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This paper considers the constrained consensus problem over multi-cluster networks. It is assumed that the agents’ states are constrained by different sets, where each constraint set is privately known by the corresponding agent. Within this framework, a hierarchical projection-based consensus algorithm is presented to solve the considered problem. Technically, the consensus analysis of the proposed algorithm consists of the following three aspects: First, by using the property of the projection operator, the limiting behaviors of the agents’ states generated by the algorithm are investigated. Then, based on the limiting behaviors, it is proven that the agents’ states in the whole network achieve a constrained consensus. Furthermore, by introducing an important auxiliary variable that relates to the agents’ states, the linear convergence of the proposed algorithm is proved. Compared with the existing results, this paper generalizes the constrained consensus methods under single-cluster networks to the multi-cluster ones. Finally, simulations are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

By introducing the real linear operator, this paper offers a finite iterative algorithm for solving the complex generalized coupled Sylvester matrix equations. The properties of this algorithm are discussed and the finite convergence of this algorithm is proven. This algorithm unifies some finite iterative algorithms proposed by the earlier papers. Two numerical examples are offered to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Many-objective problems refer to the optimization problems containing more than three conflicting objectives. To obtain a representative set of well-distributed non-dominated solutions close to Pareto front in the objective space remains a challenging problem. Many papers have proposed different Multi-Objective Evolutionary Algorithms to solve the lack of the convergence and diversity in many-objective problems. One of the more promising approaches uses a set of reference points to discriminate the solutions and guide the search process. However, this approach was incorporated mainly in Multi-Objective Evolutionary Algorithms, and there are just some few promising adaptations of Particle Swarm Optimization approaches for effectively tackling many-objective problems regarding convergence and diversity. Thus, this paper proposes a practical and efficient Many-Objective Particle Swarm Optimization algorithm for solving many-objective problems. Our proposal uses a set of reference points dynamically determined according to the search process, allowing the algorithm to converge to the Pareto front, but maintaining the diversity of the Pareto front. Our experimental results demonstrate superior or similar performance when compared to other state-of-art algorithms. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a novel algorithm to solve real-world constrained optimization problems, which hybridizes multiobjective optimization techniques with an ϵ-constrained method. First, a constrained optimization problem at hand is transformed into a bi-objective optimization problem. By the transformation, the advantage of multiobjective optimization techniques can be utilized in the constrained optimization area to balance population diversity and convergence. Meanwhile, the ϵ-constrained method is applied, which keeps the population evolving toward feasible region of the constrained optimization problem. In our proposed algorithm, the differential evolution is employed as a search engine to create offspring at each generation. Further, different combinations of mutation operators have been developed to improve the search ability and the population convergence at different stages. The performance of our approach is evaluated on 64 benchmark test functions from three popular test suits. Experimental results demonstrate that our proposed approach is capable of obtaining high-quality solutions on the majority of benchmark test functions, when compared with some other state-of-the-art constrained optimization algorithms. [ABSTRACT FROM AUTHOR]

Highlights • The robustness of our solver is proved for fully incompressible 2D–3D FSI problems. • A partitioned smoother to a monolithic GMRES is more robust than a partitioned solver. • An algorithm for the direct-to-steady-state FSI problem is proposed. • Our formulation solved with the MUMPS package shows a very good convergence rate. Abstract In this paper we study a monolithic Newton–Krylov solver with exact Jacobian for the solution of fully incompressible Fluid-Structure Interaction problems of either steady-state or time-dependent type. Unlike common approaches, the enforcement of the incompressibility conditions both for the fluid and for the solid parts is taken care of by using an inf-sup stable finite element pair, without stabilization terms. The Krylov solver is preconditioned using geometric multigrid with smoothers of Richardson type, in turn preconditioned by additive Schwarz algorithms. The separate solution of fluid or solid operators occurs only at the preconditioning stage of the smoother, thus guaranteeing at each level an accurate interface momentum balance. The definition of the subdomains in the Schwarz smoother is driven by the natural splitting between fluid and solid. For each part and level, the domain is subdivided into a number of minimally overlapping subdomains. Numerical investigations of two and three-dimensional benchmark tests with Newtonian fluids and nonlinear hyperelastic solids are carried out by reporting several performance indices, including condition number estimates. A robust performance of the proposed fully incompressible solver is observed, especially for the more challenging direct-to-steady-state problems. [ABSTRACT FROM AUTHOR]

This paper presents a nonhomogeneous continuous super-twisting algorithm for systems of relative degree more than one. The conditions of finite-time convergence to the origin are obtained and the robustness of the designed algorithm is discussed. The paper concludes with numerical simulations illustrating performance of the designed algorithms. [ABSTRACT FROM AUTHOR]

In addition to implicitly resolving the velocity pressure coupling at interior faces, it is also critical for a coupled solver to implicitly resolve this coupling for boundary faces. Failure to account for this leads to substantial degradation in the convergence characteristics of the solver. In this paper, details on the implicit treatment of boundary conditions for a coupled solver are presented in the context of the OpenFOAM ® framework. The boundary conditions presented include two geometric conditions namely, cyclicMMI and symmetry condition and a number of physical boundary conditions (inlet, outlet, and wall). The treatment is illustrated with modification to the boundary element coefficients and its effectiveness demonstrated for the case of “NASA Rotor 37”, a standard validation case. [ABSTRACT FROM AUTHOR]

“ Fuzzy Theoretic Approach to Signals and Systems ” assumes all system variables and parameters as uncertain (i.e. being characterized by membership functions), develops a mathematical theory for analytically determining the membership functions on system variables and parameters, derives algorithms for estimating the parameters of membership functions, and establishes robustness and convergence properties of the estimation algorithms. The membership functions are analytically determined via solving a variational optimization problem that maximizes the “ over-uncertainties-averaged-log-membership ” of the observed data around an initial guess. This paper develops the analytical fuzzy theory for the particular case of a multi-input single-output static system affected by noises. The theory facilitates designing an adaptive filtering algorithm. The robustness of the adaptive filtering algorithm is proved theoretically via a mathematical analysis. Numerical experiments further demonstrate the robustness of the filtering algorithm. A comparison of the algorithm with the state-of-art methods is made using the practical biomedical applications related to the modeling and analysis of heart rate signals for assessing the physiological state of an individual. [ABSTRACT FROM AUTHOR]

Various real-world applications can be formulated as feature selection problems, which have been known to be NP-hard. In this paper, we propose an effective feature selection method based on firefly algorithm (FFA), called return-cost-based binary FFA (Rc-BBFA). The proposed method has the capability of preventing premature convergence and is particularly efficient attributed to the following three aspects. An indicator based on the return-cost is first defined to measure a firefly’s attractiveness from other fireflies. Then, a Pareto dominance-based strategy is presented to seek the attractive one for each firefly. Finally, a binary movement operator based on the return-cost attractiveness and the adaptive jump is developed to update the position of a firefly. The experimental results on a series of public datasets show that the proposed method is competitive in comparison with other feature selection algorithms, including the traditional algorithms, the GA-based algorithm, the PSO-based algorithm, and the FFA-based algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose sparse adaptive channel estimation algorithms based on a mixed controlled l 2 and l p -norm error criterion and zero attracting theory. In the proposed algorithms, a controlling parameter within the range of [0, 1] is adopted to control the mixture of the l 2 and l p norms which are exerted on the estimation error. The sparsity-aware characteristic is implemented by an l 1 -norm penalty, a correntropy-induced metric penalty and a log-sum function constraint which are to exploit the in-nature sparseness of the channels. The proposed sparsity-aware algorithms give desired zero attractors in their iterations to speed up the convergence. The derivation of the proposed algorithms is presented in detail. We can find that the previously proposed sparsity-aware algorithms can be regarded as a special case of the proposed sparse adaptive algorithms. Also, the behaviors of the proposed algorithms are well verified over a multi-path wireless communication channel. As a result, our proposed algorithms are superior to the previously reported sparse mixed adaptive filters with respect to both the convergence and steady-state error for handling sparse signals. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the convergence and stability analysis for iterative processes such as numerical iterative algorithms by using a novel trajectory distance based approach. Iterative dynamics are widespread in distributed algorithms and numerical analysis. However, efficient analysis of convergence and sensitivity of iterative dynamics is quite challenging due to the lack of systematic tools. For instance, the trajectories of iterative dynamics are usually not continuous with respect to the initial condition. Hence, the classical dynamical systems theory cannot be applied directly. In this paper, a trajectory distance based Lyapunov approach is proposed as a means to tackling convergence and sensitivity to the initial condition of iterative processes. Technically the problem of convergence and sensitivity is converted into finiteness of trajectory distance and semistability analysis of discrete-time systems. A semidefinite Lyapunov function based trajectory distance approach is proposed to characterize convergence and semistability of iterative dynamics. Three examples are provided to elucidate the proposed method. Finally, the proposed framework is used to solve the convergence and stability of iterative algorithms developed for balanced resource allocation and damage mitigation problems under adversarial attacks. [Copyright &y& Elsevier]

Abstract: Most real world multi-objective problems (MOPs) have a complicated solution space. Facing such problems, a direction vectors based co-evolutionary multi-objective optimization algorithm (DVCMOA) that introduces the decomposition idea from MOEA/D to co-evolutionary algorithms is proposed in this paper. It is novel in the sense that DVCMOA applies the concept of direction vectors to co-evolutionary algorithms. DVCMOA first divides the entire population into several subpopulations on the basis of the initial direction vectors in the objective space. Then, it solves MOPs through the co-evolutionary interaction among the subpopulations in which individuals are classified according to their direction vectors. Finally, it explores the less developed regions to maintain the relatively uniform distribution of the solution space. In this way, DVCMOA has advantages in convergence, diversity and uniform distribution of the non-dominated solution set, which are explained through comparison with other state-of-the-art multi-objective optimization evolutionary algorithms (MOEAs) in this paper. DVCMOA is shown to be effective on 6 multi-objective 0–1 knapsack problems. [Copyright &y& Elsevier]

Abstract: The research on optimal design of infinite-impulse response (IIR) filters based on optimization techniques has gained much attention in recent years. However, due to the limited performance of the applied optimization techniques, the orders of the filters, which can be obtained, are very low in the previous research. Memetic algorithms (MAs) are widely recognized to have better convergence capability than their conventional counterparts. However, the universality of the MAs, e.g. the ability of solving diverse kinds of digital IIR filter designs, is still limited. In this paper, we design a Two-Stage ensemble Memetic Algorithm (TSMA) framework to more appropriately synthesize the strengths of the evolutionary global search and local search techniques. In the first optimization stage, a competition is held among the candidate local search techniques. Its major idea is to choose the best local search technique and to obtain good initial state. Inheriting the good information of the first stage, the second optimization stage is to implement effective adaptive MA to pursue high-quality solution. The experimental studies presented in this paper contain three aspects: (1) the benefits of the TSMA framework are experimentally investigated by comparing TSMA with its sub-optimizers and recent effective evolutionary algorithms (EAs) on 26 test functions; then (2) TSMA is compared with 4 MAs on the CEC05 functions to comprehensively show the advantages of TSMA; and (3) the TSMA and 6 state-of-the-art algorithms are applied to design high-order digital infinite-impulse response (IIR) filters. The experimental results definitely demonstrate the excellent effectiveness, efficiency and reliability of TSMA on both function optimization and digital IIR filter design tasks. [Copyright &y& Elsevier]

In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an automatic computation of the centered Hausdorff and packing measures of a totally disconnected self-similar set. We evaluate these rates empirically through the numerical analysis of three standard classes of self-similar sets, namely, the families of Cantor type sets in the real line and the plane and the class of Sierpinski gaskets. For these three classes and for small contraction ratios, sharp bounds for the exact values of the corresponding measures are obtained and it is shown how these bounds automatically yield estimates of the corresponding measures, accurate in some cases to as many as 14 decimal places. In particular, the algorithms accurately recover the exact values of the measures in all cases in which these values are known by geometrical arguments. Positive results, which confirm some conjectural values given in [13] and [14] for the measures, are also obtained for an intermediate range of larger contraction ratios. We give an argument showing that, for this range of contraction ratios, the problem is inherently computational in the sense that any theoretical proof, such as those mentioned above, might be impossible, so that in these cases, our method is the only available approach. For contraction ratios close to those of the connected case our computational method becomes intractably time consuming, so the computation of the exact values of the packing and centered Hausdorff measures in the general case, with the open set condition, remains a challenging problem. [ABSTRACT FROM AUTHOR]

This paper proposes a parameter estimation-based coupling control for the generalized cascade systems with uncertain parameters, where the single driven system is actuated by the multi-driving subsystems, resulting in the complicated coupling problem of output tracking and subsystems synchronization. To address this issue, a prescribed performance function (PPF) is firstly incorporated with the filtered representation of the driven system dynamics to design the adaptive parameter law, which maintains the finite-time parameter estimation with the prescribed performances. Then, the desired position of each driving subsystem is proposed to attain the driven system tracking with the sub-guaranteed cost, which is employed for the generalized coupling error (GCE) design to convert the complicated coupling issue into the GCE convergence, such that the complexity of controller design is extremely simplified. By applying the Chebyshev neural network (CNN), a novel integral sliding mode controller is presented to successfully eliminate the reaching phase and guarantee the finite-time GCE convergence with the suboptimal time. For the nonlinearity compensation, the novel learning law is derived to lessen the computational cost, where only a scalar weight needs to be updated online for each output of CNN. Finally, the comparative experiments illustrate the benefits of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Dissimilarity measures play a key role in exploring the inherent cluster structure of the data for any partitional clustering algorithm. Commonly used dissimilarity functions for clustering purpose are so far confined to the Euclidean, exponential and Mahalanobish distances. In this article we develop generalized algorithms to solve the partitional clustering problems formulated with a general class of Inner Product Induced Norm (IPIN) based dissimilarity measures. We provide an in-depth mathematical analysis of the underlying optimization framework and analytically address the issue of existence of a solution and its uniqueness. In absence of a closed form solution, we develop a fast stochastic gradient descent algorithm and the Minimization by Incremental Surrogate Optimization (MISO) algorithm (in case of constrained optimization) with exponential convergence rate to obtain the solution. We carry out a convergence analysis of the fuzzy and k -means clustering algorithms with the IPIN based dissimilarity measures and also establish how these algorithms guarantee convergence to a stationary point. In addition, we investigate the nature of the stationary point. Novelty of the paper lies in the introduction of a generalized class of divergence measures, development of fuzzy and k -means clustering algorithms with the general class of divergence measures and a thorough convergence analysis of the developed algorithms. [ABSTRACT FROM AUTHOR]

In order to improve the filter׳s performance when identifying sparse system, this paper develops two sparse-aware algorithms by incorporating the l 0 -norm constraint of the weight vector into the conventional normalized subband adaptive filter (NSAF) algorithm. The first algorithm is obtained from the principle of the minimum perturbation; and the second one is based on the gradient descent principle. The resulting algorithms have almost the same convergence and steady-state performance while the latter saves computational complexity. What׳s more, the performance of both algorithms is analyzed by resorting to some assumptions commonly used in the analyses of adaptive algorithms. Simulation results in the context of sparse system identification not only demonstrate the effectiveness of the proposed algorithms, but also verify the theoretical analyses. [ABSTRACT FROM AUTHOR]

This paper first discusses the inherent instability of the interpolating moving least squares (IMLS) method. In the original IMLS method, non-scaled polynomial bases are used. Theoretical and numerical results indicate that the stability of the original IMLS method decreases as the separation distance decreases. Then, using shifted and scaled polynomial bases, a stabilized algorithm of the IMLS method is proposed and analyzed. As an application, the stabilized IMLS method is finally introduced into the meshless Galerkin boundary node method (GBNM) to produce a stabilized GBNM for potential problems and Stokes problems. Numerical examples are given to demonstrate the stability and convergence of the presented stabilized algorithms. [ABSTRACT FROM AUTHOR]

The least mean p th power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filter have been successfully developed for nonlinear system identification in α -stable noise environments. However, there exists an inherent tradeoff between the convergence rate and steady-state performance. To address this compromise, a collaborative adaptive Volterra filter based on the convex combination scheme is proposed under the α -stable noise in this paper. By utilizing the convex combination which performs at least as well as the best component filter, the proposed algorithms achieve fast convergence rate and small misadjustment. Furthermore, by following a frame of the generalized combination scheme, two novel combination structures of Volterra filter are presented. Simulations in nonlinear system identification contexts demonstrate that the performances of the proposed algorithms are superior to the existing algorithms under the α -stable noise in terms of the convergence speed and steady state kernel error. [ABSTRACT FROM AUTHOR]

The symmetric solutions of linear matrix equations are extensively required in mathematics and engineering problems. The purpose of this paper is on deriving the biconjugate residual (BCR) algorithm for finding the least Frobenius norm symmetric solution pair ( X , Y ) of the coupled generalized Sylvester matrix equations { A 1 XB 1 + C 1 XD 1 + E 1 YF 1 = G 1 , A 2 XB 2 + C 2 XD 2 + E 2 YF 2 = G 2 . The convergence analysis shows that the BCR algorithm can compute the least Frobenius norm symmetric solution pair of the coupled generalized Sylvester matrix equations within a finite number of iterations in the absence of round-off errors. Finally, we give three numerical examples to illustrate the performance of the BCR algorithm. [ABSTRACT FROM AUTHOR]

Numerical simulations of high strain rate plastic flow have historically been built in a hypoelastic framework and use radial return (Wilkins’ method) as the solution algorithm. We show how each of these choices can lead to inaccurate and possibly nonconvergent results. We describe an alternative solution procedure based on a simple multiple time scale perturbation theory that is stable, accurate, computationally efficient and simple to implement. Further extension of these results then leads to a strain space formulation that has additional computational advantages. We illustrate our development with numerical experiments. This paper is dedicated to my friend and colleague Christo Christov on the occasion of his 60th birthday, in recognition of his many important and creative contributions to the formulation of continuum mechanics. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, two pivotal quantities are modified to construct prediction intervals for future lifetime based on random number of three parameters Weibull distribution, which can be widely applied in reliability theory and lifetime problems. The case of fixed sample size is presented as a special case. The random number has one of three important distributions as special cases. An algorithm is constructed to explain the importance of the theoretical results in applications. Simulation studies are conducted to investigate the efficiency of the purposed results. Finally, two numerical examples for real lifetime data are presented to illustrate the paper. [Copyright &y& Elsevier]

Abstract: Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an analysis of an adaptive random search (ARS) algorithm, a global minimization method. A probability model is introduced to characterize the statistical properties of the number of iterations required to find an acceptable solution. Moreover, based on this probability model, a new stopping criterion is introduced to predict the maximum number of iterations required to find an acceptable solution with a pre-specified level of confidence. Finally, this paper presents a systematic procedure for choosing the user-specified parameters in the ARS algorithm for fastest convergence. The results, which are valid for search spaces of arbitrary dimensions, are illustrated on a simple three-dimensional example. [Copyright &y& Elsevier]

Structure learning is a very important problem in the field of Bayesian networks (BNs). It is also an active research area for more than 2 decades; therefore, many approaches have been proposed in order to find an optimal structure based on training samples. In this paper, a Particle Swarm Optimization (PSO)-based algorithm is proposed to solve the BN structure learning problem; named BNC-PSO ( B ayesian N etwork C onstruction algorithm using PSO ). Edge inserting/deleting is employed in the algorithm to make the particles have the ability to achieve the optimal solution, while a cycle removing procedure is used to prevent the generation of invalid solutions. Then, the theorem of Markov chain is used to prove the global convergence of our proposed algorithm. Finally, some experiments are designed to evaluate the performance of the proposed PSO-based algorithm. Experimental results indicate that BNC-PSO is worthy of being studied in the field of BNs construction. Meanwhile, it can significantly increase nearly 15% in the scoring metric values, comparing with other optimization-based algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce the reconstruction of variational iteration method (RVIM) to solve multi-order fractional differential equations (M-FDEs), which include linear and nonlinear ones. We will easily obtain approximate analytical solutions of M-FDEs by means of the RVIM based on the properties of fractional calculus. Moreover, the convergence of proposed method will be shown. Our scheme has been constructed for the fully general set of M-FDEs without any special assumptions, and is easy to implement numerically. Therefore, our method is more practical and helpful for solving a broad class of M-FDEs. Numerical results are carried out to confirm the accuracy and efficiency of proposed method. Several numerical examples are presented in the format of table and graphs to make comparison with the results that previously obtained by some other well known methods. [ABSTRACT FROM AUTHOR]

The asymptotic stability of distributed-event triggered control for large-scale interconnected systems can be achieved with time-dependent trigger functions. The choice of some of the parameters in the trigger functions relies on some properties of the overall system, which are not known a priori by the individual nodes. This paper presents an iterative method for the distributed estimation of such parameters, which allows the event-triggered control algorithm to evolve to a less conservative design. We provide proofs of convergence while the asymptotic stability and the existence of a lower bound for the inter-event times are preserved. The complexity of the proposed approach is analyzed, and the results are illustrated through simulations. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic mentoring scheme along with a self-regulation scheme have been incorporated in the standard Particle Swarm Optimization (PSO) algorithm to empower the searching particles with human-like characteristics. The algorithm is referred to as a Dynamic Mentoring and Self-Regulation based Particle Swarm Optimization (DMeSR-PSO) algorithm. Based on their experiences, the particles are divided into three groups, viz., the mentor group, the mentee group and the independent learner group where the number of particles in each group is dynamically changing in every iteration. In human learning psychology, mentoring is regarded as a powerful and effective learning process and independent learners are the ones who do not need mentoring and are capable of performing self-regulation of their own knowledge. Therefore, the particles in each of the above three groups have different learning strategies for their velocity updates where the mentors are equipped with a strong self-belief based search, the mentees are taking guidance from the mentors and the independent learners employ self-perception strategy. The DMeSR-PSO algorithm has been extensively evaluated using the simple unimodal and multimodal benchmark functions from CEC2005, more complex shifted and rotated benchmark functions fromCEC2013 and also based on eight real- world problems from CEC2011. The results have been compared with six state-of-the-art PSO variants and five meta-heuristic algorithms for the CEC2005 problems. Further, a comparative analysis on CEC2013 benchmark functions with different PSO variants has also been presented. Finally, DMeSR-PSO's performance on the real-world problems is compared with the top two algorithms from the CEC2011 competition. The results indicate that the proposed learning strategies help DMeSR-PSO to achieve faster convergence and provide better solutions in most of the problems with a 95% confidence level, yielding an effective optimization algorithm for real-world applications. [ABSTRACT FROM AUTHOR]

Recently, krill herd algorithm (KHA) is proposed for the solution of global optimization problem. Various chaotic maps are considered in the proposed chaotic KHA (CKHA) of the present work to improve the performance of basic KHA method. It is observed that Logistic map based CKHA offers better results as compared other chaotic maps. The performance of the proposed CKHA is tested on standard 26-bus and IEEE 57-bus test power systems for the solution of optimal power flow of power system with different objectives that reflect minimization of fuel cost or active power loss or sum of total voltage deviation. Results obtained by using CKHA are compared to other evolutionary optimization techniques surfaced in the recent state-of-the-art literature. The results presented in this paper show that the proposed CKHA algorithm outperforms the other techniques in terms of convergence rate and global search ability. [ABSTRACT FROM AUTHOR]

In this paper, we consider the multi-dimensional Kesten algorithm studied in Xu and Dai (2012). The convergence in r th mean for the algorithm is established under the weaker assumptions than Xu and Dai (2012). Moreover, we obtain also the almost sure convergence of the algorithm under the conditions of Xu and Dai (2012). [ABSTRACT FROM AUTHOR]

In a recent paper, we investigated the uniform convergence of Lagrange interpolation at the zeros of the orthogonal polynomials with respect to a Freud-type weight in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with respect to the given constraints well approximates a given function. Here, starting from the interest to construct a suitable interpolation operator with a preassigned node, we introduce an algorithm that allows us to obtain new matrices. For the Lagrange operator related to these new matrices that have the preassigned node among their elements, we prove results about the optimal rate of convergence as well as we apply successfully this method to some applications. [ABSTRACT FROM AUTHOR]

In this paper, we provide the almost-sure convergence and the asymptotic normality of a smooth version of the Robbins-Monro algorithm for the quantile estimation. A Monte Carlo simulation study shows that our proposed method works well within the framework of a data stream. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a finite-time particle swarm optimization algorithm for odor source localization. First, a continuous-time finite-time particle swarm optimization (FPSO) algorithm is developed based on the continuous-time model of the particle swarm optimization (PSO) algorithm. Since the introduction of a nonlinear damping item, the proposed continuous-time FPSO algorithm can converge over a finite-time interval. Furthermore, in order to enhance its exploration capability, a tuning parameter is introduced into the proposed continuous-time FPSO algorithm. The algorithm’s finite-time convergence is analyzed by using the Lyapunov approach. Second, the discrete-time FPSO algorithm is obtained by using a given dicretization scheme. The corresponding convergence condition is derived by using a linear matrix inequality (LMI) approach. Finally, the features and performance of the proposed FPSO algorithm are illustrated by using two ill-posed functions and twenty-five benchmark functions, respectively. In numerical simulation results, the problem of odor source localization is presented to validate the effectiveness of the proposed FPSO algorithm. [Copyright &y& Elsevier]

Abstract: Recently, Gandomi and Alavi proposed a meta-heuristic optimization algorithm, called Krill Herd (KH). This paper introduces the chaos theory into the KH optimization process with the aim of accelerating its global convergence speed. Various chaotic maps are considered in the proposed chaotic KH (CKH) method to adjust the three main movements of the krill in the optimization process. Several test problems are utilized to evaluate the performance of CKH. The results show that the performance of CKH, with an appropriate chaotic map, is better than or comparable with the KH and other robust optimization approaches. [Copyright &y& Elsevier]

Abstract: Parameter estimation for nonlinear differential equations is notoriously difficult because of poor or even no convergence of the nonlinear fit algorithm due to the lack of appropriate initial parameter values. This paper presents a method to gather such initial values by a simple estimation procedure. The method first determines the tangent slope and coordinates for a given solution of the ordinary differential equation (ODE) at randomly selected points in time. With these values the ODE is transformed into a system of equations, which is linear for linear appearance of the parameters in the ODE. For numerically generated data of the Lorenz attractor good estimates are obtained even at large noise levels. The method can be generalized to nonlinear parameter dependency. This case is illustrated using numerical data for a biological example. The typical problems of the method as well as their possible mitigation are discussed. Since a rigorous failure criterion of the method is missing, its results must be checked with a nonlinear fit algorithm. Therefore the method may serve as a preprocessing algorithm for nonlinear parameter fit algorithms. It can improve the convergence of the fit by providing initial parameter estimates close to optimal ones. [Copyright &y& Elsevier]

Abstract: We consider the number of survivors in a broad class of fair leader election algorithms after a number of election rounds. We give sufficient conditions for the number of survivors to converge to a product of independent identically distributed random variables. The number of terms in the product is determined by the round number considered. Each individual term in the product is a limit of a scaled random variable associated with the splitting protocol. The proof is established via convergence (to 0) of the first-order Wasserstein distance from the product limit. In a broader context, the paper is a case study of a class of stochastic recursive equations. We give two illustrative examples, one with binomial splitting protocol (for which we show that a normalized version is asymptotically Gaussian) and one with uniform splitting protocol. [Copyright &y& Elsevier]

Abstract: We consider the problem of finding the most probable explanation (also known as the MAP assignment) on probabilistic graphical models. The dual decomposition algorithms based on coordinate descent are efficient approximate techniques for this problem, where the local dual functions are constructed and optimized to monotonically increase the cost of the dual function. In this paper, we present a unifying framework for constructing and optimizing these local dual functions, and introduce an energy distribution view to analyze the convergence rates of these algorithms. To optimize the local dual functions, we first propose a new concept—the energy distribution ratio—to describe the features of the solutions, and then derive an explicit optimal solution, which covers most of the monotonic dual decomposition algorithms. It is shown that the differences of these algorithms lie in both the forms of the local dual functions and the settings of the energy distribution ratios, and the existing algorithms mainly focus on constructing compact and solvable local dual functions. In contrast, we study the impact of the energy distribution ratios and introduce two energy distribution criteria for fast convergence. Moreover, we exploit dynamic energy distribution ratios to optimize the local dual functions, and propose a series of improved algorithms. The experimental results on synthetic and real problems show the improved algorithms outperform the existing ones on the convergence performance. [Copyright &y& Elsevier]

Abstract: The fast global k-means (FGKM) clustering algorithm is one of the most effective approaches for resolving the local convergence of the k-means clustering algorithm. Numerical experiments show that it can effectively determine a global or near global minimizer of the cost function. However, the FGKM algorithm needs a large amount of computational time or storage space when handling large data sets. To overcome this deficiency, a more efficient FGKM algorithm, namely FGKM+A, is developed in this paper. In the development, we first apply local geometrical information to describe approximately the set of objects represented by a candidate cluster center. On the basis of the approximate description, we then propose an acceleration mechanism for the production of new cluster centers. As a result of the acceleration, the FGKM+A algorithm not only yields the same clustering results as that of the FGKM algorithm but also requires less computational time and fewer distance calculations than the FGKM algorithm and its existing modifications. The efficiency of the FGKM+A algorithm is further confirmed by experimental studies on several UCI data sets. [Copyright &y& Elsevier]

Abstract: In cellular mobile systems, the received carrier-to-interference ratio (CIR) can be maintained within the desirable range provided that the path gain remains approximately constant over a number of consecutive power control steps. However, when channels suffer short-term fading, it is not clear whether existing power control algorithms remain convergent. This paper proposes a distributed fixed-step power control algorithm with binary feedback via window concept for cellular mobile systems. The essence of the proposed algorithm is that the power control step size can be regulated by window size. The performance of the proposed scheme is analyzed in short-term fading channels. A sufficient condition for system stability is derived using a simple received CIR model and a power control window. It is shown herein that the bound of the received CIR of each user varies as a function of the target CIR, the size of the power control step and the link gain. The analysis and simulation results show that if the step size is properly set according to the window size, the proposed algorithm can achieve a small convergence region and a fast convergence rate. [Copyright &y& Elsevier]

Abstract: In this paper, we prove the convergence of a numerical algorithm that switches in some deterministic or random manner, the control parameter of a class of continuous-time nonlinear systems while the underlying initial value problem is numerically integrated. The numerically obtained attractor is a good approximation of the attractor obtained when the control parameter is replaced with the average of the switched values. In this way, a generalization of Parrondo’s paradox can be obtained. As an application, the Lorenz and Rabinovich–Fabrikant systems are used for illustration. [Copyright &y& Elsevier]

Abstract: Load balancers distribute workload across multiple nodes based on a variation of the round robin algorithm, or a more complex algorithm that optimizes a specified objective or allows for horizontal scalability and higher availability. In this paper, we investigate whether robust load balancing can be achieved using a local co-operative mechanism between the resources (nodes). The local aspect of the mechanism implies that each node interacts with a small subset of the nodes that define its neighborhood. The co-operative aspect of the mechanism implies that a node may offload some of load to its neighbor nodes that have lesser load or accept jobs from neighbor nodes that have higher load. Each node is thus only aware of the state of its neighboring nodes and there is no central entity that has the knowledge of the state of all the nodes. We model the overall mechanism of load balancing based on local interactions as a congestion game and show that convergence to the Nash equilibrium is possible using only local interactions. We derive worst case bounds on the number of transfers (time) required to achieve global load balancing under this setup. We also include simulation results to demonstrate emergent global load balancing based only on local interactions and local information. [Copyright &y& Elsevier]

Abstract: In this paper, a ship lock scheduling problem is investigated. Ships arrive randomly over time, and the instantaneous arrival rates are allowed to vary both temporally and stochastically in an arbitrary manner. A data-driven approach is applied to a single ship lock scheduling, which is a typical optimizing and decision-making problem. The objective is to minimize the operation costs and other costs(e.g. water cost, electricity cost, and staff welfare cost) by selecting an appropriate slot number during a planned period. The convergence of data-driven approach is discussed from three aspects: the convergence of ant colony optimization algorithm, the convergence of the proposed algorithm, and the error between the historical ship data and the current arrival ship data. The research findings are beneficial for the convergence analysis of data-driven theory and the management of waterway transportation. [Copyright &y& Elsevier]

Abstract: Classification is one of the key issues in the fields of decision sciences and knowledge discovery. In this paper, we present a new classification method based on gravitational potential energy between particles. The basic principle of gravitation based classification (GBC) algorithm is to find the equilibrium condition of the classifier, which is modeled as a classifier line between two groups of fixed particles. In the proposed approach, the input data is a collection of masses, which interact with each other based on Newton’s universal law of gravitation and the laws of motion. We present a convex formulation for this problem that always converges to a global optimum solution. The proposed method has been compared with some well-known classification approaches, and the results confirm the high performance of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper presents a novel Constrained Optimization based on Modified Differential Evolution algorithm (COMDE). In the new algorithm, a new directed mutation rule, based on the weighted difference vector between the best and the worst individuals at a particular generation, is introduced. The new directed mutation rule is combined with the modified basic mutation strategy DE/rand/1/bin, where only one of the two mutation rules is applied with the probability of 0.5. The proposed mutation rule is shown to enhance the local search ability of the basic Differential Evolution (DE) and to get a better trade-off between convergence rate and robustness. Two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction. Additionally, a dynamic non-linear increased crossover probability is utilized to balance the global exploration and local exploitation. COMDE also includes a modified constraint handling technique based on feasibility and the sum of constraints violations. A new dynamic tolerance technique to handle equality constraints is also adopted. The effectiveness and benefits of the new directed mutation strategy and modified basic strategy used in COMDE has been experimentally investigated. The effect of the parameters of the crossover probability function and the parameters of the dynamic tolerance equation on the performance of COMDE have been analyzed and evaluated by different experiments. Numerical experiments on 13 well-known benchmark test functions and five engineering design problems have shown that the new approach is efficient, effective and robust. The comparison results between the COMDE and the other 28 state-of-the-art evolutionary algorithms indicate that the proposed COMDE algorithm is competitive with, and in some cases superior to, other existing algorithms in terms of the quality, efficiency, convergence rate, and robustness of the final solution. [Copyright &y& Elsevier]

Abstract: Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was proposed as a variant of PSO with better global search ability. Although it has been shown to perform well in finding optimal solutions for many optimization problems, there has so far been little theoretical analysis on its convergence and performance. This paper presents a convergence analysis and performance evaluation of the QPSO algorithm and it also proposes two variants of the QPSO algorithm. First, we investigate in detail the convergence of the QPSO algorithm on a probabilistic metric space and prove that the QPSO algorithm is a form of contraction mapping and can converge to the global optimum. This is the first time that the theory of probabilistic metric spaces has been employed to analyze a stochastic optimization algorithm. We provided a new definition for the convergence rate of a stochastic algorithm as well as definitions for three types of convergence according to the correlations between the convergence rate and the objective function values. With these definitions, the effectiveness of the QPSO is evaluated by computing and analyzing the time complexity and the convergence rate of the algorithm. Then, the QPSO with random mean best position (QPSO-RM) and the QPSO with ranking operator (QPSO-RO) are proposed as two improvements of the QPSO algorithm. Finally, some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison between QPSO, QPSO-RM, QPSO-RO and other variants of PSO. [Copyright &y& Elsevier]

Abstract: In this paper, we consider and study a class of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators in Hilbert spaces. We also construct a new perturbed iterative algorithm framework with errors and investigate variational graph convergence analysis for this algorithm framework in the context of solving the nonlinear operator inclusion couple along with some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. The obtained results improve and generalize some well known results in recent literatures. [Copyright &y& Elsevier]

Abstract: In this paper, a hybrid of algorithms for electromagnetism-like mechanisms (EM) and particle swarm optimisation (PSO), called HEMPSO, is proposed for use in designing a functional-link-based Petri recurrent fuzzy neural system (FLPRFNS) for nonlinear system control. The FLPRFNS has a functional link-based orthogonal basis function fuzzy consequent and a Petri layer to eliminate the redundant fuzzy rule for each input calculation. In addition, the FLPRFNS is trained by the proposed hybrid algorithm. The main innovation is that the random-neighbourhood local search is replaced by a PSO algorithm with an instant-update strategy for particle information. Each particle updates its information instantaneously and in this way receives the best current information. Thus, HEMPSO combines the advantages of multiple-agent-based searching, global optimisation, and rapid convergence. Simulation results confirm that HEMPSO can be used to perform global optimisation and offers the advantage of rapid convergence; they also indicate that the FLPRFNS exhibits high accuracy. [Copyright &y& Elsevier]

Abstract: When the Newton–Raphson algorithm or the Fisher scoring algorithm does not work and the EM-type algorithms are not available, the quadratic lower-bound (QLB) algorithm may be a useful optimization tool. However, like all EM-type algorithms, the QLB algorithm may also suffer from slow convergence which can be viewed as the cost for having the ascent property. This paper proposes a novel ‘shrinkage parameter’ approach to accelerate the QLB algorithm while maintaining its simplicity and stability (i.e., monotonic increase in log-likelihood). The strategy is first to construct a class of quadratic surrogate functions that induces a class of QLB algorithms indexed by a ‘shrinkage parameter’ () and then to optimize over under some criterion of convergence. For three commonly used criteria (i.e., the smallest eigenvalue, the trace and the determinant), we derive a uniformly optimal shrinkage parameter and find an optimal QLB algorithm. Some theoretical justifications are also presented. Next, we generalize the optimal QLB algorithm to problems with penalizing function and then investigate the associated properties of convergence. The optimal QLB algorithm is applied to fit a logistic regression model and a Cox proportional hazards model. Two real datasets are analyzed to illustrate the proposed methods. [Copyright &y& Elsevier]

Abstract: In this paper, the boundary detection problem, which is governed by the Laplace equation, is analyzed by the modified collocation Trefftz method (MCTM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the boundary detection problem, the Cauchy data is given on part of the boundary and the Dirichlet boundary condition on the other part of the boundary, whose spatial position is unknown a priori. By adopting the MCTM, which is meshless and integral-free, the numerical solution is expressed by a linear combination of the T-complete functions of the Laplace equation. The use of a characteristic length in MCTM can stabilize the numerical procedure and ensure highly accurate solutions. Since the coefficients of MCTM and the position of part of the boundary are unknown, to collocate the boundary conditions will yield a system of nonlinear algebraic equations; the ECSHA, which is exponentially convergent, is adopted to solve the system of nonlinear algebraic equations. Several numerical examples are provided to demonstrate the ability and accuracy of the proposed meshless scheme. In addition, the consistency of the proposed scheme is validated by adding noise into the boundary conditions. [Copyright &y& Elsevier]

Abstract: The sandwich algorithm (SA) is an alternative to the data augmentation (DA) algorithm that uses an extra simulation step at each iteration. In this paper, we show that the sandwich algorithm always converges at least as fast as the DA algorithm, in the Markov operator norm sense. We also establish conditions under which the spectrum of SA dominates that of DA. An example illustrates the results. [Copyright &y& Elsevier]