Weibull分布下基于遗传算法的设备寿命预测

本文研究了Weibull分布下设备可靠性寿命预测的问题.利用改进后的遗传算法,主要是对遗传算法编码、目标函数和遗传操作的改进,实现对Weibull参数的估计.获得了Weibull分布模型和设备的可靠性寿命模型.     

一种基于自适应混合遗传算法的非线性函数优化方法

遗传算法因其具有的特性,它采用交换、复制和突变等方法,获取的解为全局最优解,而且无需计算函数的导数,是一种只考虑输入与输出关系的黑箱问题,适用于处理各种复杂问题.此文基于最优保存的思想,把最速下降法与最优保存和自适应遗传算法相结合,用于求解非线性函数优化问题,提出一种基于自适应混合遗传算法的非线性函数全局优化方法.     

遗传算子的代数形式和概率特征

采用矩阵形式表示遗传操作过程 ,可为设计遗传算法程序提供简单的数学模型 .遗传操作的概率特征 ,揭示了遗传算子各自在遗传优化过程中的作用及相互关系 .     

不确定环境下再制造生产调度研究

针对再制造过程中存在的再制造件质量状况和加工时间不确定性调度问题,分别采用随机数和三角模糊数表示质量状况和加工时间的不确定性。在满足工序顺序、机器等限制下,将各自带有权重系数的最大完工时间和总成本之和最小值当做目标函数,构造不确定环境下再制造生产调度模糊模型且转换成确定的单目标非线性规划模型。应用多层编码遗传算法求解某个再制造子系统算例得到,决策者对于最大完工时间和总成本的重视程度不同,调度方案不同,其需要根据自身关注的重点做出决策,选择合适的调度方案。并且调度结果会受到决策者消极或积极态度的影响,态度越积极,结果越好,反之,态度越消极,结果越差,从而检验了再制造生产调度模型的正确性。希望为再制造实现产业化,规模化提供相关参考意见。     

基于“货到人”拣选模式的储位分配问题研究

研究了“货到人”拣选模式下的储位分配问题,以订单拣选过程中搬运货架总时间最短为目标建立了整数非线性规划模型,并证明其为NP-hard问题,分别设计了求解模型的贪婪算法和单亲进化遗传算法。首先根据订单和物品的关联关系对物品进行聚类,基于聚类结果设计了求解模型的贪婪算法。然后设计了直接求解模型的单亲进化遗传算法,遗传算法中采用了0-1矩阵编码、多点基因倒位算子、单点基因突变算子和精英保留等策略,通过合理选取参数,能够很快求解出问题的近似最优解。最后利用模拟算例和一个具体实例进行计算,并对贪婪算法和遗传算法的求解时间和求解效果进行了比较分析。结果显示,对于小规模问题,两种算法均能在较短的时间内以很高的概率得到问题的全局最优解,对于中等规模的实际问题,利用两种算法得到的储位分配方案均优于企业目前采取的基于出库频率的储位分配方案,遗传算法得到的储位分配方案对应的货架搬运次数、货架搬运总时间等均优于贪婪算法。本文设计的遗传算法可以作为智能仓库管理信息系统的核心算法。     

An improved determination approach to the structure and parameters of dynamic structure-based neural networks

Dynamic structure-based neural networks are being extensively applied in many fields of science and engineering. A novel dynamic structure-based neural network determination approach using orthogonal genetic algorithm with quantization is proposed in this paper. Both the parameter (the threshold of each neuron and the weight between neurons) and the transfer function (the transfer function of each layer and the network training function) of the dynamic structure-based neural network are optimized using this approach. In order to satisfy the dynamic transform of the neural network structure, the population adjustment operation was introduced into orthogonal genetic algorithm with quantization for dynamic modification of the population’s dimensionality. A mathematical example was applied to evaluate this approach. The experiment results suggested that this approach is feasible, correct and valid.     

Precise evaluation of a polynomial at a point given in staggered correction format

The problem of the evaluation in floating-point arithmetic of a polynomial with floating-point coefficients at a point which is a finite sum of floating-point numbers is studied. The solution is obtained as an infinite convergent series of floating-point numbers. The algorithm requires a precise scalar product, but this can always be implemented by software in a high-level language without assembly language routines as we indicate. A convergence result is proved under a very weak restriction on the size of the degree of the polynomial in terms of the unit roundoff u; roughly speaking, the degree should not be larger than the square root of (1 + u)(2u). Even in the particular case when the point at which to evaluate the polynomial reduces to one floating-point number, we find a new simplified algorithm among the whole family that the preceding convergence result allows.

This problem occurs, among others, in the convergence of the Newton method to some real root of the given polynomial p. If we simply use the Horner scheme to evaluate the polynomial p in a neighbourhood of the root, in some cases the evaluation will contain no correct digits and will prevent us from getting convergence even to machine accuracy. The convergence of iterative methods, among which the Newton method, with added perturbations was the central theme of my talk given at the ICCAM'92. The second part will appear in a forthcoming paper. These added perturbations can represent for example forward or backward errors occurring in finite-precision computations.

The problem discussed here appears in validating some hypotheses of these general convergence results (see the forthcoming paper).     

航线联盟下航空货运网络枢纽点选址问题研究

本文研究航空联盟下航空货运网络的枢纽点选址问题(HLP),基于枢纽点的数量及位置随机与容量的限制。首先引入航线联盟选择概率函数,确定不同航段上的航线自营运输或外包运输的概率;其次根据选址中心法则,以网络总成本最小化为目标,建立枢纽点选址模型;再次采用改进的免疫混沌遗传算法求解模型;最后,以顺丰航空公司案例进行实例分析。结果表明:1)本文改进的算法较免疫混沌遗传算法并与免疫遗传算法及CPLEX结果对比,发现本文设计的算法有较强的收敛性和计算速度,且计算结果与CPLEX求解器求解结果相差不大;2)枢纽点数量不确定时,枢纽点的位置多集中在东部城市;3)航空公司选择联盟环境可以大大降低运营成本,航空公司为提高自身利润,应考虑加入联盟,从而降低自身成本。     

Effects of diversity control in single-objective and multi-objective genetic algorithms

This paper covers an investigation on the effects of diversity control in the search performances of single-objective and multi-objective genetic algorithms. The diversity control is achieved by means of eliminating duplicated individuals in the population and dictating the survival of non-elite individuals via either a deterministic or a stochastic selection scheme. In the case of single-objective genetic algorithm, onemax and royal road R ₁ functions are used during benchmarking. In contrast, various multi-objective benchmark problems with specific characteristics are utilised in the case of multi-objective genetic algorithm. The results indicate that the use of diversity control with a correct parameter setting helps to prevent premature convergence in single-objective optimisation. Furthermore, the use of diversity control also promotes the emergence of multi-objective solutions that are close to the true Pareto optimal solutions while maintaining a uniform solution distribution along the Pareto front.     

Overflow, Underflow, and Severe Loss of Significance in Floating-Point Addition and Subtraction

In this paper it is shown that, under the assumption of thelogarithmic distribution of numbers, floating-point additionand subtraction can result in overflow or underflow with alarmingfrequency—a frequency that increases rapidly with machinespeed unless the range of the exponent is also increased. Ifnumbers are assumed to be distributed in accordance with Sweeney's(1965) experiments, then severe loss of significance occurswith large probability in floating point subtraction. Theseresults have implications for computer design and lead to thesuggestion of a long word format which will reduce the risksto acceptable levels.     

LOOK: A Lazy Object-Oriented Kernel design for geometric computation

In this paper we describe and discuss a new kernel design for geometric computation in the plane. It combines different kinds of floating-point filter techniques and a lazy evaluation scheme with the exact number types provided by LEDA allowing for efficient and exact computation with rational and algebraic geometric objects.

It is the first kernel design which uses floating-point filter techniques on the level of geometric constructions.

The experiments we present—partly using the CGAL framework—show a great improvement in speed and—maybe even more important for practical applications—memory consumption when dealing with more complex geometric computations.     

Schemata, Distributions and Graphical Models in Evolutionary Optimization

In this paper the optimization of additively decomposed discrete functions is investigated. For these functions genetic algorithms have exhibited a poor performance. First the schema theory of genetic algorithms is reformulated in probability theory terms. A schema defines the structure of a marginal distribution. Then the conceptual algorithm BEDA is introduced. BEDA uses a Boltzmann distribution to generate search points. From BEDA a new algorithm, FDA, is derived. FDA uses a factorization of the distribution. The factorization captures the structure of the given function. The factorization problem is closely connected to the theory of conditional independence graphs. For the test functions considered, the performance of FDA—in number of generations till convergence—is similar to that of a genetic algorithm for the OneMax function. This result is theoretically explained.     

考虑潮汐影响的离散型泊位和岸桥集成调度

泊位和岸桥是集装箱港口最紧缺的资源,二者的调度问题存在很强的内在关联。针对大型船需乘潮进出港的离散型泊位,为提高集装箱码头运作效率和客户满意度,将泊位分配、岸桥指派和岸桥调度集成为一体。首先,考虑潮汐的影响以及岸桥作业中可动态调度的现实,以计划期内所有抵港船舶的岸桥作业成本和滞期成本之和最少为目标,建立一个混合整数规划模型,然后设计了一个嵌入启发式规则的遗传算法对其进行求解。最后,算例结果中给出了每艘船舶在确切时刻对应的具体岸桥和每个岸桥的动态作业时间窗,并通过与单独优化的方案对比,验证了集成方案的有效性。     

A fuzzy goal programming approach to multi-objective optimization problem with priorities

In goal programming problem, the general equilibrium and optimization are often two conflicting factors. This paper proposes a generalized varying-domain optimization method for fuzzy goal programming (FGP) incorporating multiple priorities. According to the three possible styles of the objective function, the varying-domain optimization method and its generalization are proposed. This method can generate the results consistent with the decision-maker (DM)’s expectation, that the goal with higher priority may have higher level of satisfaction. Using this new method, it is a simple process to balance between the equilibrium and optimization, and the result is the consequence of a synthetic decision between them. In contrast to the previous method, the proposed method can make that the higher priority achieving the higher satisfactory degree. To get the global solution of the nonlinear nonconvex programming problem resulting from the original problem and the varying-domain optimization method, the co-evolutionary genetic algorithms (GAs), called GENOCOPIII, is used instead of the SQP method. In this way the DM can get the optimum of the optimization problem. We demonstrate the power of this proposed method by illustrative examples.     

概率因果模型结合改进遗传算法的核动力系统故障分析

将概率因果模型的似然函数作为遗传算法的适应函数,从而将复杂系统的故障诊断转化为最优问题,建立了一种将概率因果模型和遗传算法相结合的故障诊断方法,并利用改进算法与概率因果故障诊断模型对船用核动力装置进行故障诊断实例分析,分析结果对船用核动力装置故障诊断具有重要的指导意义,而改进遗传算法是进行船用核动力装置故障诊断有效而实用的方法。     

Mean Convergence Time of Inhomogeneous Genetic Algorithm with Elitism

The theoretical study of a genetic algorithm (GA) has focused mainly on establishing its convergence in probability and almost always to the global optimum. In this article, we establishsufficient conditions for the finiteness of convergence mean time of the genetic algorithm with elitism. We obtain bounds for the probability of convergence to the global optimum in the first n iterations as a by-product.     

Roundoff errors in floating-point summation

All possible schemes for the calculation of the sum ofn addends by means ofn–1 floating-point additions is considered and in case of positive addends it is shown how to use the Huffman algorithm to choose a scheme to obtain the least upper bound on the accumulated roundoff error in the result.     

Estimation of 1-dimensional nonlinear stochastic differential equations based on higher-order partial differential equation numerical scheme and its application

A method based on higher-order partial differential equation (PDE) numerical scheme are proposed to obtain the transition cumulative distribution function (CDF) of the diffusion process (numerical differentiation of the transition CDF follows the transition probability density function (PDF)), where a transformation is applied to the Kolmogorov PDEs first, then a new type of PDEs with step function initial conditions and 0, 1 boundary conditions can be obtained. The new PDEs are solved by a fourth-order compact difference scheme and a compact difference scheme with extrapolation algorithm. After extrapolation, the compact difference scheme is extended to a scheme with sixth-order accuracy in space, where the convergence is proved. The results of the numerical tests show that the CDF approach based on the compact difference scheme to be more accurate than the other estimation methods considered; however, the CDF approach is not time-consuming. Moreover, the CDF approach is used to fit monthly data of the Federal funds rate between 1983 and 2000 by CKLS model.     

Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications

This paper is concerned with accurate matrix multiplication in floating-point arithmetic. Recently, an accurate summation algorithm was developed by Rump et al. (SIAM J Sci Comput 31(1):189–224, 2008). The key technique of their method is a fast error-free splitting of floating-point numbers. Using this technique, we first develop an error-free transformation of a product of two floating-point matrices into a sum of floating-point matrices. Next, we partially apply this error-free transformation and develop an algorithm which aims to output an accurate approximation of the matrix product. In addition, an a priori error estimate is given. It is a characteristic of the proposed method that in terms of computation as well as in terms of memory consumption, the dominant part of our algorithm is constituted by ordinary floating-point matrix multiplications. The routine for matrix multiplication is highly optimized using BLAS, so that our algorithms show a good computational performance. Although our algorithms require a significant amount of working memory, they are significantly faster than ‘gemmx’ in XBLAS when all sizes of matrices are large enough to realize nearly peak performance of ‘gemm’. Numerical examples illustrate the efficiency of the proposed method.     

A Differential Free Point Generation Scheme in the Differential Evolution Algorithm

In this paper we derive the probability distribution of trial points in the differential evolution (de) algorithm, in particular the probability distribution of points generated by mutation. We propose a point generation scheme that uses an approximation to this distribution. The scheme can dispense with the differential vector used in the mutation of de. We propose a de algorithm that replaces the differential based mutation scheme with a probability distribution based point generation scheme. We also propose a de algorithm that uses a probabilistic combination of the point generation by the probability distribution and the point generation by mutation. A numerical study is carried out using a set of 50 test problems, many of which are inspired by practical applications. Numerical results suggest that the new algorithms are superior to the original version both in terms of the number of function evaluations and cpu times.