An efficient labeling technique for solving sparse assignment problems

We describe a new implementation of the shortest augmenting path approach for solving sparse assignment problems and report computational experience documenting its efficiency.     

An algorithm for solving multi-point boundary value problems

We describe a method for computing solutions of multi-point boundary value problems, where the polychotomic structure of the underlying solution space is specifically exploited. After the system is integrated in a multiple shooting way, the resulting linear system is solved by a special decoupling algorithm that takes into account the fact that the dichotomy on each interval is potentially different (in contrast to the two point case). A number of examples sustains the theory.     

A Method for Nonlinear Least Squares With Structured Residuals

This note develops a modification of standard nonlinear least squares methods with reduced sensitivity to the quality of the initial guess. The technique is presented in the context of least squares fitting of dynamic system models, but may apply to other kinds of problems. The performance of the technique is compared to standard methods for a variety of test problems.     

An efficient algorithm for solving constrained nonlinear programming problems

This paper discusses the basis for an efficient technique which transforms a general constrained nonlinear programming problem to a single unconstrained problem. The theoretical considerations are first presented. This is followed by a development of the algorithm. Lastly, an illustrated example is given to demonstrate the methodology.     

时序数据的非线性最小二乘迭代分解算法

从时序数据中精确地分解出趋势、周期及随机噪声等数据成分，能有助于人们掌握事物在演变过程中所蕴藏的内在规律.基于非线性最小二乘法，提出一种性能更为高效的时序数据分解算法。首先，基于关键转折点和趋势导数的方法从待分解序列中概要地析出各种不同的数据成分，然后，分别利用多项式函数、正弦谐波级数及自回归模型对相应的数据成分进行拟合，最后，在加法模型中迭代求解各种数据成分的非线性最小二乘参数。实验表明，新设计的算法在分解精度和计算成本等指标上均优于现有的算法。     

非线性系统辨识的改进双对角化最小二乘算法

本文提出了一种新的有效的非线性系统最小二乘辨识算法－－改进的双对角化最小二乘（ＭＢＬＳ）算法，在存在舍入误差的条件下，给出了算法的收敛性证明，事实上，算法的收敛性几何不受舍入误差的影响，算法是大范围数值稳定的，仿真结果说明了新算法的有效性。     

An improved firefly algorithm for solving dynamic multidimensional knapsack problems

There is a wide range of publications reported in the literature, considering optimization problems where the entire problem related data remains stationary throughout optimization. However, most of the real-life problems have indeed a dynamic nature arising from the uncertainty of future events. Optimization in dynamic environments is a relatively new and hot research area and has attracted notable attention of the researchers in the past decade. Firefly Algorithm (FA), Genetic Algorithm (GA) and Differential Evolution (DE) have been widely used for static optimization problems, but the applications of those algorithms in dynamic environments are relatively lacking. In the present study, an effective FA introducing diversity with partial random restarts and with an adaptive move procedure is developed and proposed for solving dynamic multidimensional knapsack problems. To the best of our knowledge this paper constitutes the first study on the performance of FA on a dynamic combinatorial problem. In order to evaluate the performance of the proposed algorithm the same problem is also modeled and solved by GA, DE and original FA. Based on the computational results and convergence capabilities we concluded that improved FA is a very powerful algorithm for solving the multidimensional knapsack problems for both static and dynamic environments.     

求解高维优化问题的改进正弦余弦算法*

提出一种改进的正弦余弦算法(简记为ISCA)。受粒子群优化(PSO)算法的启发,引入惯性权重以提高正弦余弦算法的收敛精度和加快收敛速度。此外,采取反向学习策略产生初始个体以提高种群的多样性和解的质量。采用8个高维基准测试函数进行仿真实验：在相同的最大适应度函数评价次数下,ISCA总体性能上均优于基本SCA算法和HGWO算法;当维数较高(D=1000)时,ISCA所用计算量远小于HDEOO。实验结果表明ISCA在收敛精度和收敛速度指标上均优于对比算法。     

求解大规模优化问题的改进麻雀搜索算法

针对麻雀搜索算法在求解大规模优化问题时存在收敛速度慢、寻优精度低和易陷入局部极值的缺点,提出一种基于精英反向学习策略的萤火虫麻雀搜索算法(ELFASSA).首先,通过反向学习策略初始化种群,为全局寻优奠定基础;其次,利用萤火虫扰动策略提高算法跳出局部最优的能力并加速收敛;最后,在麻雀位置更新后引入精英反向学习策略以获取精英解及动态边界,使精英反向解可以定位在狭窄的搜索空间中,有利于算法收敛.通过选取10个高维标准测试函数进行仿真实验,将其与麻雀搜索算法(SSA)及4种先进的改进算法进行性能对比,并与3种单一策略改进的麻雀搜索算法进行改进策略的有效性分析,仿真结果表明, ELFASSA算法在收敛速度和求解精度两方面明显优于其他对比算法.     

两种新的有效的非线性系统最小二乘辨识算法

提出了两种新的有效的最小二乘算法--改进的双对角化最小二乘算法MBLS-Ⅰ与MBLS-Ⅱ.在存在舍入误差的条件下,证明了算法的收敛性.该算法具有几乎不受舍入误差影响的优点,优于一般常用的最小二乘算法.包括数值性态极佳的SVD算法.同时,基于该算法及SVD算法,构造出了一种新的NARMAX模型结构与参数辨识的一体化算法.仿真结果证明了此新算法的优越性.     

Fast Nonlinear Least Squares Optimization of Large-Scale Semi-Sparse Problems

Many problems in computer graphics and vision can be formulated as a nonlinear least squares optimization problem, for which numerous off-the-shelf solvers are readily available. Depending on the structure of the problem, however, existing solvers may be more or less suitable, and in some cases the solution comes at the cost of lengthy convergence times. One such case is semi-sparse optimization problems, emerging for example in localized facial performance reconstruction, where the nonlinear least squares problem can be composed of hundreds of thousands of cost functions, each one involving many of the optimization parameters. While such problems can be solved with existing solvers, the computation time can severely hinder the applicability of these methods. We introduce a novel iterative solver for nonlinear least squares optimization of large-scale semi-sparse problems. We use the nonlinear Levenberg-Marquardt method to locally linearize the problem in parallel, based on its first-order approximation. Then, we decompose the linear problem in small blocks, using the local Schur complement, leading to a more compact linear system without loss of information. The resulting system is dense but its size is small enough to be solved using a parallel direct method in a short amount of time. The main benefit we get by using such an approach is that the overall optimization process is entirely parallel and scalable, making it suitable to be mapped onto graphics hardware (GPU). By using our minimizer, results are obtained up to one order of magnitude faster than other existing solvers, without sacrificing the generality and the accuracy of the model. We provide a detailed analysis of our approach and validate our results with the application of performance-based facial capture using a recently-proposed anatomical local face deformation model.     

基于最小二乘支持向量机的非线性均衡

从支持向量机(SupportVectorMachine,SVM)学习理论出发,介绍了最小二乘支持向量机(LeastSquaresSupportVectorMachine,LS-SVM)的原理[1],并详细描述了使用共轭梯度(ConjugateGradient,CG)算法来实现LS-SVM。结合通信中常见的非线性均衡问题,讨论了在信道呈现非线性,色噪声干扰情况下,使用LS-SVM实现均衡任务,通过同最优贝叶斯均衡器性能的比较,证明了LS-SVM处理非线性均衡问题的有效性。在实际数字通信中,接收端可以在不知道信道状态的前提下,通过接收训练序列并对其进行学习,确定均衡器模型参数,从而对未知的发送信号进行预测。     

An effective hybrid harmony search-based algorithm for solving multidimensional knapsack problems

This study presents an effective hybrid algorithm based on harmony search (HHS) for solving multidimensional knapsack problems (MKPs). In the proposed HHS algorithm, a novel harmony improvisation mechanism is developed with the modified memory consideration rule and the global-best pitch adjustment scheme to enhance the global exploration. A parallel updating strategy is employed to enrich the harmony memory diversity. To well balance the exploration and the exploitation, the fruit fly optimization (FFO) scheme is integrated as a local search strategy. For solving MKPs, binary strings are used to represent solutions and two repair operators are applied to guarantee the feasibility of the solutions. The HHS is calibrated based on the Taguchi method of design-of-experiment. Extensive numerical investigations based on well-known benchmark instances are conducted. The comparative evaluations indicate the HHS is much more effective than the existing HS and FFO variants in solving MKPs.     

应用改进区块遗传算法求解置换流水车间调度问题

针对最小化最大完工时间的置换流水车间调度问题，提出一种将遗传算法与蚁群算法相结合的改进区块遗传算法。算法利用随机机制和改进反向学习机制相结合的方式产生初始解，以兼顾初始种群的多样性和质量。通过若干代简单遗传算法操作产生精英群体，借鉴蚁群算法中利用蚂蚁信息度浓度统计路径和节点信息的思想，对精英群体所携带信息进行统计分析并建立位置信息素矩阵和相依信息素矩阵，根据两矩阵挖掘区块并将区块与非区块组合形成染色体。将染色体进行切段与重组，以提高染色体的质量，使用二元竞赛法保留适应度较高的染色体。算法通过Reeves实例和Taillard实例进行测试，并将结果与其他算法进行比较，验证了该算法的有效性。     

An effective L-MONG algorithm for solving multi-objective flow-shop inverse scheduling problems

Generally, in handling traditional scheduling problems, ideal manufacturing system environments are assumed before determining effective scheduling. Unfortunately, “ideal environments” are not always possible. Real systems often encounter some uncertainties which will change the status of manufacturing systems. These may cause the original schedule to no longer to be optimal or even feasible. Traditional scheduling methods are not effective in coping with these cases. Therefore, a new scheduling strategy called “inverse scheduling” has been proposed to handle these problems. To the best of our knowledge, this research is the first to provide a comprehensive mathematical model for multi-objective permutation flow-shop inverse scheduling problem (PFISP). In this paper, first, a PFISP mathematical model is devised and an effective hybrid multi-objective evolutionary algorithm is proposed to handle uncertain processing parameters (uncertainties) and multiple objectives at the same time. In the proposed algorithm, we take an insert method NEH-based (Nawaz–Enscore–Ham) as a local improving procedure and propose several adaptations including efficient initialization, decimal system encoding, elitism and population diversity. Finally, 119 public problem instances with different scales and statistical performance comparisons are provided for the proposed algorithm. The results show that the proposed algorithm performs better than the traditional multi-objective evolution algorithm (MOEA) in terms of searching quality, diversity level and efficiency. This paper is the first to propose a mathematical model and develop a hybrid MOEA algorithm to solve PFISP in inverse scheduling domain.     

An artificial bee colony-least square algorithm for solving harmonic estimation problems

Solving harmonic estimation problems in power quality signals has attained significant importance in recent times. Stochastic optimization algorithms have been successfully employed to determine magnitude of this information in an unknown signal contaminated with noise or containing additive dc decaying components. The present paper shows how a recently proposed stochastic optimization algorithm, called artificial bee colony algorithm, can be hybridized with least square algorithm to solve these problems effectively. The proposed algorithm has been tested for a series of case studies employing different benchmark environment situations and our extensive simulation tests validate the usefulness of the proposed algorithm and it could largely outperform several competing simulation algorithms, proposed in the recent past. The effectiveness of the proposed algorithm is further demonstrated for those situations where the number of harmonics present in the signal is also not known, along with the magnitude and phase of each harmonic.     

一种求解约束优化问题的混合算法

提出一种基于修改增广Lagrange函数和PSO的混合算法用于求解约束优化问题。将约束优化问题转化为界约束优化问题,混合算法由两层迭代结构组成,在内层迭代中,利用改进PSO算法求解界约束优化问题得到下一个迭代点。外层迭代主要修正Lagrange乘子和罚参数,检查收敛准则是否满足,重构下次迭代的界约束优化子问题,检查收敛准则是否满足。数值实验结果表明该混合算法的有效性。