Mixed Approximation Scheme of the Finite-Element Method for the Solution of Two-Dimensional Problems of the Elasticity Theory

For the solution of two-dimensional boundary-value problems of the elasticity theory, a triangular finite element, ensuring stability and convergence of mixed approximation, is proposed. The system of resolving equations of the mixed method is derived with account of strict satisfaction of static boundary conditions at the surface. To solve matrix equations of the mixed method, various algorithms of the conjugate-gradient method with the pre-conditional matrix have been considered. Numerical data on convergence and accuracy of the solution for a number of test problems of the elasticity theory and fracture mechanics are given. The results obtained by the conventional and mixed finite-element method approaches are compared.     

求解实对称矩阵区间特征值问题的直接优化法

提出了一种用于对称区间矩阵特征值问题求解的直接优化法。将区间矩阵中为区间量的各元素作为优化设计变量,将区间量的分布区间作为相应的设计变量的边界约束,运用约束优化法求出区间矩 最大特征值和最小特征值,从而获得区间矩阵特征值问题的解。本文提出的直接优化法适用于对称区间矩阵的标准特征值问题和广义特征值问题。文中给出的两个计算实例显示了该法的有效性。     

Solving Pseudo-Convex Mixed Integer Optimization Problems by Cutting Plane Techniques

In the present paper a cutting plane approach to solve mixed-integer non-linear programming (MINLP) problems, containing pseudo-convex functions, is given. It is shown how valid cutting planes for pseudo convex functions can be obtained and, furthermore, it is shown how a class of non-convex MINLP problems with a pseudo-convex objective function and pseudo-convex constraints, can be solved to global optimality with the considered cutting plane technique. Finally the numerical efficiency of the procedure, when solving some example problems, is illustrated.     

凹二次规划问题的一个融合割平面方法的分支定界混合算法

把割平面方法融于分支定界方法之中,本文提出了求解凹二次规划问题的一个融合割平面方法的分支定界混合算法,证明了该算法是收敛的.数值例子也表明这个算法是有效的,并且好于单纯形分支定界算法。     

Concurrent Implementation of the Optimal Incremental Approximation Method for the Adaptive and Meshless Solution of Differential Equations

The optimal incremental function approximation method is implemented for the adaptive and meshless solution of differential equations. The basis functions and associated coefficients of a series expansion representing the solution are selected optimally at each step of the algorithm according to appropriate error minimization criteria. Thus, the solution is built incrementally. In this manner, the computational technique is adaptive in nature, although a grid is neither built nor adapted in the traditional sense using a posteriori error estimates. Since the basis functions are associated with the nodes only, the method can be viewed as a meshless method. Variational principles are utilized for the definition of the objective function to be extremized in the associated optimization problems. Complicated data structures, expensive remeshing algorithms, and systems solvers are avoided. Computational efficiency is increased by using low-order local basis functions and the parallel direct search (PDS) optimization algorithm. Numerical results are reported for both a linear and a nonlinear problem associated with fluid dynamics. Challenges and opportunities regarding the use of this method are discussed.     

Enhanced Heap-Based Optimizer Algorithm for Solving Team FormationProblem

Team Formation (TF) is considered one of the most significant problems in computer science and optimization. TF is defined as forming the best team of experts in a social network to complete a task with least cost. Many real-world problems, such as task assignment, vehicle routing, nurse scheduling, resource allocation, and airline crew scheduling, are based on the TF problem. TF has been shown to be a Nondeterministic Polynomial time (NP) problem, and high-dimensional problem with several local optima that can be solved using efficient approximation algorithms. This paper proposes two improved swarm-based algorithms for solving team formation problem. The first algorithm, entitled Hybrid Heap-Based Optimizer with Simulated Annealing Algorithm (HBOSA), uses a single crossover operator to improve the performance of a standard heap-based optimizer (HBO) algorithm. It also employs the simulated annealing (SA) approach to improve model convergence and avoid local minima trapping. The second algorithm is the Chaotic Heap-based Optimizer Algorithm (CHBO). CHBO aids in the discovery of new solutions in the search space by directing particles to different regions of the search space. During HBO’s optimization process, a logistic chaotic map is used. The performance of the two proposed algorithms (HBOSA) and (CHBO) is evaluated using thirteen benchmark functions and tested in solving the TF problem with varying number of experts and skills. Furthermore, the proposed algorithms were compared to well-known optimization algorithms such as the Heap-Based Optimizer (HBO), Developed Simulated Annealing (DSA), Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), and Genetic Algorithm (GA). Finally, the proposed algorithms were applied to a real-world benchmark dataset known as the Internet Movie Database (IMDB). The simulation results revealed that the proposed algorithms outperformed the compared algorithms in terms of efficiency and performance, with fast convergence to the global minimum.     

An Enhanced Formulation of the Maximum Entropy Method for Structural Optimization

A numerical optimization method was proposed time ago by Templeman based on the maximum entropy principle. That approach combined the Kuhn-Tucker condition and the information theory postulates to create a probabilistic formulation of the optimality criteria techniques. Such approach has been enhanced in this research organizing the mathematical process in a single optimization loop and linearizing the constraints. It turns out that such procedure transforms the optimization process in a sequence of systems of linear equations which is a very efficient way of obtaining the optimum solution of the problem. Some examples of structural optimization, namely, a planar truss, a spatial truss and a composite stiffened panel, are presented to demonstrate the capabilities of the methodology.     

Mixed Fourier-Jacobi Spectral Method for Two-Dimensional Neumann Boundary Value Problems

In this paper, we propose a mixed Fourier-Jacobi spectral method for two dimensional Neumann boundary value problem. This method differs from the classical spectral method. The homogeneous Neumann boundary condition is satisfied exactly. Moreover, a tridiagonal matrix is employed, instead of the full stiffness matrix encountered in the classical variational formulation. For analyzing the numerical error, we establish the mixed Fourier-Jacobi orthogonal approximation. The convergence of proposed scheme is proved. Numerical results demonstrate the efficiency of this approach.     

Iteration Algorithms for Solving Boundary-Value Problems of the Theory of Small Elastic-Plastic Strains on the Basis of the Mixed Finite Element Method

A mixed projection-mesh scheme has been formulated for the solution of nonlinear boundary-value problems of the theory of small elastic-plastic strains in displacements, strains, and stresses. Iteration algorithms of the solution of nonlinear equations of the mixed method have been considered. Numerical results of the solution of two model problems are presented. The data obtained on the basis of the classical and mixed finite element methods are compared.__________Translated from Problemy Prochnosti, No. 3, pp. 111 – 127, May – June, 2005.     

AMBO: All Members-Based Optimizer for Solving Optimization Problems

There are many optimization problems in different branches of science that should be solved using an appropriate methodology. Population-based optimization algorithms are one of the most efficient approaches to solve this type of problems. In this paper, a new optimization algorithm called All Members-Based Optimizer (AMBO) is introduced to solve various optimization problems. The main idea in designing the proposed AMBO algorithm is to use more information from the population members of the algorithm instead of just a few specific members (such as best member and worst member) to update the population matrix. Therefore, in AMBO, any member of the population can play a role in updating the population matrix. The theory of AMBO is described and then mathematically modeled for implementation on optimization problems. The performance of the proposed algorithm is evaluated on a set of twenty-three standard objective functions, which belong to three different categories: unimodal, high-dimensional multimodal, and fixed-dimensional multimodal functions. In order to analyze and compare the optimization results for the mentioned objective functions obtained by AMBO, eight other well-known algorithms have been also implemented. The optimization results demonstrate the ability of AMBO to solve various optimization problems. Also, comparison and analysis of the results show that AMBO is superior and more competitive than the other mentioned algorithms in providing suitable solution.     

一类求解带随机成本的生产运输问题的线性逼近方法

生产和运输集成计划问题在许多工业工程领域都普遍存在。要给出最优的生产和运输计划就必须考虑实际工业管理过程中存在的不确定性因素。本文研究了生产厂家的生产能力、商家的需求量和单位运输成本等因素为随机变量情况下的产品生产与运输成本问题,建立了该类问题的随机优化模型。在一定的假设条件下,推导了所建模型的确定等价类。基于问题的结构特征,提出了求解生产和运输计划的一种线性逼近方法,数值例子表明该种方法的应用前景。     

Mixed Projection-Mesh Scheme of the Finite-Element Method for the Solution of Problems of the Elasticity Theory

A mixed projection-mesh scheme for solving the boundary-value problems of the elasticity theory has been formulated. Correctness and convergence of the mixed approximations for strains and displacements are studied. Application of the numerical integration has been analyzed, and the obtained results are given. The theory of generalized functions and the functional analysis methods have been used for the convergence and accuracy estimates. Iteration algorithms for solving the discrete problems have been proposed.     

求解变分不等式的非单调混合Newton算法

本文运用广义D-间隙函数可以将变分不等式问题转化为一个无约束最优化问题,即极小化广义D-间隙函数的一般形式gαβ,基于非单调线搜索技术提出一种非单调混合Newton算法,并给出了算法的全局收敛性分析.在适当条件下,证明了算法具有全局二次收敛性.同时在映射F强单调但不需要Lipschitz连续的情况下,为算法提供了一个全局误差界.数值结果表明新算法是有效的.     

Analysis-of-Marginal-Tail-Means (ATM): A Robust Method for Discrete Black-Box Optimization

Abstract

We present a new method, called analysis-of-marginal-tail-means (ATM), for effective robust optimization of discrete black-box problems. ATM has important applications in many real-world engineering problems (e.g., manufacturing optimization, product design, and molecular engineering), where the objective to optimize is black-box and expensive, and the design space is inherently discrete. One weakness of existing methods is that they are not robust: these methods perform well under certain assumptions, but yield poor results when such assumptions (which are difficult to verify in black-box problems) are violated. ATM addresses this by combining both rank- and model-based optimization, via the use of marginal tail means. The trade-off between rank- and model-based optimization is tuned by first identifying important main effects and interactions from data, then finding a good compromise which best exploits additive structure. ATM provides improved robust optimization over existing methods, particularly in problems with (i) a large number of factors, (ii) unordered factors, or (iii) experimental noise. We demonstrate the effectiveness of ATM in simulations and in two real-world engineering problems: the first on robust parameter design of a circular piston, and the second on product family design of a thermistor network.     

求解约束优化问题的改进布谷鸟搜索算法

为了提高约束优化问题的求解精度和收敛速度,提出求解约束优化问题的改进布谷鸟搜索算法。首先分析了基本布谷鸟搜索算法全局搜索和局部搜索过程中的不足,对其中全局搜索和局部搜索迭代公式进行重新定义,然后以一定概率在最优解附近进行搜索。对12个标准约束优化问题和4个工程约束优化问题进行测试并与多种算法进行对比,实验结果和统计分析表明所提算法在求解约束优化问题上具有较强的优越性。     

泡沫衬垫缓冲性能模型参数混合优化方法

有一类模型参数,由于取值间不明确,目标函数不属显函数,目标函数计算工作量大,采用通常优化方法很难求解。研究提出一种利用知识信息识别模型参数的混合优化方法。该方法用于识别泡沫塑料包装衬垫缓冲性能模型参数时十分有效。     

解梁的平衡方程的混合有限体积元方法

针对梁的平衡方程导出了一类混合有限体积元格式，并用非常直观的方法证明了该格式按离散H^1半模及离散L^2模具有一阶精度。最后，具体算例表明，该算法计算效果良好。     

An Integrated Optimization Model for Inventory and Quality Control Problems

In this paper, we develop an integrated economic model for inventory and quality control problems, extending the work of Rahim ( IIE Transactions 1994; 26(6): 2–11) and Rahim and Ben-Daya (IJPR 1998; 36(1): 277–289). The production process is subject to an assignable cause which shifts the process from an in-control state to an out-of-control state. We consider the shifts in both the process mean and the process variance. When a signal for an assignable cause is triggered, a search is initiated and is terminated upon finding the cause within a pre-specified target time. The process is then brought back to an in-control state by repair. However, if the assignable cause is not discovered within the pre-specified time, production is allowed to continue until the next sampling or warning, whichever occurs first. In this case, either the alarm is considered to be false with a probability of Type I error, or the assignable cause has not been eliminated with a probability of Type II error. In the latter case, the process produces products in an out-of-control state until the next sampling or warning, whichever occurs first. However, this state does not indicate any severe damage to the system. Joint X and R charts are used for monitoring both process mean and variance. Under these conditions, a generalized economic model for the joint determination of production quantity, an inspection schedule, and the design of the X and R control charts are developed. A direct search optimization method is used to determine the optimal decision variables of the economic model.     

求解包装生产中复杂问题的布谷鸟算法改进

目的 为了解决在求解复杂的高维函数优化问题时存在的求解精度不够高和易陷入局部最优等问题,提出一种基于莱维飞行发现概率的变步长布谷鸟搜索算法(LFCS).方法 在相同环境下,选取6个不同难度、不同类型的测试函数,将LFCS算法与IPSO,IDE,IABC,CS算法比较,分析算法的收敛速度和收敛精度.结果 相比其他4种算法,LFCS算法迭代次数更少,收敛速度更快,收敛精度更高.结论 无论是低维函数还是高维函数,LFCS算法在收敛速度和收敛精度方面都有所提高,尤其是针对复杂的高维函数优化问题,在取值范围较大的情况下,LFCS算法能够更快、更准地找到最优解.