单台机器E-T随机排序问题的多项式算法

本文研究排序问题中的E—T问题，工件在单台机器上加工，n个工件的加工时间都为整数P，相同的工期d为离散分布，满足∑i=1^mP（d=ξi）=1,其中ξ为整数，目标是使E（∑（Ei＋Tj））的期望值最小。应用贪婪算法和二分法思想，我们提出解决该问题的一个最优算法，并得出该算法的复杂性为O（nmlogp）。     

求解无容量设施选址问题的拉格朗日蝙蝠算法

无容量设施选址问题(Uncapacitated Facility Location Problem,UFLP)是一类经典的组合优化问题,被证明是一种NP-hard问题,易于描述却难于求解.首先根据UFLP的数学模型及其具体特征,重新设计了蝙蝠算法的操作算子,给出了求解UFLP的蝙蝠算法.其次构建出三种可行化方法,并将其与求解UFLP的蝙蝠算法和拉格朗日松弛算法相结合,设计了求解该问题的拉格朗日蝙蝠算法.最后通过仿真实例和与其他算法进行比较的方式,验证了该混合算法用来求解UFLP的可行性,是解决离散型问题的一种有效方式.     

正态云模型果蝇优化算法及其应用

提出了一种基于正态云模型的果蝇优化算法(NCMFOA).该算法通过直接将果蝇位置赋值给气味浓度判定值和引入正态云模型来刻画果蝇嗅觉搜索行为的随机性与模糊性,从而解决了果蝇优化算法(FOA)不能搜索负值空间的缺陷,并有效克服了FOA算法在解决复杂优化问题时容易陷入局部极值的不足.通过正态云模型熵值的动态调整,使得NCMFOA算法在进化的前期阶段具有较强的随机性与模糊性,以提高算法的全局探索能力;随着迭代次数的增加,算法搜索行为的随机性与模糊性逐渐减弱,使得其局部开发能力逐渐增强,算法收敛精度得到提高.此外,通过引入视觉实时更新方案,进一步加速了算法的收敛速度.用经典的基准测试函数验证了NCMFOA算法的可行性与有效性,结果表明该算法具有收敛速度快、收敛精度高以及鲁棒性好等优点,对于高维复杂优化问题,该算法同样获得了良好的优化效果.将NCMFOA算法用于解决混沌系统的参数估计问题,进一步验证了该算法具有较强的解决实际工程优化问题的能力.     

混料模型D—最优试验设计的改进DE算法研究

差分进化算法(Differential Evolution Algorithm)有较强的全局收敛能力和稳健性,应用该算法可解决工程学、计算机科学等领域的一些复杂优化问题。本文介绍一个改进DE算法,该算法适用于混料模型的近似最优设计问题,对于具有附加约束试验域的混料问题也可高效求解。最后,本文给出应用改进DE算法求解混料模型D-最优试验设计的例子。     

线性规划基于预-校正的组合同伦多项式算法

本文针对线性规划问题提出了一个新的内点方法——组合同伦内点方法，并采用预估校正算法来跟踪组合同伦路径从而得到问题的ε-解.最后讨论了该算法的收敛性，并证明了该算法为多项式算法。     

基于乌鸦喝水的元启发式优化算法

启发式优化算法已成为求解复杂优化问题的一种有效方法,可用于解决传统的优化方法难以求解的问题.受乌鸦喝水寓言故事启发,提出一种新型元启发式优化算法—乌鸦喝水算法,首先建立了乌鸦喝水算法数学模型;其次,给出实现该算法的详细步骤;最后,将该算法用于基准函数优化,并将该算法与乌鸦搜索算法、粒子群优化算法、多元宇宙优化算法、花授粉算法、布谷鸟算法等群智能算法进行了比较.仿真实验结果表明,乌鸦喝水算法优于其他算法.     

鞍点问题的修正对称超松弛迭代算法

为了提高求解鞍点问题的迭代算法的速度,通过设置合适的加速变量,对修正超松弛迭代算法（简记作MSOR-like算法）和广义对称超松弛迭代算法（简记作GSSOR-like算法）进行了修正,给出了修正对称超松弛迭代算法,即MSSOR-like （modified symmetric successiveover-relaxation）算法,并研究了该算法收敛的充分必要条件.最后,通过数值例子表明,选择合适的参数后,新算法的迭代速度和迭代次数均优于MSOR-like （modified successive overrelaxation）和GSSOR-like （generalized symmetric successive over-relaxation）算法,因此,它是一种较好的解决鞍点问题的算法.     

求解一类约束优化问题的Newton分裂算法

本文给出了求解一类约束优化问题的一个Newton分裂算法，并证明了算法的局部平方收敛性，该算法与已有算法相比，具有计算量小的特点，因而特别适合于求解大规模问题，为进一步降低算法的计算复杂性，我们结合Broyden算法，给出了两类Broyden类分裂算法。     

结点有约束的交通网络最短路径模型

结点有约束的网络是一类特殊的网络，如具有禁止通行限制信息的交通路网等，由于最短路径的求解是有后效性的，经典的Dijkstra算法等不能直接用来求解该问题，本文提出了一种结点有约束的交通网络最短路径建模方法，该方法所建模型为一般网络模型，可用任一传统高效的算法求其最短路径，从根本上降低了问题的复杂性，为很好地解决交通、通信等领域中的此类问题提供了有益的方法。     

基于速度越界处理与高斯扰动的改进蝙蝠算法

蝙蝠算法(Bat algorithm,BA)是一种新型的、搜索全局最优解的元启发式算法.为解决蝙蝠算法局部搜索时易陷入局部极值的问题,提出一种基于速度越界处理与高斯扰动的改进蝙蝠算法(VGBA).该算法利用速度的越界处理控制蝙蝠位置更新的范围,利用高斯扰动增强蝙蝠算法的全局搜索能力.选取8个测试问题进行数值实验,实验结果表明,VGBA算法在收敛精度和稳定性上比BA算法有显著提升.     

Local and Parallel Finite Element Algorithms for Eigenvalue Problems

Abstract Some new local and parallel finite element algorithms are proposed and analyzed in this paper foreigenvalue problems.With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced tothe solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraicsystems on fine grid by using some local and parallel procedure.A theoretical tool for analyzing these algorithmsis some local error estimate that is also obtained in this paper for finite element approximations of eigenvectorson general shape-regular grids.     

基于特殊混料模型D-最优设计搜索的交换点式门限接受算法

在搜索混料模型D-最优设计的计算机算法领域,主流算法包括经典的Fedorov算法,以及元启发类算法,但两者在一些特定的优化问题上,分别在收敛速度和收敛精度方面有进一步提升的空间.文章分别探讨了可能造成这种情况的两类算法各自的局限性,并采取优势互补的策略,构建了交换点式门限接受算法,即ETA (exchange threshold accepting)算法.以含倒数项混料模型为例,文章验证了ETA算法生成设计的D-最优性,并分别与Fedorov算法和元启发类的ProjPSO算法作比较.结果表明,至少在某些特殊的混料模型D-最优设计的搜索方面,ETA算法在收敛速度和精度方面均具有一定的优势.     

Column generation decomposition with the degenerate constraints in the subproblem

In this paper, we propose a new Dantzig–Wolfe decomposition for degenerate linear programs with the non degenerate constraints in the master problem and the degenerate ones in the subproblem. We propose three algorithms. The first one, where some set of variables of the original problem are added to the master problem, corresponds to the Improved Primal Simplex algorithm (IPS) presented recently by Elhallaoui et al. [7]. In the second one, some extreme points of the subproblem are added as columns in the master problem. The third algorithm is a mixed implementation that adds some original variables and some extreme points of a subproblem to the master problem. Experimental results on some degenerate instances show that the proposed algorithms yield computational times that are reduced by an average factor ranging from 3.32 to 13.16 compared to the primal simplex of CPLEX.     

Gbest-guided artificial bee colony algorithm for numerical function optimization

Artificial bee colony (ABC) algorithm invented recently by Karaboga is a biological-inspired optimization algorithm, which has been shown to be competitive with some conventional biological-inspired algorithms, such as genetic algorithm (GA), differential evolution (DE) and particle swarm optimization (PSO). However, there is still an insufficiency in ABC algorithm regarding its solution search equation, which is good at exploration but poor at exploitation. Inspired by PSO, we propose an improved ABC algorithm called gbest-guided ABC (GABC) algorithm by incorporating the information of global best (gbest) solution into the solution search equation to improve the exploitation. The experimental results tested on a set of numerical benchmark functions show that GABC algorithm can outperform ABC algorithm in most of the experiments.     

装箱问题的算法及最新进展

装箱问题在经济社会发展中扮演着重要的角色,该问题研究的是寻找较好的布局方式,尽可能实现利益的最大化.装箱问题具有NP-难性质,其理论和应用研究存在一定的挑战,但因其有广泛的应用背景而受到研究者高度的关注.本文主要总结近几十年来装箱问题的研究成果,特别针对一维、二维和三维单目标装箱问题和算法,以及多目标装箱问题的算法进行概括和总结,并提出装箱问题算法上有待进一步的研究工作.     

关于销售集团投资设置销售分店问题的IP模型

针对一个实际投资实例建立了一个基于 0 -1背包问题的数学模型 ,并利用多个算法加以求解 ,并对结果进行了比较 .该模型具有很高的应用价值和参考价值 .     

A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem

One of the most fundamental results in combinatorial optimization is the polynomial-time 3/2-approximation algorithm for the metric traveling salesman problem. It was presented by Christofides in 1976 and is well known as “the Christofides algorithm”. Recently, some authors started calling it “Christofides-Serdyukov algorithm”, pointing out that it was published independently in the USSR in 1978. We provide some historic background on Serdyukov's findings and a translation of his article from Russian into English.     

混沌遗传算法对BP神经网络的改进研究

BP神经网络算法是目前应用最广泛的一种神经网络算法,但有收敛速度慢和易陷入局部极小值等缺陷.本文利用混沌遗传算法(CGA)具有混沌运动遍历性、遗传算法反演性的特性来改进BP神经网络算法.该算法的基本思想是用混沌遗传算法对BP神经网络算法的初始权值和初始阈值进行优化.把混沌变量加入遗传算法中,提高遗传算法的全局搜索能力和收敛速度;用混沌遗传算法优化后得到的最优解作为BP神经网络算法的初始权值和阈值.通过实验观察,改进后的结果与普通的BP神经网络算法的结果相比,具有更高的准确率.     

An Evolutionary Approach to Spatial Fuzzy c-Means Clustering

Fuzzy c-means clustering algorithm (FCM) can provide a non-parametric and unsupervised approach to the cluster analysis of data. Several efforts of fuzzy clustering have been undertaken by Bezdek and other researchers. Earlier studies in this field have reported problems due to the setting of optimum initial condition, cluster validity measure, and high computational load. More recently, the fuzzy clustering has benefited of a synergistic approach with Genetic Algorithms (GA) that play the role of an useful optimization technique that helps to better tolerate some classical drawbacks, such as sensitivity to initialization, noise and outliers, and susceptibility to local minima. We propose a genetic-level clustering methodology able to cluster objects represented by R ^p spaces. The unsupervised cluster algorithm, called SFCM (Spatial Fuzzy c-Means), is based on a fuzzy clustering c-means method that searches the best fuzzy partition of the universe assuming that the evaluation of each object with respect to some features is unknown, but knowing that it belongs to circular regions of R ² space. Next we present a Java implementation of the algorithm, which provides a complete and efficient visual interaction for the setting of the parameters involved into the system. To demonstrate the applications of SFCM, we discuss a case study where it is shown the generality of our model by treating a simple 3-way data fuzzy clustering as example of a multicriteria optimization problem.