A method of estimating computational complexity based on input conditions for N-vehicle problem

This paper proposes a method of estimating computational complexity of problem through analyzing its input condition for N-vehicle exploration problem. The N-vehicle problem is firstly formulated to determine the optimal replacement in the set of permutations of 1 to N. The complexity of the problem is factorial of N （input scale of problem）. To balance accuracy and efficiency of general algorithms, this paper mentions a new systematic algorithm design and discusses correspondence between complexity of problem and its input condition, other than just putting forward a uniform approximation algorithm as usual. This is a new technique for analyzing computation of NP problems. The method of corresponding is then presented. We finally carry out a simulation to verify the advantages of the method： 1） to decrease computation in enumeration; 2） to efficiently obtain computational complexity for any N-vehicle case; 3） to guide an algorithm design for any N-vehicle case according to its complexity estimated by the method.     

A new iterative method for many eigenpair partial derivatives

A new iterative method is proposed for computing partial derivatives of many eigenpairs. This method simultaneously computes a few eigenpair partial derivatives. For each origin shift, partial derivatives of eigenpairs whose eigenvalues are closest to the origin shift can be computed. Hence, this method may be used for partial derivatives of all eigenpairs. Convergence of the proposed method is established. Finally numerical experiments are given to show the effectiveness of the proposed method.     

A new error estimation approach based on fuzzy logic system for H-R adaptive boundary element method

Conventional adaptive boundary element method cannot be universally applied to solve many more problems than the subject it discussed, and different error estimation formulas need to be designed for varied problems. This paper put forward a new error analysis method based on the fuzzy logic system, which is able to make error estimation effectively using human expert experience, and solve the two classical elasticity problems in conjunction with the H-R adaptive boundary element method. Numerical examples have illustrated the effectiveness, superiority and potential of a fuzzy logic approach in the adaptive boundary element method.     

A new approach for the optimal distribution of assemblies in a nuclear reactor

Summary. The aim of this paper is to propose a new approach for optimizing the position of fuel assemblies in a nuclear reactor core. This is a control problem for the neutronic diffusion equation where the control acts on the coefficients of the equation. The goal is to minimize the power peak (i.e. the neutron flux must be as spatially uniform as possible) and maximize the reactivity (i.e. the efficiency of the reactor measured by the inverse of the first eigenvalue). Although this is truly a discrete optimization problem, our strategy is to embed it in a continuous one which is solved by the homogenization method. Then, the homogenized continuous solution is numerically projected on a discrete admissible distribution of assemblies. Received January 13, 2000 / Published online February 5, 2001     

A new tree method for pricing financial derivatives in a regime-switching mean-reverting model

This paper develops a new tree method for pricing financial derivatives in a regime-switching mean-reverting model. The tree achieves full node recombination and grows linearly as the number of time steps increases. Conditions for non-negative branch probabilities are presented. The weak convergence of the discrete tree approximations to the continuous regime-switching mean-reverting process is established. To illustrate the application in mathematical finance, the recombining tree is used to price commodity options and zero-coupon bonds. Numerical results are provided and compared.     

A method for estimating interpolating polynomials

The question of obtaining a lower bound for some interpolating polynomials is considered. Under specific conditions it is proved that these bounds are sharp. As a corollary of the general theorem, under specific restrictions on the points of interpolation, lower bounds for Goncharov interpolation polynomials are obtained which coincide with known upper bounds.Translated from Matematicheskie Zametki, Vol. 17, No. 4, pp. 555–561, April, 1975.     

A new approach based on the surrogating method in the project time compression problems

This paper develops a mathematical model for project time compression problems in CPM/PERT type networks. It is noted this formulation of the problem will be an adequate approximation for solving the time compression problem with any continuous and non-increasing time-cost curve. The kind of this model is Mixed Integer Linear Program (MILP) with zero-one variables, and the Benders' decomposition procedure for analyzing this model has been developed. Then this paper proposes a new approach based on the surrogating method for solving these problems. In addition, the required computer programs have been prepared by the author to execute the algorithm. An illustrative example solved by the new algorithm, and two methods are compared by several numerical examples. Computational experience with these data shows the superiority of the new approach.     

Noise correction in gene expression data: a new approach based on subspace method

We present a new approach for removing the nonspecific noise from Drosophila segmentation genes. The algorithm used for filtering here is an enhanced version of singular spectrum analysis method, which decomposes a gene profile into the sum of a signal and noise. Because the main issue in extracting signal using singular spectrum analysis procedure lies in identifying the number of eigenvalues needed for signal reconstruction, this paper seeks to explore the applicability of the new proposed method for eigenvalues identification in four different gene expression profiles. Our findings indicate that when extracting signal from different genes, for optimised signal and noise separation, different number of eigenvalues need to be chosen for each gene. Copyright © 2016 John Wiley & Sons, Ltd.     

A Tikhonov regularization method for Cauchy problem based on a new relaxation model

In this paper, we consider a Cauchy problem of recovering both missing value and flux on inaccessible boundary from Dirichlet and Neumann data measured on the remaining accessible boundary. Associated with two mixed boundary value problems, a regularized Kohn-Vogelius formulation is proposed. With an introduction of a relaxation parameter, the Dirichlet boundary conditions are approximated by two Robin ones. Compared to the existing work, weaker regularity is required on the Dirichlet data. This makes the proposed model simpler and more efficient in computation. A series of theoretical results are established for the new reconstruction model. Several numerical examples are provided to show feasibility and effectiveness of the proposed method. For simplicity of the statements, we take Poisson equation as the governed equation. However, the proposed method can be applied directly to Cauchy problems governed by more general equations, even other linear or nonlinear inverse problems.     

A moments based distribution bounding method

We present a numerical procedure to bound distributions based on their finite number of moments. Numerical examples demonstrate the properties of the proposed method.     

A new approach for solving stokes systems arising from a distributive relaxation method

The distributed relaxation method for the Stokes problem has been advertised as an adequate change of variables that leads to a lower triangular system with Laplace operators on the main diagonal for which multigrid methods are very efficient. We show that under high regularity of the Laplacian, the transformed system admits almost block‐lower triangular form. We analyze the distributed relaxation method and compare it with other iterative methods for solving the Stokes system. We also present numerical experiments illustrating the effectiveness of the transformation which is well established for certain finite difference discretizations of Stokes problems. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 898–914, 2011     

Fractal methods and the problem of estimating scaling exponents: A new approach based on upper and lower linear bounds

The characterization of irregular objects with fractal methods often leads to the estimation of the slope of a function which is plotted versus a scale parameter. The slope is usually obtained with a linear regression. The problem is that the fit is usually not acceptable from the statistical standpoint. We propose a new approach in which we use two straight lines to bound the data from above and from below. We call these lines the upper and lower linear bounds. We propose to define these bounds as the solution of an optimization problem. We discuss the solution of this problem and we give an algorithm to obtain its solution. We use the difference between the upper and lower linear bounds to define a measure of the degree of linearity in the scaling range. We illustrate our method by analyzing the fluctuations of the variogram in a microresistivity well log from an oil reservoir in the North Sea.     

New method for estimating survival curves based upon subpopulations

The overall Kaplan-Meier estimate of the survival curve underlying a study population does not individually account for the ages at which patients were first seen and thence followed up in the study. Since the number of patients in these age-specific subgroups varies quite arbitrarily for a given study, the overall Kaplan-Meier curve which assumes that all patients were seen from the beginning of the study usually either overestimates or underestimates the survival probability, depending on the varying sample sizes. In this paper, we therefore propose an estimate of the overall survival curve underlying a study population based on the individual age-specific Kaplan-Meier estimates and the probability distribution of the age at which patients were first seen in the study. In the particular case when there is no censoring, it is shown that the usual overall Kaplan-Meier survival curve which assumes that all patients irrespective of their age at entry into the study were followed from the beginning of the study is identical with the proposed estimate. This result does not seem to necessarily hold good in the presence of arbitrary censoring. Further, the estimate is unbiased and consistent, a property which the Kaplan-Meier estimate also enjoys. The efficiency of the proposed estimate relative to the Kaplan-Meier estimate is being investigated and will be reported along with results of its application in a separate communication.     

A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method

In this paper, we propose the THESEUS method, a new approach based on fuzzy outranking relations to multi-criteria sorting problems. Compared with other outranking-based methods, THESEUS is inspired by another view of multi-criteria classification problems. It utilizes a new way of evaluating the assignment of an object to an element of the set of ordered categories that were previously defined. This way is based on comparing every possible assignment with the information from various preference relations that are derived from a fuzzy outranking relation defined on the universe of objects. The appropriate assignment is determined by solving a simple selection problem.The capacity of a reference set for making appropriate assignments is related to a good characterization of the categories. A single reference action characterizing a category may be insufficient to achieve well-determined assignments. In this paper, the reference set capacity to perform appropriate assignments is characterized by some new concepts. This capacity may be increased when more objects are added to the reference set. THESEUS is a method for handling the preference information contained in such larger reference sets.     

A smoothing Newton method for second-order cone optimization based on a new smoothing function

A new smoothing function is given in this paper by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this new smoothing function, we present a smoothing Newton method for solving the second-order cone optimization (SOCO). The method solves only one linear system of equations and performs only one line search at each iteration. Without requiring strict complementarity assumption at the SOCO solution, the proposed algorithm is shown to be globally and locally quadratically convergent. Numerical results demonstrate that our algorithm is promising and comparable to interior-point methods.     

A shift sequence based approach for nurse scheduling and a new benchmark dataset

This paper investigates an adaptive constructive method for solving nurse rostering problems. The constraints considered in the problems are categorised into three classes: those that are sequence related, those that are nurse schedule related and those that are roster related. We propose a decomposition approach (to construct solutions) that consists of two stages: (1) to construct high quality sequences for nurses by only considering the sequence constraints, and (2) to iteratively construct schedules for nurses and the overall rosters, based on the sequences built and considering the schedule and roster constraints. In the second stage of the schedule construction, nurses are ordered and selected adaptively according to the quality of the schedules they were assigned to in the last iteration. Greedy local search is carried out during and after the roster construction, in order to improve the (partial) rosters built. We show that the local search heuristic during the roster construction can further improve the constructed solutions for the benchmark problems tested.     

Efficiency of the even-frequency method for estimating the parameters of a three-parameter compound Poisson distribution

Point estimation issues are investigated for the three-parameter family of compound Poisson distributions. Formulas for parameter estimators and their covariance matrix are derived by the even-frequency method; the asymptotic efficiency of the estimators is expressed with an informant in series form. The efficiency of even-frequency estimation is computed and analyzed for the parameter characteristics. __________ Translated from Prikladnaya Matematika i Informatika, No. 25, pp. 99–106, 2007.     

A method for solving fuzzy goal programming problems based on MINMAX approach

Narasimhan incorporated fuzzy set theory within goal programming formulation in 1980. Since then numerous research has been carried out in this field. One of the well-known models for solving fuzzy goal programming problems was proposed by Hannan in 1981. In this paper the conventional MINMAX approach in goal programming is applied to solve fuzzy goal programming problems. It is proved that the proposed model is an extension to Hannan model that deals with unbalanced triangular linear membership functions. In addition, it is shown that the new model is equivalent to a model proposed in 1991 by Yang et al. Moreover, a weighted model of the new approach is introduced and is compared with Kim and Whang’s model presented in 1998. A numerical example is given to demonstrate the validity and strengths of the new models.     

A new multi objective optimization approach in distribution systems

This paper presents a multi objective optimal location of AVRs in distribution systems at the presence of distributed generators based on modified teaching-learning-based optimization (MTLBO) algorithm. In the proposed MTLBO algorithm, teacher and learner phases are modified. The proposed objective functions are energy generation costs, electrical energy losses and the voltage deviations. The proposed algorithm utilizes several teachers and considers the teachers as an external repository to save found Pareto optimal solutions during the search process. Since the objective functions are not the same, a fuzzy clustering method is used to control the size of the repository. The proposed technique allows the decision maker to select one of the Pareto optimal solutions (by trade-off) for different applications. The performance of the suggested algorithm on a 70-bus distribution network in comparison with other evolutionary methods such as GA, PSO and TLBO, is extraordinary.     

A primal-dual interior-point algorithm for symmetric optimization based on a new method for finding search directions

We introduce an interior-point method for symmetric optimization based on a new method for determining search directions. In order to accomplish this, we use a new equivalent algebraic transformation on the centring equation of the system which characterizes the central path. In this way, we obtain a new class of directions. We analyse a special case of this class, which leads to the new interior-point algorithm mentioned before. Another way to find the search directions is using barriers derived from kernel functions. We show that in our case the corresponding direction cannot be deduced from a usual kernel function. In spite of this fact, we prove the polynomial complexity of the proposed algorithm.