二维恒定各向同性介质渗透系数反演的遗传算法

给出了利用遗传算法求解二维恒定各项同性介质渗透系数反演的一种新方法,该方法把参数反演问题转化为优化问题通过遗传算法求解.数值模拟结果表明:该方法具有精度高、收敛速度快、编程简单、易于计算机实现等优点,值得在实际工作采用.     

基于最佳摄动量法反演浅水海湾水质模型的综合扩散系数

作为浅水海湾水质模型基本参数的综合扩散系数,常通过试算来率定,耗时、经验性强.该文应用渤海湾化学需氧量(COD)的部分监测资料,对污染物的综合扩散系数进行了反演.由于问题的非线性,结合正则化方法对求解过程的不适定性进行处理,应用算子识别摄动法进行求解.利用反演得到的综合扩散系数对渤海湾化学需氧量(COD)、无机氮(IN)、无机磷(IP)的分布进一步模拟,并与监测数据进行对比,结果表明反演的综合扩散系数是合理的.该方法还可用于反演水质模型中的其他参数.     

生物斑图中Gray-Scott模型的数值求解及参数反演

生物斑图中反应扩散模型数值解及其参数反演的研究是非常有趣和重要的.主要以生物斑图中Gray-Scott模型为研究对象,对其正、反问题进行研究,提出了一种新的算法-DE-ME算法,并通过数值算例模拟验证了其在求解Gray-Scott模型参数反演问题中的可行性及有效性.结果表明此混合算法能快速有效地解决此类反应扩散模型参数反演问题.     

求解波场变换反演问题的连续正则化方法

本文研究波场变换反演问题.利用连续正则化方法求解波场变换反演问题,构造展平泛函,基于已经正则化的变分问题用差分法作有限维逼近.利用偏差原理和Newton三阶迭代收敛格式选出最优的正则化参数,实施数值求解.通过对数值计算结果与已知波场函数对比,证明该方法的有效性和可行性.与离散正则化算法相比,本文的连续正则化算法具有保结构和收敛速度快等优点.     

改进的最佳摄动量法及在反问题中的应用

给出了改进的最佳摄动量法,并应用在双曲型方程参数反演问题的求解中.由遗传算法借助交叉和变异算子控制全局搜索来获得参数的初始迭代值,代入最佳摄动量法求解出稳定的高精度数值解.     

热传导(对流-扩散)方程源项识别的粒子群优化算法

提出了利用粒子群优化(PSO)算法反演热传导方程与对流-扩散方程源项的一种新方法,在已有文献方法的基础上,求解出这两类方程正问题的解析解,再把源项识别问题转化为最优化问题,结合粒子群优化算法寻优求解.通过数值模拟与统计检验,结果表明,此方法可快速有效地实现热传导方程与对流-扩散方程源项的识别,并可推广应用到其它数学物理方程的源项或参数的反演识别.     

非线性抛物型方程参数反问题数值求解的重心插值配点法

非线性抛物型方程的参数反演在工程技术领域具有重要的应用价值.但由于此类问题的非线性和不适定性,给求解带来了很大困难.本文主要利用重心插值配点法给出了求解一类非线性抛物型方程正问题的高精度数值解,在此基础上,根据某时刻在不同空间点和同一空间点在不同时刻的观测值,利用牛顿迭代正则化算法对其参数进行了反演,讨论了不同初始猜测以及数据随机扰动对该算法的影响,并给出了数值模拟,结果表明本文的方法可行且有效.     

用于寻源导热反问题的自适应蚁群算法研究

建立以蚁群算法(ant colony optimization,ACO)为基础的二维稳态导热反问题的求解模型.模型根据边界测点的测量信息与计算所得到的测点温度进行比较,将导热反问题转化为一个优化问题.对蚁群算法进行改进,利用不同路径构造方法的自适应蚁群算法对热源强度、热源位置进行反演,得到较为精确的反演结果.结果表明,所采用的蚁群算法和针对不同反演参数的路径构造方法具有较强的稳定性,能够较好反演热源强度及热源位置.     

基于时域精细积分算法的瞬态传热多宗量反演

基于有限元法和精细积分算法,提出了一种求解瞬态热传导多宗量反演问题的新方法．采用有限元法和精细积分算法分别对空间、时间变量进行离散,可以得到正演问题高精度的半解析数值模型,由此建立了多宗量反演的计算模式,并给出敏度分析的计算公式．对一维和二维的热物性参数、热源项、边界条件等进行了单宗量和多宗量的反演求解,初步考虑了初值和噪音等对反演结果的影响,数值算例验证了该方法的有效性．     

Mackey-Glass方程参数反演的微分进化算法及其灵敏度分析

本文研究了Mackey-Glass混沌时滞微分方程的参数反演问题.利用微分进化算法对其进行求解,并对参数的灵敏度进行了详细的分析,最后给出了数值模拟,结果表明了该算法的可行性与有效性.     

Invertibility of systems with unstable zero dynamics

We consider the problem of robust inversion of an uncertain dynamical system with unstable zero dynamics. The solution of the problem is reduced to estimating in real time the bounded solution of an unstable linear differential equation. Estimation algorithms are proposed for one- and two-output systems. Convergence of the inversion algorithms is assessed and the effect of observation errors on the algorithms, i.e., their robustness, is investigated.Translated from Nelineinaya Dinamika i Upravlenie, No. 2, pp. 33–40, 2002.     

A parameter-free self-adapting boundary genetic search for pipe network optimization

Commercial application of genetic algorithms (GAs) to engineering design problems, including optimal design of pipe networks, could be facilitated by the development of algorithms that require the least number of parameter tuning. This paper presents an attempt to eliminate the need for defining a priori the proper penalty parameter in GA search for pipe networks optimal designs. The method is based on the assumption that the optimal solution of a pipe network design problem lies somewhere on, or near, the boundary of the feasible region. The proposed method uses the ratio of the best feasible and infeasible designs at each generation to guide the direction of the search towards the boundary of the feasible domain by automatically adjusting the value of the penalty parameter. The value of the ratio greater than unity is interpreted as the search being performed in the feasible region and vice versa. The new adapted value of the penalty parameter at each generation is therefore calculated as the product of its current value and the aforementioned ratio. The genetic search so constructed is shown to converge to the boundary of the feasible region irrespective of the starting value of the constraint violation penalty parameter. The proposed method is described here in the context of pipe network optimisation problems but is equally applicable to any other constrained optimisation problem. The effectiveness of the method is illustrated with a benchmark pipe network optimization example from the literature.     

Construction of Invertible Input-Output Mappings and Parameter Identification

The problem of continuation of an input-output mapping to a right invertible mapping is solved. The proposed solution is based on transforming the system to a normal form and solving the problem for such systems. The well-known Singh inversion algorithm is modified to calculate the normal forms. It is proved that each step of the modified algorithm can be realized and the result of the algorithm application is a normal form. A new approach to the parameter identification problem based on the inversion of the input-output mapping is proposed to illustrate the application of the results.     

Inversion of polynomial and rational matrices

The inversion of polynomial and rational matrices is considered. For regular matrices, three algorithms for computing the inverse matrix in a factored form are proposed. For singular matrices, algorithms of constructing pseudoinverse matrices are considered. The algorithms of inversion of rational matrices are based on the minimal factorization which reduces the problem to the inversion of polynomial matrices. A class of special polynomial matrices is regarded whose inverse matrices are also polynomial matrices. Inversion algorithms are applied to the solution of systems with polynomial and rational matrices. Bibliography: 3 titles. Translated by V. N. Kublanovskaya. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 97–109.     

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。     

Algorithms for solving matrix polynomial equations of special form

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author’s work, concerning parameter identification of linear dynamic stochastic system. Special attention is given to searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.     

The eigenvalue problem for Hermitian matrices with time reversal symmetry

This paper describes a computational method for dealing with a class of matrices which arise in quantum mechanics involving time reversal and inversion symmetry. The algorithms presented here have greatly reduced the computational effort required to solve this problem and also produce a stable, more accurate solution.     

Value-Estimation Function Method for Constrained Global Optimization

A novel value-estimation function method for global optimization problems with inequality constraints is proposed in this paper. The value-estimation function formulation is an auxiliary unconstrained optimization problem with a univariate parameter that represents an estimated optimal value of the objective function of the original optimization problem. A solution is optimal to the original problem if and only if it is also optimal to the auxiliary unconstrained optimization with the parameter set at the optimal objective value of the original problem, which turns out to be the unique root of a basic value-estimation function. A logarithmic-exponential value-estimation function formulation is further developed to acquire computational tractability and efficiency. The optimal objective value of the original problem as well as the optimal solution are sought iteratively by applying either a generalized Newton method or a bisection method to the logarithmic-exponential value-estimation function formulation. The convergence properties of the solution algorithms guarantee the identification of an approximate optimal solution of the original problem, up to any predetermined degree of accuracy, within a finite number of iterations.     

Computational Solutions of Matrix Problems Over an Integral Domain

Recent methods for handling matrix problems over an integraldomain are investigated from a unifying point of view. Emphasizedare symbolic matrix inversion and numerically exact methodsfor solving Ax = b. New proofs are given for the theory of themultistep method. A proof for the existence and an algorithmfor the exact solution of Tx = b, where T is a finite Toeplitzmatrix, is given. This algorithm reduces the number of requiredsingle precision multiplications by a factor of order n overthe corresponding Gaussian elimination method. The use of residuearithmetic is enhanced by a new termination process. The matrixinversion problem with elements in the ring of polynomials isreduced to operations over a Galois field. It is shown thatinterpolation methods are equivalent to congruence methods withlinear modulus and that the Chinese remainder theorem over GF(x-p_k)is the Lagrange interpolation formula. With regard to the numerical problem of exact matrix inversion,the One- and Two-step Elimination methods are critically comparedwith the methods using modular or residue arithmetic. Formulasfor estimating maximum requirements for storage and timing ofthe salient parts of the algorithms are developed. The resultsof a series of recent tests, using existing codes, standardmatrices and matrices with random elements are reported andsummarized in tabular form. The paper concludes that the two-stepelimination method be used for the inversion problem of numericmatrices, and in particular when a black-box approach to thematrix inversion problem is attempted such as in commercialtime sharing systems. It is recommended that the inversion problemof matrices with elements over the polynomial ring be reducedto the numeric inversion problem with subsequent interpolation.An extensive Reference list is added.     

Positional robust inversion in nonlinear dynamical systems

The article studies robust inversion of nonlinear dynamical systems using a known phase vector. Inversion algorithms are proposed for the case when the system dynamics is exactly known. These algorithms solve the inversion problem with any prespecified accuracy. Algorithms solving the inversion problem with perturbed system dynamics are also considered. Accuracy bounds are obtained for the various algorithms. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 3, pp. 5–18, 2003.