees the existence of interpolating B-spline curves to each row of points. Then we calculate a set of interpolating B-spline curves defined on the common knot vector by energy minimization. Using this method, fewer control points are employed while maintaining a visually pleasing shape of the lofted surface. Several experimental results demonstrate the usability and quality of the proposed method.