INTERVAL ADJUSTABLE ENTROPY ALGORITHM FOR A CLASS OF UNCONSTRAINED DISCRETE MINIMAX PROBLEMS

In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function with adjustable entropy function.By constructing an interval extension of adjustable entropy function an d some region deletion test rules,a new interval algorithm is presented.The rele vant properties are proven.The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum entropy algorithm.Both theoretical and numerica l results show that the method is reliable and efficient.

An Interval Maximum Entropy Method for Quadratic Programming Problem

With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.

DYNAMIC ADVANCED PLANNING AND SCHEDULING WITH FROZEN INTERVAL FOR NEW ORDERS

A dynamic advanced planning and scheduling （DAPS） problem is addressed where new orders arrive on a continuous basis. A periodic policy with frozen interval is adopted to increase stability on the shop floor. A genetic algorithm is developed to find a schedule at each rescheduling point for both original orders and new orders that both production idle time and penalties on tardiness and earliness of orders are minimized. The proposed methodology is tested on a small example to illustrate the effect of the frozen interval. The results indicate that the suggested approach can improve the schedule stability while retaining efficiency.

Application of Interval Newton Method to Solve Nonlinear Equations and Global Optimization

The basic principle of interval arithmetic and the basic algorithm of the interval Newton methods are introduced.The prototype algorithm can not find any zero in an interval that has zero sometimes,that is,it is instable.So the prototype relaxation procedure is improved in this paper.Additionally,an immediate test of the existence of a solution following branch_and_bound is proposed,which avoids unwanted computations in those intervals that have no solution.The numerical results demonstrat that the improved interval Newton method is superior to prototype algorithm in terms of solution quality,stability and convergent speed.

Application of Interval Algorithm in Rural Power Network Planning

Rural power network planning is a complicated nonlinear optimized combination problem which based on load forecasting results, and its actual load is affected by many uncertain factors, which influenced optimization results of rural power network planning. To solve the problems, the interval algorithm was used to modify the initial search method of uncertainty load mathematics model in rural network planning. Meanwhile, the genetic/tabu search combination algorithm was adopted to optimize the initialized network. The sample analysis results showed that compared with the certainty planning, the improved method was suitable for urban medium-voltage distribution network planning with consideration of uncertainty load and the planning results conformed to the reality.

Interval Algorithm for a Kind of Nonsmooth Global Optimization

Based on the interval analysis,a practical interval algorithm is developed for finding all global minimizers of a nonsmooth function on a closed domain XR n, which is given by defining a special derivative to the function and using the interval inclusion of derivative. Both theoretical analysis and numerical results show that this method is practical and effective.

FWNN for Interval Estimation with Interval Learning Algorithm

In this paper, a wavelet based fuzzy neural network for interval estimation of processed data with its interval learning algorithm is proposed. It is also proved to be an efficient approach to calculate the wavelet coefficient.

Computational intelligence approach for uncertainty quantification using evidence theory

As an alternative or complementary approach to the classical probability theory,the ability of the evidence theory in uncertainty quantification（UQ） analyses is subject of intense research in recent years.Two state-of-the-art numerical methods,the vertex method and the sampling method,are commonly used to calculate the resulting uncertainty based on the evidence theory.The vertex method is very effective for the monotonous system,but not for the non-monotonous one due to its high computational errors.The sampling method is applicable for both systems.But it always requires a high computational cost in UQ analyses,which makes it inefficient in most complex engineering systems.In this work,a computational intelligence approach is developed to reduce the computational cost and improve the practical utility of the evidence theory in UQ analyses.The method is demonstrated on two challenging problems proposed by Sandia National Laboratory.Simulation results show that the computational efficiency of the proposed method outperforms both the vertex method and the sampling method without decreasing the degree of accuracy.Especially,when the numbers of uncertain parameters and focal elements are large,and the system model is non-monotonic,the computational cost is five times less than that of the sampling method.

Influence Analysis of Machining and Installation Errors on the Radial Stiffness of a Non-Pneumatic Mechanical Elastic Wheel

Machining and installation errors are unavoidable in mechanical structures. However, the effect of errors on radial stiffness of the mechanical elastic wheel(ME-Wheel) is not considered in previous studies. To this end, the interval mathematical model and interval finite element model of the ME-Wheel were both established and compared with bench test results. The intercomparison of the influence of the machining and installation errors on the ME-Wheel radial stiffness revealed good consistency among the interval mathematical analysis, interval finite element simulation,and bench test results. Within the interval range of the ME-Wheel machining and installation errors, parametric analysis of the combined elastic rings was performed at different initial radial rigidity values. The results showed that the initial radial stiffness of the flexible tire body significantly influenced the ME-Wheel radial stiffness, and the inverse relationship between the hinge unit length or suspension hub and the radial stiffness was nonlinear. The radial stiffness of the ME-Wheel is predicted by using the interval algorithm for the first time, and the regularity of the radial stiffness between the error and the load on the ME-Wheel is studied, which will lay the foundation for the exact study of the ME-Wheel dynamic characteristics in the future.

An Improved Underwater Acoustic Network Localization Algorithm

Underwater sensor network can achieve the unmanned environmental monitoring and military monitoring missions.Underwater acoustic sensor node cannot rely on the GPS to position itself,and the traditional indirect positioning methods used in Ad Hoc networks are not fully applicable to the localization of underwater acoustic sensor networks.In this paper,we introduce an improved underwater acoustic network localization algorithm.The algorithm processes the raw data before localization calculation to enhance the tolerance of random noise.We reduce the redundancy of the calculation results by using a more accurate basic algorithm and an adjusted calculation strategy.The improved algorithm is more suitable for the underwater acoustic sensor network positioning.

Improved interpolation method based on singular spectrum analysis iteration and its application to missing data recovery

A novel interval quartering algorithm （IQA） is proposed to overcome insufficiency of the conventional singular spectrum analysis （SSA） iterative interpolation for selecting parameters including the number of the principal components and the embedding dimension. Based on the improved SSA iterative interpolation, interpolated test and comparative analysis are carried out to the outgoing longwave radiation daily data. The results show that IQA can find globally optimal parameters to the error curve with local oscillation, and has advantage of fast computing speed. The improved interpolation method is effective in the interpolation of missing data.

New reconstruction and forecasting algorithm for TEC data

To reconstruct the missing data of the total electron content （TEC） observations, a new method is proposed, which is based on the empirical orthogonal functions （EOF） decomposition and the value of eigenvalue itself. It is a self-adaptive EOF decomposition without any prior information needed, and the error of reconstructed data can be estimated. The interval quartering algorithm and cross-validation algorithm are used to compute the optimal number of EOFs for reconstruction. The interval quartering algorithm can reduce the computation time. The application of the data interpolating empirical orthogonal functions （DINEOF） method to the real data have demonstrated that the method can reconstruct the TEC map with high accuracy, which can be employed on the real-time system in the future work.

Parallel Solutions for Large-Scale General Sparse Nonlinear Systems of Equations

In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of nonzero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner. To overcome this difficulty, we define a new storage scheme for general sparse matrices in this paper. With the new storage scheme, we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.In Section 1, we provide an introduction to the addressed problem and the interval Newton's methods. In Section 2, some currently used storage schemes for sparse sys-terns are reviewed. In Section 3, new index schemes to store general sparse matrices are reported. In Section 4, we present a parallel algorithm to evaluate a general sparse Jarobian matrix. In Section 5, we present a parallel algorithm to solve the correspond-ing interval linear 8ystem by the all-row preconditioned scheme. Conclusions and future work are discussed in Section 6.