Search

We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.

This paper proposes a new scientific decision framework (SDF) under interval valued intuitionistic fuzzy (IVIF) environment for supplier selection (SS). The framework consists of two phases, where, in the first phase, criteria weights are estimated in a sensible manner using newly proposed IVIF based statistical variance (SV) method and, in the second phase, the suitable supplier is selected using ELECTRE (ELimination and Choice Expressing REality) ranking method under IVIF environment. This method involves three categories of outranking, namely, strong, moderate, and weak. Previous studies on ELECTRE ranking reveal that scholars have only used two categories of outranking, namely, strong and weak, in the formulation of IVIF based ELECTRE, which eventually aggravates fuzziness and vagueness in decision making process due to the potential loss of information. Motivated by this challenge, third outranking category, called moderate, is proposed, which considerably reduces the loss of information by improving checks to the concordance and discordance matrices. Thus, in this paper, IVIF-ELECTRE (IVIFE) method is presented and popular TOPSIS method is integrated with IVIFE for obtaining a linear ranking. Finally, the practicality of the proposed framework is demonstrated using SS example and the strength of proposed SDF is realized by comparing the framework with other similar methods.

There is a growing interest in finding a global optimal path in transportation networks particularly when the network suffers from unexpected disturbance. This paper studies the problem of finding a global optimal path to guarantee a given probability of arriving on time in a network with uncertainty, in which the travel time is stochastic instead of deterministic. Traditional path finding methods based on least expected travel time cannot capture the network user’s risk-taking behaviors in path finding. To overcome such limitation, the reliable path finding algorithms have been proposed but the convergence of global optimum is seldom addressed in the literature. This paper integrates the K-shortest path algorithm into Backtracking method to propose a new path finding algorithm under uncertainty. The global optimum of the proposed method can be guaranteed. Numerical examples are conducted to demonstrate the correctness and efficiency of the proposed algorithm.

This paper focuses on the periodic event-triggered consensus problem for multiagent systems under undirected graph. In the periodic event-triggered control, the event condition is tested only periodically to decide when to exert the control behaviors and when to broadcast the sampling data. Two sets of event-triggered strategies combining with sampled-data control are designed based on an exponential decay function and a quadratic Lyapunov function, respectively. Some useful theorems for these two periodic event-triggered strategies about the choice of period are derived to guarantee the asymptotical stability of the closed-loop multiagent systems. In addition, this paper gives a sufficient condition about the bounds of communication delay for the multiagent systems. It is rigorously proved that the overall system will achieve the consensus under the proposed strategy if the period and time delay satisfy the theorems. Finally, we extend these solutions to general linear dynamical systems. Simulation results are presented to show the effectiveness.

This paper studies the portfolio selection problem in hybrid uncertain decision systems. Firstly the return rates are characterized by random fuzzy variables. The objective is to maximize the total expected return rate. For a random fuzzy variable, this paper defines a new equilibrium risk value (ERV) with credibility level beta and probability level alpha. As a result, our portfolio problem is built as a new random fuzzy expected value (EV) model subject to ERV constraint, which is referred to as EV-ERV model. Under mild assumptions, the proposed EV-ERV model is a convex programming problem. Furthermore, when the possibility distributions are triangular, trapezoidal, and normal, the EV-ERV model can be transformed into its equivalent deterministic convex programming models, which can be solved by general purpose optimization software. To demonstrate the effectiveness of the proposed equilibrium optimization method, some numerical experiments are conducted. The computational results and comparison study demonstrate that the developed equilibrium optimization method is effective to model portfolio selection optimization problem with twofold uncertain return rates.

Judgment matrix aggregation, as an important part of group decision-making, has been widely and deeply studied due to the universality and importance of group decision-making in the management field. For the variety of judgment matrix in group decision-making, the matrix aggregation result can be obtained by using the mode of glowworm swarm optimization. First, this paper introduces the basic principle of the glowworm swarm optimization (GSO) algorithm and gives the improved GSO algorithm to solve the matrix aggregation problems. In this approach, the consistency ratio is introduced to the objective function of the glowworm swarm optimization, thus reducing the subjectivity and information loss in the aggregation process. Then, the improved GSO algorithm is applied to the solution of the deterministic matrix and the fuzzy matrix. The method optimization can provide an effective and relatively uniform aggregation method for matrix aggregation. Finally, through comparative analysis, it is shown that the method of this paper has certain advantages in terms of adaptability, accuracy, and stability to solving the matrix aggregation problems.

WOS: 000374093400001, Ordering and ranking fuzzy numbers and their comparisons play a significant role in decision-making problems such as social and economic systems, forecasting, optimization, and risk analysis problems. In this paper, a new method for ordering triangular fuzzy numbers using the Nagel point of a triangle is presented. With the aid of the proposed method, reasonable properties of ordering fuzzy numbers are verified. Certain comparative examples are given to illustrate the advantages of the new method. Many papers have been devoted to studies on fuzzy ranking methods, but some of these studies have certain shortcomings. The proposed method overcomes the drawbacks of the existing methods in the literature. The suggested method can order triangular fuzzy numbers as well as crisp numbers and fuzzy numbers with the same centroid point. An application to the fuzzy risk analysis problem is given, based on the suggested ordering approach., Anadolu University Scientific Research Projects Commission [1403F077], This study was supported by the Anadolu University Scientific Research Projects Commission under Grant no. 1403F077.

This paper proposes a stable adaptive fuzzy control scheme for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is established to represent the unknown complex systems. A parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error due to fuzzy modelling and the sufficient conditions of the closed-loop system stability with respect to decay rateαare derived by linear matrix inequalities (LMIs). Then the errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. The main contribution is to deal with the differences between the T-S fuzzy bilinear model and the real system; a global asymptotically stable adaptive control scheme is presented for real complex systems. Finally, illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

This paper presents a dynamic stochastic decision-making method that considers the characteristics of stochastic variable variances under time-sequence contingency environments for solving stochastic decision-making problems with information from different periods and of indeterminate attribute weights. First, time-sequence weights are obtained using the technique for order preference by similarity to ideal solution (TOPSIS), corresponding with the idea of “stressing the present rather than the past.” After determining the time degree and fully considering the characteristics of normally distributed stochastic variable variances, the attribute weight is determined based on vertical projection distance. Decision-making information is then assembled from two dimensions of time-sequence and attributes, based on the two categories of weighted arithmetic averaging operators of normally distributed stochastic variables, resulting in comprehensive dynamic decision-making from single solution dimensions and a priority sequence of solutions per the order relation criteria of normally distributed stochastic variables. Finally, the validity and practicability of the methods proposed in this paper are verified using an example numerical analysis.

Multiplicative relations are one of most powerful techniques to express the preferences over alternatives (or criteria). In this paper, we propose a wide range of hesitant multiplicative fuzzy power aggregation geometric operators on multiattribute group decision making (MAGDM) problems for hesitant multiplicative information. In this paper, we first develop some compatibility measures for hesitant multiplicative fuzzy numbers, based on which the corresponding support measures can be obtained. Then we propose several aggregation techniques, and investigate their properties. In the end, we develop two approaches for multiple attribute group decision making with hesitant multiplicative fuzzy information and illustrate a real world example to show the behavior of the proposed operators.

Vehicles are often caught in dilemma zone when they approach signalized intersections in yellow interval. The existence of dilemma zone which is significantly influenced by driver behavior seriously affects the efficiency and safety of intersections. This paper proposes the driver behavior models in yellow interval by logistic regression and fuzzy decision tree modeling, respectively, based on camera image data. Vehicle’s speed and distance to stop line are considered in logistic regression model, which also brings in a dummy variable to describe installation of countdown timer display. Fuzzy decision tree model is generated by FID3 algorithm whose heuristic information is fuzzy information entropy based on membership functions. This paper concludes that fuzzy decision tree is more accurate to describe driver behavior at signalized intersection than logistic regression model.

This paper is devoted to the average consensus problems in directed networks of agents with unknown control direction. In this paper, by using Nussbaum function techniques and Laplacian matrix, novel average consensus protocols are designed for multiagent systems with unknown control direction in the cases of directed networks with fixed and switching topology. In the case of switching topology, the disagreement vector is utilized. Finally, simulation is provided to demonstrate the effectiveness of our results.

Multiobjective programming problems have been widely applied to various engineering areas which include optimal design of an automotive engine, economics, and military strategies. In this paper, we propose a noninterior path following algorithm to solve a class of multiobjective programming problems. Under suitable conditions, a smooth path will be proven to exist. This can give a constructive proof of the existence of solutions and lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

This paper presents two methods for dual-rate sampled-data nonlinear output-error systems. One method is the missing output estimation based stochastic gradient identification algorithm and the other method is the auxiliary model based stochastic gradient identification algorithm. Different from the polynomial transformation based identification methods, the two methods in this paper can estimate the unknown parameters directly. A numerical example is provided to confirm the effectiveness of the proposed methods.

Spheroid disturbance of input data brings great challenges to support vector regression; thus it is essential to study the robust regression model. This paper is dedicated to establish a robust regression model which makes the regression function robust against disturbance of data and system parameter. Firstly, two theorems have been given to show that the robust linearε-support vector regression problem could be settled by solving the dual problems. Secondly, it has been focused on the development of robust support vector regression algorithm which is extended from linear domain to nonlinear domain. Finally, the numerical experiments result demonstrates the effectiveness of the models and algorithms proposed in this paper.

By simplifying tolerance problem and treating faulty voltages on different test points as independent variables, integer-coded table technique is proposed to simplify the test point selection process. Usually, simplifying tolerance problem may induce a wrong solution while the independence assumption will result in over conservative result. To address these problems, the tolerance problem is thoroughly considered in this paper, and dependency relationship between different test points is considered at the same time. A heuristic graph search method is proposed to facilitate the test point selection process. First, the information theoretic concept of entropy is used to evaluate the optimality of test point. The entropy is calculated by using the ambiguous sets and faulty voltage distribution, determined by component tolerance. Second, the selected optimal test point is used to expand current graph node by using dependence relationship between the test point and graph node. Simulated results indicate that the proposed method more accurately finds the optimal set of test points than other methods; therefore, it is a good solution to minimize the size of the test point set. To simplify and clarify the proposed method, only catastrophic and some specific parametric faults are discussed in this paper.

This paper researched three definitions of Gauss map and found that the definition of “Gauss map” in the paper of Arasomwan and Adewumi may be incoherent with other publications. In addition, we analyzed the difference of continuous Gauss map and the floating-point Gauss map, and we pointed out that the floating-point simulation behaved significantly differently from the continuous Gauss map.

This paper is concerned with the problem of the robustH∞filtering for the Takagi-Sugeno (T-S) fuzzy stochastic systems with bounded parameter uncertainties. For a given T-S fuzzy stochastic system, this paper focuses on the stochastically mean-square stability of the filtering error system and theH∞performance level of the output error and the disturbance input. The design method for delay-dependent filter is developed based on linear matrix inequalities. Finally, the effectiveness of the proposed methods is substantiated with an illustrative example.

We propose a novel online manifold regularization framework based on the notion of duality in constrained optimization. The Fenchel conjugate of hinge functions is a key to transfer manifold regularization from offline to online in this paper. Our algorithms are derived by gradient ascent in the dual function. For practical purpose, we propose two buffering strategies and two sparse approximations to reduce the computational complexity. Detailed experiments verify the utility of our approaches. An important conclusion is that our online MR algorithms can handle the settings where the target hypothesis is not fixed but drifts with the sequence of examples. We also recap and draw connections to earlier works. This paper paves a way to the design and analysis of online manifold regularization algorithms.

This paper studies the stability problem of a grey neutral stochastic system with distributed delays. The main feature of a grey system is that the parameters of system are evaluated by grey numbers, and system has the strong background in engineering applications. However, the literature dealing with the stability problem for grey system seems to be scarce. The main aim of this paper is to fill the gap. Based on the Lyapunov stability theorem and Itô’s formula, especially, using the decomposition technique of the continuous matrix-covered sets of grey matrix, we propose several novel sufficient conditions, which ensure our considered grey system in mean-square exponential stability and almost surely exponential stability. Furthermore, two examples are provided to show the effectiveness of the obtained results.

In order to improve the effects of denoising, this paper introduces the basic principles of wavelet threshold denoising and traditional structures threshold functions. Meanwhile, it proposes wavelet threshold function and fixed threshold formula which are both improved here. First, this paper studies the problems existing in the traditional wavelet threshold functions and introduces the adjustment factors to construct the new threshold function basis on soft threshold function. Then, it studies the fixed threshold and introduces the logarithmic function of layer number of wavelet decomposition to design the new fixed threshold formula. Finally, this paper uses hard threshold, soft threshold, Garrote threshold, and improved threshold function to denoise different signals. And the paper also calculates signal-to-noise (SNR) and mean square errors (MSE) of the hard threshold functions, soft thresholding functions, Garrote threshold functions, and the improved threshold function after denoising. Theoretical analysis and experimental results showed that the proposed approach could improve soft threshold functions with constant deviation and hard threshold with discontinuous function problems. The proposed approach could improve the different decomposition scales that adopt the same threshold value to deal with the noise problems, also effectively filter the noise in the signals, and improve the SNR and reduce the MSE of output signals.

In this paper, an improved NSGA2 algorithm is proposed, which is used to solve the multiobjective problem. For the original NSGA2 algorithm, the paper made one improvement: joining the local search strategy into the NSGA2 algorithm. After each iteration calculation of the NSGA2 algorithm, a kind of local search strategy is performed in the Pareto optimal set to search better solutions, such that the NSGA2 algorithm can gain a better local search ability which is helpful to the optimization process. Finally, the proposed modified NSGA2 algorithm (MNSGA2) is simulated in the two classic multiobjective problems which is called KUR problem and ZDT3 problem. The calculation results show the modified NSGA2 outperforms the original NSGA2, which indicates that the improvement strategy is helpful to improve the algorithm.

Single-objection function cannot describe the characteristics of the complicated hydrologic system. Consequently, it stands to reason that multiobjective functions are needed for calibration of hydrologic model. The multiobjective algorithms based on the theory of nondominate are employed to solve this multiobjective optimal problem. In this paper, a novel multiobjective optimization method based on differential evolution with adaptive Cauchy mutation and Chaos searching (MODE-CMCS) is proposed to optimize the daily streamflow forecasting model. Besides, to enhance the diversity performance of Pareto solutions, a more precise crowd distance assigner is presented in this paper. Furthermore, the traditional generalized spread metric (SP) is sensitive with the size of Pareto set. A novel diversity performance metric, which is independent of Pareto set size, is put forward in this research. The efficacy of the new algorithm MODE-CMCS is compared with the nondominated sorting genetic algorithm II (NSGA-II) on a daily streamflow forecasting model based on support vector machine (SVM). The results verify that the performance of MODE-CMCS is superior to the NSGA-II for automatic calibration of hydrologic model.

This paper addresses the short-term scheduling problem of hydrothermal power systems, which results in a large-scale mixed-integer nonlinear programming problem. The objective consists in minimizing the operation cost over a two-day horizon with a one-hour time resolution. To solve this difficult problem, a Lagrangian Relaxation (LR) based on variable splitting is designed where the resulting dual problem is solved by a Bundle method. Given that the LR usually fails to find a feasible solution, we use an inexact Augmented Lagrangian method to improve the quality of the solution supplied by the LR. We assess our approach by using a real-life hydrothermal configuration extracted from the Brazilian power system, proving the conceptual and practical feasibility of the proposed algorithm. In summary, the main contributions of this paper are (i) a detailed and compatible modelling for this problem is presented; (ii) in order to solve efficiently the entire problem, a suitable decomposition strategy is presented. As a result of these contributions, the proposed model is able to find practical solutions with moderate computational burden, which is absolutely necessary in the modern power industry.

This paper studies a perishable inventory model, which assumes that each perishable item has finite lifetime, and only one item is consumed each time. The lifetimes of perishable items are independent random variables with the general distribution and so are the consumption internal. Under this assumption, by using backward equations and limit distribution of Markov skeleton processes, this paper obtains the existence conditions and the explicit expression of the limit distribution of the inventory level of perishable inventory model.

The objective function and the constraints can be formulated as linear functions of independent variables in most of the real-world optimization problems. Linear Programming (LP) is the process of optimizing a linear function subject to a finite number of linear equality and inequality constraints. Solving linear programming problems efficiently has always been a fascinating pursuit for computer scientists and mathematicians. The computational complexity of any linear programming problem depends on the number of constraints and variables of the LP problem. Quite often large-scale LP problems may contain many constraints which are redundant or cause infeasibility on account of inefficient formulation or some errors in data input. The presence of redundant constraints does not alter the optimal solutions(s). Nevertheless, they may consume extra computational effort. Many researchers have proposed different approaches for identifying the redundant constraints in linear programming problems. This paper compares five of such methods and discusses the efficiency of each method by solving various size LP problems and netlib problems. The algorithms of each method are coded by using a computer programming language C. The computational results are presented and analyzed in this paper.

This paper aims at deriving an efficient criterion for the robust stability analysis of discrete-time systems with time-varying delay. In the derivation, to obtain a larger stability region under the requirement of less computational complexity, this paper proposes a valuable method capable of establishing a less conservative stability criterion without using the free-weighting approach and an extremely augmented state. In parallel, the stabilization problem of systems with time-delayed control input is addressed in connection with the derived stability criterion.

Virtual power plant (VPP) is an aggregation of multiple distributed generations, energy storage, and controllable loads. Affected by natural conditions, the uncontrollable distributed generations within VPP, such as wind and photovoltaic generations, are extremely random and relative. Considering the randomness and its correlation of uncontrollable distributed generations, this paper constructs the chance constraints stochastic optimal dispatch of VPP including stochastic variables and its random correlation. The probability distributions of independent wind and photovoltaic generations are described by empirical distribution functions, and their joint probability density model is established by Frank-copula function. And then, sample average approximation (SAA) is applied to convert the chance constrained stochastic optimization model into a deterministic optimization model. Simulation cases are calculated based on the AIMMS. Simulation results of this paper mathematic model are compared with the results of deterministic optimization model without stochastic variables and stochastic optimization considering stochastic variables but not random correlation. Furthermore, this paper analyzes how SAA sampling frequency and the confidence level influence the results of stochastic optimization. The numerical example results show the effectiveness of the stochastic optimal dispatch of VPP considering the randomness and its correlations of distributed generations.

This paper studies a production scheduling problem with deteriorating jobs, which frequently arises in contemporary manufacturing environments. The objective is to find an optimal sequence of the set of jobs to minimize the total weighted tardiness, which is an indicator of service quality. The problem belongs to the class of NP-hard. When the number of jobs increases, the computational time required by an optimization algorithm to solve the problem will increase exponentially. To tackle large-scale problems efficiently, a two-stage method is presented in this paper. We partition the set of jobs into a few subsets by applying a neural network approach and thereby transform the large-scale problem into a series of small-scale problems. Then, we employ an improved metaheuristic algorithm (called GTS) which combines genetic algorithm with tabu search to find the solution for each subproblem. Finally, we integrate the obtained sequences for each subset of jobs and produce the final complete solution by enumeration. A fair comparison has been made between the two-stage method and the GTS without decomposition, and the experimental results show that the solution quality of the two-stage method is much better than that of GTS for large-scale problems.

Degree constrained minimum spanning tree (DCMST) refers to constructing a spanning tree of minimum weight in a complete graph with weights on edges while the degree of each node in the spanning tree is no more thand(d≥ 2). The paper proposes an improved multicolony ant algorithm for degree constrained minimum spanning tree searching which enables independent search for optimal solutions among various colonies and achieving information exchanges between different colonies by information entropy. Local optimal algorithm is introduced to improve constructed spanning tree. Meanwhile, algorithm strategies in dynamic ant, random perturbations ant colony, and max-min ant system are adapted in this paper to optimize the proposed algorithm. Finally, multiple groups of experimental data show the superiority of the improved algorithm in solving the problems of degree constrained minimum spanning tree.

This paper analyses the dynamics of dual-channel energy supply chain model with heterogeneous retailers (as regards the type of expectations’ formation). On the basis of analyzing the stabilities of four fixed points in the three-dimensional dynamic system, local stable regions of Nash equilibrium are obtained. Effects ofSon the stable regions and profit are studied. Simulation results show that the adjustment of price speed has an obvious impact on the complexity of competition. The performances of the model in different period are measured by using the index of average profit. The results show that unstable behavior in economic system is often an unfavorable outcome. So this paper discusses the application of parameters control method when the model is in chaos and then allows the oligarchs to eliminate the negative effects.

This paper develops a version of Robust Stochastic Maximum Principle (RSMP) applied to the Minimax Mayer Problem formulated for stochastic differential equations with the control-dependent diffusion term. The parametric families of first and second order adjoint stochastic processes are introduced to construct the corresponding Hamiltonian formalism. The Hamiltonian function used for the construction of the robust optimal control is shown to be equal to the Lebesque integral over a parametric set of the standard stochastic Hamiltonians corresponding to a fixed value of the uncertain parameter. The paper deals with a cost function given at finite horizon and containing the mathematical expectation of a terminal term. A terminal condition, covered by a vector function, is also considered. The optimal control strategies, adapted for available information, for the wide class of uncertain systems given by an stochastic differential equation with unknown parameters from a given compact set, are constructed. This problem belongs to the class of minimax stochastic optimization problems. The proof is based on the recent results obtained for Minimax Mayer Problem with a finite uncertainty set [14,43-45] as well as on the variation results of [53] derived for Stochastic Maximum Principle for nonlinear stochastic systems under complete information. The corresponding discussion of the obtain results concludes this study.

Loss and closed queueing network models have long been of interest to telephone and computer engineers and becoming increasingly important as models of data transmission networks. This paper describes a uniform approach that has been developed during the last decade for asymptotic analysis of large capacity networks with product form of the stationary probability distribution. Such a distribution has an explicit form up to the normalization constant, or the partition function. The approach is based on representing the partition function as a contour integral in complex space and evaluating the integral using the saddle point method and theory of residues. This paper provides an introduction to the area and a review of recent work.

A number of acceleration schemes for speeding up the time-consuming bilateral filter have been proposed in the literature. Among these techniques, the histogram-based bilateral filter trades the flexibility for achievingO(1) computational complexity using box spatial kernel. A recent study shows that this technique can be leveraged forO(1) bilateral filter with arbitrary spatial and range kernels by linearly combining the results of multiple-box bilateral filters. However, this method requires many box bilateral filters to obtain sufficient accuracy when approximating the bilateral filter with a large spatial kernel. In this paper, we propose approximating arbitrary spatial kernel using a fixed number of boxes. It turns out that the multiple-box spatial kernel can be applied in manyO(1) acceleration schemes in addition to the histogram-based one. Experiments on the application to the histogram-based acceleration are presented in this paper. Results show that the proposed method has better accuracy in approximating the bilateral filter with Gaussian spatial kernel, compared with the previous histogram-based methods. Furthermore, the performance of the proposed histogram-based bilateral filter is robust with respect to the parameters of the filter kernel.

This paper aims to efficiently implement the maximum likelihood estimator (MLE) for Hurst exponent, a vital parameter embedded in the process of fractional Brownian motion (FBM) or fractional Gaussian noise (FGN), via a combination of the Levinson algorithm and Cholesky decomposition. Many natural and biomedical signals can often be modeled as one of these two processes. It is necessary for users to estimate the Hurst exponent to differentiate one physical signal from another. Among all estimators for estimating the Hurst exponent, the maximum likelihood estimator (MLE) is optimal, whereas its computational cost is also the highest. Consequently, a faster but slightly less accurate estimator is often adopted. Analysis discovers that the combination of the Levinson algorithm and Cholesky decomposition can avoid storing any matrix and performing any matrix multiplication and thus save a great deal of computer memory and computational time. In addition, the first proposed MLE for the Hurst exponent was based on the assumptions that the mean is known as zero and the variance is unknown. In this paper, all four possible situations are considered: known mean, unknown mean, known variance, and unknown variance. Experimental results show that the MLE through efficiently implementing numerical computation can greatly enhance the computational performance.

The purpose of this paper is to propose a three-dimensional grey interval relational degree model for dynamic Multiattribute decision making. In the model, the observed values are interval grey numbers. Elements are selected in the system as the points in anm-dimensional linear space. Then observation data of each element to different time and objects are as the coordinates of point. An optimization model is employed to obtain each scheme’s affiliate degree for the positive and negative ideal schemes. And a three-dimensional grey interval relational degree model based on time, index, and scheme is constructed in the paper. The result shows that the three-dimensional grey relational degree simplifies the traditional dynamic multiattribute decision making method and can better resolve the dynamic multiattribute decision making problem of interval numbers. The example illustrates that the method presented in the paper can be used to deal with problems of uncertainty such as dynamic multiattribute decision making.

This paper experimentally investigates the effect of nine chaotic maps on the performance of two Particle Swarm Optimization (PSO) variants, namely, Random Inertia Weight PSO (RIW-PSO) and Linear Decreasing Inertia Weight PSO (LDIW-PSO) algorithms. The applications of logistic chaotic map by researchers to these variants have led to Chaotic Random Inertia Weight PSO (CRIW-PSO) and Chaotic Linear Decreasing Inertia Weight PSO (CDIW-PSO) with improved optimizing capability due to better global search mobility. However, there are many other chaotic maps in literature which could perhaps enhance the performances of RIW-PSO and LDIW-PSO more than logistic map. Some benchmark mathematical problems well-studied in literature were used to verify the performances of RIW-PSO and LDIW-PSO variants using the nine chaotic maps in comparison with logistic chaotic map. Results show that the performances of these two variants were improved more by many of the chaotic maps than by logistic map in many of the test problems. The best performance, in terms of function evaluations, was obtained by the two variants using Intermittency chaotic map. Results in this paper provide a platform for informative decision making when selecting chaotic maps to be used in the inertia weight formula of LDIW-PSO and RIW-PSO.

This paper presents a combination of variable neighbourhood search and mathematical programming to minimize the sum of earliness and tardiness penalty costs of all operations for just-in-time job-shop scheduling problem (JITJSSP). Unlike classical E/T scheduling problem with each job having its earliness or tardiness penalty cost, each operation in this paper has its earliness and tardiness penalties, which are paid if the operation is completed before or after its due date. Our hybrid algorithm combines (i) a variable neighbourhood search procedure to explore the huge feasible solution spaces efficiently by alternating theswapandinsertionneighbourhood structures and (ii) a mathematical programming model to optimize the completion times of the operations for a given solution in each iteration procedure. Additionally, a threshold accepting mechanism is proposed to diversify the local search of variable neighbourhood search. Computational results on the 72 benchmark instances show that our algorithm can obtain the best known solution for 40 problems, and the best known solutions for 33 problems are updated.

This paper is concerned with an optimal shape design problem in aerodynamics. The inverse problem in question consists in finding the optimal shape an airfoil placed in a potential flow at a given angle of attack should have such that the pressure distribution on its surface matches a desired one. The numerical method to achieve this aim is based on a body-fitted grid generation technique (elliptic, O-type) to generate a mesh over the airfoil surface and solve for the flow equation. The O-type scheme is used due to its ability to generate a high quality (fine and orthogonal) grid around the airfoil surface. This paper describes a novel and very efficient sensitivity analysis scheme to compute the sensitivity of the pressure distribution to variation of grid node positions and both the conjugate gradient method (CGM) and a version of the quasi-Newton method (i.e., BFGS) are used as optimization algorithms to minimize the difference between the computed pressure distribution on the airfoil surface and desired one. The elliptic grid generation technique allows us to map the physical domain (body) onto a fixed computational domain and to discretize the flow equation using the finite difference method (FDM).

In this paper, some basic concepts of multimodal transportation and swarm intelligence were described and reviewed and analyzed related literatures of multimodal transportation scheme decision and swarm intelligence methods application areas. Then, this paper established a multimodal transportation scheme decision optimization mathematical model based on transportation costs, transportation time, and transportation risks, explained relevant parameters and the constraints of the model in detail, and used the weight coefficient to transform the multiobjective optimization problems into a single objective optimization transportation scheme decision problem. Then, this paper is proposed by combining particle swarm optimization algorithm and ant colony algorithm (PSACO) to solve the combinatorial optimization problem of multimodal transportation scheme decision for the first time; this algorithm effectively combines the advantages of particle swarm optimization algorithm and ant colony algorithm. The solution shows that the PSACO algorithm has two algorithms’ advantages and makes up their own problems; PSACO algorithm is better than ant colony algorithm in time efficiency and its accuracy is better than that of the particle swarm optimization algorithm, which is proved to be an effective heuristic algorithm to solve the problem about multimodal transportation scheme decision, and it can provide economical, reasonable, and safe transportation plan reference for the transportation decision makers.

The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making based on attribute values of objects, we shall select an attribute subset with appropriate measurement error to minimize the total test cost. Recently, error-range-based covering rough set with uniform distribution error was proposed to investigate this issue. However, the measurement errors satisfy normal distribution instead of uniform distribution which is rather simple for most applications. In this paper, we introduce normal distribution measurement errors to covering-based rough set model, and deal with test-cost-sensitive attribute reduction problem in this new model. The major contributions of this paper are four-fold. First, we build a new data model based on normal distribution measurement errors. With the new data model, the error range is an ellipse in a two-dimension space. Second, the covering-based rough set with normal distribution measurement errors is constructed through the "3-sigma" rule. Third, the test-cost-sensitive attribute reduction problem is redefined on this covering-based rough set. Fourth, a heuristic algorithm is proposed to deal with this problem. The algorithm is tested on ten UCI (University of California - Irvine) datasets. The experimental results show that the algorithm is more effective and efficient than the existing one. This study is a step toward realistic applications of cost-sensitive learning., Comment: This paper has been withdrawn by the author due to the error of the title

International audience; This paper concerns the problem of stabilizing linear time-delay systems under state and control linear constraints. For this, necessary and sufficient conditions for a given polyhedral set (possibly non-symmetrical) to be positively invariant are obtained. The existence conditions of linear state feedback control laws respecting the constraints are established, and a procedure is given in order to compute such a controller. The paper presents memoryless controlled systems but the results can be applied to cases of delayed-controlled systems. An example is given.

Finite-horizon optimal control problems for discrete-time switched linear control systems are investigated in this paper. Two kinds of quadratic cost functions are considered. The weight matrices are different. One is subsystem dependent; the other is time dependent. For a switched linear control system, not only the control input but also the switching signals are control factors and are needed to be designed in order to minimize cost function. As a result, optimal design for switched linear control systems is more complicated than that of non-switched ones. By using the principle of dynamic programming, the optimal control laws including both the optimal switching signal and the optimal control inputs are obtained for the two problems. Two examples are given to verify the theory results in this paper.

The main objective of our paper is to solve a problem which was encountered in an industrial firm. It concerns the conception of a weekly production planning with the aim to optimize the quantities to be launched. Indeed, one of the problems raised in that company could be modeled as a linear multiobjective program where the decision variables are of two kinds: the first ones are upper and lower bounded, and the second ones are nonnegative. During the resolution process of the multiobjective case, we were faced with the necessity of developing an effective method to solve the mono-objective case without any increase in the linear program size, since the industrial case to solve is already very large. So, we propose an extension of the direct support method presented in this paper. Its particularity is that it avoids the preliminary transformation of the decision variables. It handles the bounds as they are initially formulated. The method is really effective, simple to use, and permits speeding up the resolution process.

In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP) problem approach is proposed, which strikes the balance between previous models available in the literature.

This paper is intended to model a decision maker as a rational probabilistic decider (RPD) and to investigate its behavior in stationary and symmetric Markov switch environments. RPDs take their decisions based on penalty functions defined by the environment. The quality of decision making depends on a parameter referred to as level of rationality. The dynamic behavior of RPDs is described by an ergodic Markov chain. Two classes of RPDs are considered—local and global. The former take their decisions based on the penalty in the current state while the latter consider all states. It is shown that asymptotically (in time and in the level of rationality) both classes behave quite similarly. However, the second largest eigenvalue of Markov transition matrices for global RPDs is smaller than that for local ones, indicating faster convergence to the optimal state. As an illustration, the behavior of a chief executive officer, modeled as a global RPD, is considered, and it is shown that the company performance may or may not be optimized—depending on the pay structure employed. While the current paper investigates individual RPDs, a companion paper will address collective behavior.

In order to control pests and eventually maintain the number of pests below the economic threshold, in this paper, based on the nonsmooth dynamical system, a two-stage-structured pest control Filippov model is proposed. We take the total number of juvenile and adult pest population as the control index to determine whether or not to implement chemical control strategies. The sliding-mode domain and conditions for the existence of regular and virtual equilibria, pseudoequilibrium, boundary equilibria, and tangent points are given. Further, the sufficient condition of the locally asymptotic stability of pseudoequilibrium is obtained. By numerical simulations, the local bifurcations of the equilibria are discussed. Our results show that the total number of pest populations can be successfully controlled below the economic threshold by taking suitable threshold policy.

The temperature distribution in real-world industrial environments is often in a three-dimensional space, and developing a reliable method to predict such volumetric information is beneficial for the combustion diagnosis, the understandings of the complicated physical and chemical mechanisms behind the combustion process, the increase of the system efficiency, and the reduction of the pollutant emission. In accordance with the machine learning theory, in this paper, a new methodology is proposed to predict three-dimensional temperature distribution from the limited number of the scattered measurement data. The proposed prediction method includes two key phases. In the first phase, traditional technologies are employed to measure the scattered temperature data in a large-scale three-dimensional area. In the second phase, the Gaussian process regression method, with obvious superiorities, including satisfactory generalization ability, high robustness, and low computational complexity, is developed to predict three-dimensional temperature distributions. Numerical simulations and experimental results from a real-world three-dimensional combustion process indicate that the proposed prediction method is effective and robust, holds a good adaptability to cope with complicated, nonlinear, and high-dimensional problems, and can accurately predict three-dimensional temperature distributions under a relatively low sampling ratio. As a result, a practicable and effective method is introduced for three-dimensional temperature distribution.

To preserve the edge, multiplicative noise removal models based on the total variation regularization have been widely studied, but they suffer from the staircase effect. In this paper, to preserve the edge and reduce the staircase effect, we develop a hybrid variational model based on the variable splitting method for multiplicative noise removal; the new model is a strictly convex objective function which contains the total variation regularization and a modified regularization term. We use the linear alternative direction method to find the minimal solution and also give the convergence proof of the proposed algorithm. Experimental results verify that the proposed model can obtain the better results for removing the multiplicative noise compared with the recent method.