差分进化算法在旅行商问题中的应用

为了解决旅行商在实际应用过程中存在的离散差值及求解问题,研究差分进化算法在旅行商问题中的应用。通过差分粗粒度并行预处理,构建交叉进化运算层级,建立迭代旅行商离散矩阵,设计无线差分积累应用模型,完成C2Opt算子重复排序,设定逆向旅行域的同时,采用迭代进化完成旅行商问题的应用。测试结果表明:设计算法的规划线路数相对较多,可以达到21条方案,对旅行路线规划的最优解更加可靠、精准。

A Class of Nonlocal Boundary Value Problems for Elliptic Systems in Unbounded Domains

A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied.

On the hydrodynamic stability of a particle-laden flow in growing flat plate boundary layer

The parabolized stability equation (PSE) was derived to study the linear stability of particle-laden flow in growing Blasius boundary layer. The stability characteristics for various Stokes numbers and particle concentrations were analyzed after solving the equation numerically using the perturbation method and finite difference. The inclusion of the nonparallel terms produces a reduction in the values of the critical Reynolds number compared with the parallel flow. There is a critical value for the effect of Stokes number, and the critical Stokes number being about unit, and the most efficient instability suppression takes place when Stokes number is of order 10. But the presence of the nonparallel terms does not affect the role of the particles in gas. That is, the addition of fine particles (Stokes number is much smaller than 1) reduces the critical Reynolds number while the addition of coarse particles (Stokes number is much larger than 1) enhances it. Qualitatively the effect of nonparallel mean flow is the same as that for the case of plane parallel flows.

Some new bound estimates of the Hermitian positive definite solutions of the nonlinear matrix equation X^s+ A~*X^(-t) A = Q

The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.

Determination of minimum cover depth for shallow tunnel subjected to water pressure

Prediction of the state of roof collapse is a big challenge in tunnel engineering, while the limit analysis theory makes it possible to derive the analytical solutions of the collapse mechanisms. In this work, an exact solution of collapsing shape in shallow underwater tunnel is obtained by using the variation principle and the upper bound theorem based on nonlinear failure criterion. Numerical results under the effect of river water and supporting pressure are derived and discussed. The maximum water depth above the river bottom surface is determined under a given buried depth of shallow cavities and the critical depth of roof collapse is obtained under a constant river depth. In comparison with the previous results, the present solution shows a good agreement with the practical results.

NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.

Homoclinic orbits of first order discrete Hamiltonian systems with super linear terms

In this paper we consider the first order discrete Hamiltonian systems {x1（n＋1）-x1（n）=Hx2（n,x（n））,x2（n）-x2（n-1）=Hx1（n,x（n））,where x（n） = （x2（n）x1（n））∑ R^2N, H（n,z） = 1/2S（n）z. z ＋ R（n,z） is periodic in n and superlinear as {z} →4 ∞. We prove the existence and infinitely many （geometrically distinct） homoclonic orbits of the system by critical point theorems for strongly indefinite functionals.

ROBUST ATTITUDE CONTROL OF A 3DOF HELICOPTER WITH MULTI-OPERATION POINTS

A 3DOF (three degrees of freedom) helicopter attitude control system with multi-operationpoints is described as a MIMO time-varying uncertain nonlinear system with unknown constant param-eters,bounded disturbance and nonlinear uncertainty,and a robust output feedback control methodbased on signal compensation is proposed.A controller designed by this method consists of a nominalcontroller and a robust compensator.The controller is linear time-invariant and can be realized easily.Robust attitude tracking property of closed-loop system is proven and experimental results show thatthe designed control system can guarantee high precision robust attitude control under multi-operationpoints.

The random walking method for the steady linear convection-diffusion equation with axisymmetric disc boundary

In this article,the random walking method is used to solve the steady linear convection-diffusion equation(CDE)with disc boundary condition.The integral solution corresponding to the random walking method is deduced and the relationship between the diffusion coefficient of CDE and the intensity of the random diffusion motion is obtained.The random number generator for arbitrary axisymmetric disc boundary is deduced through the polynomial fitting and inverse transform sampling method.The proposed method is tested through two numerical cases.The results show that the random walking method can solve the steady linear CDE effectively.The influence of the parameters on the results is also studied.It is found that the error of the solution can be decreased by increasing the particle releasing rate and the total walking time.

Physical implication of two problems in transition prediction of boundary layers based on linear stability theory

Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which the growth rate of the disturbance is to be integrated.The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable.However,unlike the saddle point method applied to water waves,here its physical meaning is not so obvious,as the frequency and wave number may be complex.And on some occasions,in advancing the integration of the growth rate of the disturbance,up to a certain location,one may not be able to continue the integration,because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number.In this paper,these two problems are discussed,and suggestions for how to do transition prediction under the latter condition are provided.

EXPONENTIAL ESTIMATES FOR STOCHASTIC DELAY EQUATIONS WITH NORM-BOUNDED UNCERTAINTIES

This paper presents the sufficient conditions for the exponential stability of linear or semi-linear stochastic delay equations with time-varying norm bounded parameter uncertainties.Exponen-tial estimates for the solutions are also obtained by using a modified Lyapunov-Krasovski functional.These conditions can be tested numerically using interior point algorithms.