带回溯线搜索步的双子问题信赖域算法

无约束非线性优化问题广泛存在于工程、科学计算等实际应用领域。本文在信赖域算法的框架下提出无约束子问题,将它与信赖子问题相结合,构造了求解无约束优化问题的双子问题信赖域算法。同时利用信赖域子问题得到的试探步一定是目标函数充分下降方向的性质使得每次求解信赖域子问题之后均能得到使目标函数下降的步。在标准假设下证明了该算法具有全局收敛性和局部二次收敛速度。数值结果表明该算法比传统的信赖域算法速度更快更有效。     

一个自动确定信赖域半径的信赖域方法

本文对无约束优化问题提出一个自适应的信赖域方法,每次迭代都充分利用当前迭代点包含的二次信息自动产生一个信赖域半径,所用的计算信赖域半径的策略没有增加额外的计算量。在通常条件下,证明了全局收敛性及局部超线性收敛结果,数值结果验证了新方法的有效性。     

一种实数遗传算法及其在雷达成像中的应用

提出了一种由含实数域结构和目标函数信息的实数交叉和变异算子构成的实数遗传算法，并将其用于解决最大似然多散射点定位雷达成像问题。数字仪真结果表明，对非线性实变量函数优化问题，实数遗传算法在搜索全局最优解的收敛速度和精度等方面均能得到较理想的结果。     

求解一类非线性双层规划问题的混合遗传算法

本文研究下层目标函数为拟凹函数的非线性双层规划问题。利用下层目标的最优值能在可行域极点上达到的性质,将求极点的方法引入遗传算法,提出了一种混合遗传算法。为了提高该算法的效率,结合种群最优个体,给出了有利于产生高质量后代的杂交和变异算子。对于下层问题存在多个最优解的情况,证明了其最优解可表示为极点最优解的凸组合,并利用这一结论修正了算法,使得该算法也能求解下层多解的情形。数值结果表明本文提出的算法是有效的。     

用于结构优化设计的改进多目标群搜索算法

在多目标群搜索算法（multi-objective group search optimization, MGSO）基本原理的基础上,结合Pareto最优解理论,提出了基于约束改进的多目标群搜索算法（IMGSO）,并应用于多目标的结构优化设计．算法的改进主要有3个方面：第一,引入过渡可行域的概念来处理约束条件;第二,利用庄家法来构造非支配解集;最后,结合禁忌搜索算法和拥挤距离机制来选择发现者,以避免解集过早陷入局部最优,并提高收敛精度．采用IMGSO优化算法分别对平面和空间桁架结构进行了离散变量的截面优化设计,并与MGSO优化算法的计算结果进行了比较,结果表明改进的多目标群搜索优化算法IMGSO与MGSO算法相比具有更好的收敛精度.通过算例表明：IMGSO算法得到的解集中的解能大部分支配MGSO算法的解,在复杂高维结构中IMGSO算法的优越性更加明显,且收敛速度也有一定的提高,可有效应用于多目标的实际结构优化设计．     

增强差异演化算法及其应用

针对约束优化问题,提出一种适于约束优化的增强差异演化算法(enhanced differential evolution algorithm for constrained optimization, ECDE).在约束处理上采用不可行域与可行域更新规则的方法,避免了传统的惩罚函数方法中对惩罚因子的设置,使算法的实现变得简单.改进了DE算法的变异操作,对选择的3个父代个体进行操作遍历,产生6个候选解,取适应值最优的为变异操作的解,大大改善了算法的稳定性、鲁棒性和搜索性能.通过4个测试函数和1个设计实例仿真,表明所提出的算法具有较快的收敛速度和较好的稳定性和鲁棒性.     

求解约束优化问题的退火遗传算法

针对基于罚函数遗传算法求解实际约束优化问题的困难与缺点,提出了求解约束优化问题的退火遗传算法。对种群中的个体定义了不可行度,并设计退火遗传选择操作。算法分三阶段进行,首先用退火算法搜索产生初始种群体,随后利用遗传算法使搜索逐渐收敛于可行的全局最优解或较优解,最后用退火优化算法对解进行局部优化。两个典型的仿真例子计算结果证明该算法能极大地提高计算稳定性和精度。     

基于改进的信赖域模型管理技术识别风电转子系统不对中载荷

针对求解耗时的风电转子系统不对中载荷识别问题，提出基于改进的信赖域模型管理技术的识别算法。该算法将整个先验分布空间的不对中载荷识别问题转化为一系列信赖域上的近似优化问题，通过区域遗传智能采样技术采集样本，加强径向基函数构建代理模型，再采用遗传算法进行近似优化。通过每个信赖域上的最小目标函数和近似优化结果确定信赖度和下代域的中心、半径，进而不断地缩放、平移信赖域，来保证获得与真实模型一致的不对中载荷。通过四种方法对比表明该方法样本遗传策略，遗传落在下代信赖域空间上的样本，减少实验设计样本个数而提高效率；最小目标函数作为信赖中心调整提高了关键区域代理模型的精度而加快收敛，降低了对代理模型精度的依赖。     

低温液位传感器校准装置几何误差辨识方法的研究

针对低温液位传感器校准装置的夹具端空间姿态问题,提出了一种基于多边法原理的误差辨识方法。利用激光跟踪仪测距精度高的特点,采用多边法原理对校准装置夹具端的运动轨迹进行标定,以重力加速度方向为Z轴反方向建立虚拟坐标系,利用刚体中两点位置始终不变的特性,获得被测点6项误差的冗余数据,实现校准装置几何误差的辨识。仿真结果表明,所提出的方法具有一定的可行性,采用遗传算法与信赖域法、Guass-Ne叭加法相结合的方法,在一定程度上避免因初值难以确定造成的数据不收敛问题。     

大口径拼接望远镜成像系统的远场特性

本文根据衍射光学理论和几何光学理论,利用已得到的拼接望远镜的理论解析表达式和建立的数值仿真模型,对拼接望远镜光学系统的远场特性进行了分析计算,包括系统的理论衍射光斑直径、点扩散函数、斯特列尔比以及光学传递函数等。并根据仿真模型分析了拼接主镜中分块镜平移误差和倾斜误差对拼接望远镜系统远场的影响。分析结果表明,拼接主镜的平移误差和倾斜误差都影响系统的点扩散函数、斯特列尔比和光学传递函数,并使远场成像模糊;其中分块镜倾斜误差会额外引入平移量,如果补偿掉平移量对望远镜系统的远场性能有很大提高。     

Maximizing pseudoconvex transportation problem: a special type

The paper discusses a non-concave fractional programming problem aiming at maximization of a pseudoconvex function under standard transportation conditions. The pseudoconvex function considered here is the product of two linear functions contrasted with a positive valued linear function. It has been established that optimal solution of the problem is attainable at an extreme point of the convex feasible region. The problem is shown to be related to indefinite quadratic programming which deals with maximization of a convex function over the given feasible region. It has been further established that the local maximum point of this quadratic programming problem is the global maximum point under certain conditions, and its optimal solution provides an upper bound on the optimal value of the main problem. The extreme point solutions of the indefinite quadratic program are ranked to tighten the bounds on the optimal value of the main problem and a convergent algorithm is developed to obtain the optimal solution.     

A new mathematical model for the Weber location problem with a probabilistic polyhedral barrier

With the wide application of location theory in a variety of industries, the presence of barriers ?merits the attention of managers and engineers.? In this paper, we assess the Weber location problem in the presence of a polyhedral barrier which probabilistically occurs on a given horizontal barrier route in the rectilinear space. A left triangular distribution function is used for the starting point of the barrier and therefore an expected rectilinear barrier distance function is formulated. In addition, a modification of the polyhedral barrier is presented which is equivalent to the original problem. Therefore, a mixed integer nonlinear programming model, which has a nonconvex solution space, is presented. Furthermore, by decomposing the feasible space into a finite number of convex solution spaces, an exact heuristic solution method is proposed. Then, a lower bound problem based on the forbidden region is applied. Some theorems and an example are reported.     

A new achievement scalarizing function based on parameterization in multiobjective optimization

This paper addresses a general multiobjective optimization problem. One of the most widely used methods of dealing with multiple conflicting objectives consists of constructing and optimizing a so-called achievement scalarizing function (ASF) which has an ability to produce any Pareto optimal or weakly/properly Pareto optimal solution. The ASF minimizes the distance from the reference point to the feasible region, if the reference point is unattainable, or maximizes the distance otherwise. The distance is defined by means of some specific kind of a metric introduced in the objective space. The reference point is usually specified by a decision maker and contains her/his aspirations about desirable objective values. The classical approach to constructing an ASF is based on using the Chebyshev metric L _∞. Another possibility is to use an additive ASF based on a modified linear metric L ₁. In this paper, we propose a parameterized version of an ASF. We introduce an integer parameter in order to control the degree of metric flexibility varying from L ₁ to L _∞. We prove that the parameterized ASF supports all the Pareto optimal solutions. Moreover, we specify conditions under which the Pareto optimality of each solution is guaranteed. An illustrative example for the case of three objectives and comparative analysis of parameterized ASFs with different values of the parameter are given. We show that the parameterized ASF provides the decision maker with flexible and advanced tools to detect Pareto optimal points, especially those whose detection with other ASFs is not straightforward since it may require changing essentially the reference point or weighting coefficients as well as some other extra computational efforts.     

A Stopping Rule for Facilities Location Algorithms

The single-facility location model with Euclidean distances and its multifacility and ℓ_p distance generalizations are considered. With present algorithms a user is unable to decide how close to optimal any given feasible solution is. This article describes two procedures for calculating a lower bound on the optimal objective function when a proposed solution is given.     

Normed Distances and Their Applications in Optimal Circuit Design

A new geometric method for optimal circuit design is presented. The method treats the optimal design problem through the concept of normed distances from a feasible point to the feasible region boundaries in a norm related to the probability distribution of the circuit parameters. The method treats directly the nonlinear feasible region boundaries without any region approximation. The normed distances are found through the solution of a nonlinear optimization problem. The sufficient optimality conditions for this optimization problem are established and an ordinary explicit formula for the normed distance is also derived. An iterative boundary search technique is used to solve the nonlinear optimization problem concerning the normed distances. The convergence of this technique is proved. Practical circuit examples are given to test the method.     

A new trust region–sequential quadratic programming approach for nonlinear systems based on nonlinear model predictive control

In this article, a superlinearly convergent trust region–sequential quadratic programming approach is first proposed, developed and investigated for nonlinear systems based on nonlinear model predictive control. The method incorporates a combination algorithm that allows both the trust region technique and the sequential quadratic programming method to be used. If the attempted search of the trust region method is not accepted, the line search rule will be adopted for the next iteration. Also, having to resolve the quadratic programming subproblem for nonlinear constrained optimization problems is avoided. This gives the potential for fast convergence in the neighbourhood of an optimal solution. Moreover, additional characteristics of the algorithm are that each quadratic programming subproblem is regularized and the quadratic programming subproblem always has a consistent point. The main result is illustrated on a nonlinear system with a variable parameter and a bipedal walking robot system through simulations and is utilized to achieve rapidly stability. Numerical results show that the trust region–sequential quadratic programming algorithm is feasible and effective for a nonlinear system with a variable parameter and a bipedal walking robot system. Therefore, the simulation results demonstrate the usefulness of the trust region–sequential quadratic programming approach with nonlinear model predictive control for real-time control systems.     

Strong converse,feedback channel capacity and hypothesis testing

Abstract

In light of recent results by Verdú and Han on channel capacity, we examine three problems: the strong converse condition to the channel coding.theorem, the capacity of arbitrary channels with feedback and the Neyman‐Pearson hypothesis testing type‐II error exponent. It is first remarked that the strong converse condition holds if and only if the sequence of normalized channel information densities converges in probability to a constant. Examples illustrating this condition are provided. A general formula for the capacity of arbitrary channels with output feedback is then obtained. Finally, a general expression for the Neyman‐Pearson type‐II error exponent based on arbitrary observations subject to a constant bound on the type‐I error probability is derived.     

Application of a Genetic Algorithm to Computer-aided Bending Sequence Planning

Optimal design of the bending sequence is a key link in sheet metal free bending sequence planning,and it has an important influence on simplifying operation and guaranteeing bending precision. Bending sequence must meet the requirements for not only no collision interference of the work piece and the mold,but also working efficiency and working precision,so bending point choice,molds select,turnover and turn round of sheet metal must be considered in each bending step. In this paper,a genetic algorithm is used to design bending sequence. The interference identification is used to determine coding,exchange and mutation of the genetic algorithm. The genetic algorithm is developed to calculate the current optimal feasible solution of the bending sequence,and then the influence of initial population and evolution generations of this method on the result is analyzed by example verifications. The results prove that a global optimal solution can be obtained while the bending point number was less than 10,and optimal bending sequence which is similar to the global optimal solution can be calculated while the bending point number was more than 10. The results converge gradually to the global optimal solution with the increase of the initial population and evolution generations. As to 18 points bending work-piece,with the initial population size 150 and the evolution generations 100,we can obtain the satisfying solution.     

A new deterministic global optimization method for general twice-differentiable constrained nonlinear programming problems

A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.     

A tractable approximation of non-convex chance constrained optimization with non-Gaussian uncertainties

Chance constrained optimization problems in engineering applications possess highly nonlinear process models and non-convex structures. As a result, solving a nonlinear non-convex chance constrained optimization (CCOPT) problem remains as a challenging task. The major difficulty lies in the evaluation of probability values and gradients of inequality constraints which are nonlinear functions of stochastic variables. This article proposes a novel analytic approximation to improve the tractability of smooth non-convex chance constraints. The approximation uses a smooth parametric function to define a sequence of smooth nonlinear programs (NLPs). The sequence of optimal solutions of these NLPs remains always feasible and converges to the solution set of the CCOPT problem. Furthermore, Karush–Kuhn–Tucker (KKT) points of the approximating problems converge to a subset of KKT points of the CCOPT problem. Another feature of this approach is that it can handle uncertainties with both Gaussian and/or non-Gaussian distributions.