Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy pro jection technique

This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method （FEM） by recursive application of the one-dimensional （1D） element energy projection （EEP） technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element （FE） model is reached. This conceptual dimension-by- dimension （D-by-D） discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional （2D） and three-dimensional （3D） problems can be obtained over the domain. Numerical examples of 3D Poisson＇s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.

An Intelligent Optimization Method of Reinforcing Bar Cutting for Construction Site

To meet the requirements of specifications,intelligent optimization of steel bar blanking can improve resource utilization and promote the intelligent development of sustainable construction.As one of the most important building materials in construction engineering,reinforcing bars(rebar)account for more than 30%of the cost in civil engineering.A significant amount of cutting waste is generated during the construction phase.Excessive cutting waste increases construction costs and generates a considerable amount of CO_(2)emission.This study aimed to develop an optimization algorithm for steel bar blanking that can be used in the intelligent optimization of steel bar engineering to realize sustainable construction.In the proposed algorithm,the integer linear programming algorithm was applied to solve the problem.It was combined with the statistical method,a greedy strategy was introduced,and a method for determining the dynamic critical threshold was developed to ensure the accuracy of large-scale data calculation.The proposed algorithm was verified through a case study;the results confirmed that the rebar loss rate of the proposed method was reduced by 9.124%compared with that of traditional distributed processing of steel bars,reducing CO_(2)emissions and saving construction costs.As the scale of a project increases,the calculation quality of the optimization algorithmfor steel bar blanking proposed also increases,while maintaining high calculation efficiency.When the results of this study are applied in practice,they can be used as a sustainable foundation for building informatization and intelligent development.

APPLICATION OF INTEGER CODING ACCELERATING GENETIC ALGORITHM IN RECTANGULAR CUTTING STOCK PROBLEM

An improved genetic algorithm and its application to resolve cutting stock problem arc presented. It is common to apply simple genetic algorithm （SGA） to cutting stock problem, but the huge amount of computing of SGA is a serious problem in practical application. Accelerating genetic algorithm （AGA） based on integer coding and AGA＇s detailed steps are developed to reduce the amount of computation, and a new kind of rectangular parts blank layout algorithm is designed for rectangular cutting stock problem. SGA is adopted to produce individuals within given evolution process, and the variation interval of these individuals is taken as initial domain of the next optimization process, thus shrinks searching range intensively and accelerates the evaluation process of SGA. To enhance the diversity of population and to avoid the algorithm stagnates at local optimization result, fixed number of individuals are produced randomly and replace the same number of parents in every evaluation process. According to the computational experiment, it is observed that this improved GA converges much sooner than SGA, and is able to get the balance of good result and high efficiency in the process of optimization for rectangular cutting stock problem.

Existence Results for m-Point Boundary Value Problem at Resonance with One-dimensional p-Laplacian

By using Mawhin＇s continuation theorem, the existence of a solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of this paper.

Dynamic Calibration of the Cutting Temperature Sensor of NiCr/NiSi Thin-film Thermocouple

In high-speed cutting, natural thermocouple, artificial thermocouple and infrared radiation temperature measurement are usually adopted for measuring cutting temperature, but these methods have difficulty in measuring transient temperature accurately of cutting area on account of low response speed and limited cutting condition. In this paper, NiCr/NiSi thin-film thermocouples（TFTCs） are fabricated according to temperature characteristic of cutting area in high-speed cutting by means of advanced twinned microwave electro cyclotron resonance（MW-ECR） plasma source enhanced radio frequency（RF） reaction non-balance magnetron sputtering technique, and can be used for transient cutting temperature measurement. The time constants of the TFTCs with different thermo-junction film width are measured at four kinds of sampling frequency by using Ultra-CFR short pulsed laser system that established. One-dimensional unsteady heat conduction model is constructed and the dynamic performance is analyzed theoretically. It can be seen from the analysis results that the NiCr/NiSi TFTCs are suitable for measuring transient temperature which varies quickly, the response speed of TFTCs can be obviously improved by reducing the thickness of thin-film, and the area of thermo-junction has little influence on dynamic response time. The dynamic calibration experiments are made on the constructed dynamic calibration system, and the experimental results confirm that sampling frequency should be larger than 50 kHz in dynamic measurement for stable response time, and the shortest response time is 0.042 ms. Measurement methods and devices of cutting heat and cutting temperature measurement are developed and improved by this research, which provide practical methods and instruments in monitoring cutting heat and cutting temperature for research and production in high-speed machining.

An efficient algorithm for multi-dimensional nonlinear knapsack problems

Multi-dimensional nonlinear knapsack problem is a bounded nonlinear integer programming problem that maximizes a separable nondecreasing function subject to multiple separable nondecreasing constraints. This problem is often encountered in resource allocation, industrial planning and computer network. In this paper, a new convergent Lagrangian dual method was proposed for solving this problem. Cutting plane method was used to solve the dual problem and to compute the Lagrangian bounds of the primal problem. In order to eliminate the duality gap and thus to guarantee the convergence of the algorithm, domain cut technique was employed to remove certain integer boxes and partition the revised domain to a union of integer boxes. Extensive computational results show that the proposed method is efficient for solving large-scale multi-dimensional nonlinear knapsack problems. Our numerical results also indicate that the cutting plane method significantly outperforms the subgradient method as a dual search procedure.

Surrogate dual method for multi-dimensional nonlinear knapsack problems

Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of problems. Multiply constrained problem was relaxed to a singly constrained problem by using the surrogate technique. To compute tighter bounds of the primal problem, the cutting plane method was used to solve the surrogate dual problem, where the surrogate relaxation problem was solved by the 0-1 linearization method. The domain cut technique was employed to eliminate the duality gap and thus to guarantee the convergence of tile algorithm. Numerical results were reported for large-scale multi-dimensional nonlinear knapsack problems.

On Merging Cover Inequalities for Multiple Knapsack Problems

This paper describes methods to merge two cover inequalities and also simultaneously merge multiple cover inequalities in a multiple knapsack instance. Theoretical results provide conditions under which merged cover inequalities are valid. Polynomial time algorithms are created to find merged cover inequalities. A computational study demonstrates that merged inequalities improve the solution times for benchmark multiple knapsack instances by about 9% on average over CPLEX with default settings.

CHEBYSHEV PSEUDOSPECTRAL DOMAIN DECOMPOSITION METHOD OF ONE－DIMENSIONAL ELLIPTIC PROBLEMS

This paper is devoted to the Chebyshev pseudospectral domain decomposition method of one-dimensional elliptic problems,it is easily applied to complex geometry.The approximate accuracy can be increased by increasing the order of approximation in fixed number of subdomains,rather than by resorting to a further partitioning.The stability and the convergence of this method are proved.

一维下料问题的快速计算方法研究

一维下料问题是实际工程中经常遇到的一类问题。从工程实际应用考虑,提出了一种针对多规格切割问题的计算方法。通过对原有的数学模型增加合理的约束条件,实现快速筛选合适的切割模式的目标,然后从选出的切割模式中求解出一维下料问题的近似最优解。通过一项实际工程中的下料案例,验证了该方法的准确性和可靠性,同时探讨了余料限值L 0和模式限值N C对计算结果的影响。计算表明,选取合适的L 0和N C可以获得很好的求解结果,切割材料的利用率可以达到97.9%。计算方法简单,计算速度快,节材效果明显,可以用于实际工程中的一维下料问题。

An entropy based central cutting plane algorithm for convex min-max semi-infinite programming problems

In this paper,we present a central cutting plane algorithm for solving convex min-max semi-infinite programming problems.Because the objective function here is non-differentiable,we apply a smoothing technique to the considered problem and develop an algorithm based on the entropy function.It is shown that the global convergence of the proposed algorithm can be obtained under weaker conditions.Some numerical results are presented to show the potential of the proposed algorithm.

树上限制性k-node multi-multiway cut问题的近似算法

k-node multi-multiway cut问题作为multicut问题和multiway cut问题的推广问题是NP难的。首先,将k-严格顶点覆盖归约到此问题说明该问题与k-严格顶点覆盖具有同样的近似值。其次,运用贪婪策略设计了近似值为k的算法。最后,运用线性规划的LP-rounding技术改进算法得到近似值为min{2(q-k+1),k}的多项式时间算法。

一般图上的限制性k node multi-multiway cut问题的启发式算法

限制性k node multi-multiway cut问题作为multiway cut问题的自然推广是NP难的。论文研究了一般图上的限制k node multi-multiway cut问题,首先用LP-relaxation和LP-rounding技术确定至少断开的k个终端集合,其次用改进的域增长技术将求得的分数解调整为整数解从而设计了该问题的一个启发式算法。

变压器硅钢片下料算法的设计与实现

针对中小型变压器生产流程中的硅钢片下料问题,结合工厂生产流程,设计排样算法,实现计算机辅助排样,提高工作效率和材料利用率。前期排样采用基于遗传算法的排样方式生成方法,利用遗传算法求得段宽度方向上的最优排样,确保宽度方向上的利用率,再根据当前段宽度上排入的片型计算段长度并生成排样方式。当剩余需求片型不满足遗传算法的适用条件时,转用线性规划算法完成所有剩余片的排样,线性规划模型以原材料消耗最少为目标函数,约束条件为排样方式段长度不大于原料卷长度且排样方式能满足剩余所有片型的需求。使用本文算法对相关文献中的硅钢片实例数据进行优化排样并与其他算法比较,结果表明使用本文算法生成的排样方案能够提高原材料利用率,且计算速度较快。

基于VNABC的多规格板材二维下料问题

针对二维下料问题板材单一的特点,研究了多规格板材二维下料问题。板材规格多样、毛坯规格多样且数量庞大,是NP(Non-deterministic Polynomial)完全问题。针对该问题的特点,将下料过程设计成规整和非规整两个阶段。规整阶段完成每种矩形毛坯的主体下料任务之后,如仍有毛坯剩余,则进入非规整阶段采用BL算法(Bottom Left Algorithm)下料剩余毛坯。根据模型特点,提出变邻域人工蜂群算法(VNABC),设计两种解码策略STD和SLD,并改进了VNABC算法的操作算子。最后,采用响应面分析法对VNABC算法进行参数标定。通过仿真实验将VNABC算法与遗传算法(GA)、改进粒子群优化算法(NUS)、模拟退火算法(SA)、人工蜂群算法(ABC)进行了对比分析,实验结果验证了VNABC解决多规格板材二维下料问题的优越性。

收送货同时的城市无人物流配送问题研究

随着节能减碳的需求和人工智能的快速发展,以无人电动车等为配送装置的城市无人物流配送渐成现实。本文考虑电池容量约束和取送货同时装载容量约束,以最小配送成本为目标函数构建数学规划模型(E-VRPSDP);以列生成法和双向动态标签算法为基础,设计了分支定价算法实现模型的精确求解;针对大规模E-VRPSDP,设计改进模拟退火算法,引入构造可行解算子,将原始解进化成符合约束的可行解,提高了算法的搜索能力;最后,利用已有标准测试集生成测试算例以验证所设计的算法。本文可以为城市无人物流配送的发展提供理论指导和算法支持。

MULTIPLICITY OF POSITIVE SOLUTIONS TO MULTIPOINT BOUNDARY VALUE PROBLEM WITH ONE-DIMENSIONAL p-LAPLACIAN

In this paper, we consider a multipoint boundary value problem for one-dimensional p-Laplacian. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the boundary value problem. In this problem, the nonlinear term explicitly involves a first-order derivative, which is different from some previous ones.

Approximation bounds for quadratic maximization and max-cut problems with semidefinite programming relaxation

In this paper,we consider a class of quadratic maximization problems.For a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the ratio is dependent on the data of the problem with α being a uniform lower bound.In light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α + δd if every weight is strictly positive,where δd ＞ 0 is a constant depending on the problem dimension and data.

大采高工作面端头静态胀裂切顶技术研究

大采高工作面回采过程中,端头后方顶板不易及时垮落。优选适应性高、安全高效的大采高工作面端头切顶技术与工艺,对于煤矿安全生产具有一定现实意义。通过对高效煤岩静态胀裂剂性能和现场工程应用实践的不断探索和深入,以大柳煤矿1405大采高工作面隅角悬顶问题为研究背景,采用高效煤岩静态胀裂切顶卸压技术,通过优化设计钻孔关键参数及数值模拟分析等技术手段,构建一套适用于大采高强矿压工作面的静态胀裂切顶技术与工艺,使端头顶板实现定向垮落。经实践表明,高效煤岩静态胀裂切顶卸压技术保证了顶板及时垮落,有效防止了端头处坚硬顶板悬顶距离过长对巷道内超前支护段造成强矿压影响。

森林采伐限额管理所面临的问题与建议

在我国现行《森林法》中明确提出了要采取森林采伐限额管理措施,在法律层面上规定了森林资源过量消耗控制方法,对实现森林可持续经营具有重要意义。本研究首先对森林采伐限额相关概念进行概述,然后指出了在采伐制度实施中出现的不足之处,并制定了有效改进手段,旨在不断完善森林采伐管理制度,让我国宝贵的森林资源得到有力保护,在经营过程中也达到科学化、规范化要求。