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This study introduces a novel approach for integrating a compact mechanism into the Marine Predator Algorithm (MPA), subsequently proposing innovative parallel and communication strategies. The synergistic combination of these methodologies substantially augments the global search efficiency and accelerates the convergence rate of the original MPA. The paper culminates in presenting an enhanced version of the Marine Predator Algorithm, termed PCMPA, which leverages compact parallel technology. The performance of PCMPA, alongside a range of comparative algorithms, is rigorously evaluated using the CEC2013 benchmark test functions. These comparative algorithms encompass recent variants of MPA, PSO, DE, and other newly developed algorithms. Evaluation results reveal that PCMPA outperforms its counterparts in a more extensive array of test functions. To corroborate PCMPA's efficacy in real-world scenarios, the algorithm is applied to parameter optimization in Backpropagation neural network (BNN) and targeted engineering optimization challenges. This application demonstrates that PCMPA consistently achieves enhanced performance in practical implementations. • The study presents a novel variant of the Marine Predators Algorithm, dubbed PCMPA. • The paper benchmarks PCMPA against other Marine Predators Algorithm variants and other Algorithms. • The research applies PCMPA to optimize parameters of BNNs and to tackle engineering optimization challenges. [ABSTRACT FROM AUTHOR]

In this paper, a temporal second order two-grid difference scheme is proposed for the two-dimensional nonlinear time-fractional partial integro-differential equations with a weakly singular kernel. The first-order backward difference and L 1 formula are used in the temporal direction to estimate the first level of time, the L 2 − 1 σ formula and L 1 -type formula are used in the temporal direction for later time steps, and the central difference formula is used in the spatial directions. To improve the computational efficiency of nonlinear system, an efficient time two-grid algorithm is proposed. This algorithm firstly solves a nonlinear system on the coarse grid, and then the Lagrangian linear interpolation is applied on the coarse grid to estimate the function values on the fine grid. The stability and convergence of the two-grid difference scheme are analyzed by the energy method. The convergence order of the two-grid difference scheme is O (τ F 2 + τ C 4 + h x 2 + h y 2) , where τ F and τ C are the time step sizes of fine grid and coarse grid respectively, while h x and h y are the space step sizes. Numerical experiments show that the accuracy of the theoretical analysis and the efficiency of the two-grid algorithm. [ABSTRACT FROM AUTHOR]

Bonobo optimizer (BO) is a recent metaheuristic algorithm inspired by the social behavior of bonobos. BO maintains a robust search strategy based on two distinct phases that involve interesting mechanisms, such as the fission–fusion method for selection and an efficient process for producing new candidate solutions. Despite its remarkable capacity, BO presents a critical flaw that corresponds to an inappropriate balance between exploration and exploitation. Under such conditions, suboptimal or even poor solutions can be obtained. This paper proposes a modified BO algorithm in which the trajectory of each search agent is modified dynamically through the adaptation of the main parameters of the algorithm. With this new mechanism, the algorithm allows for the exploration and exploitation of different regions of the solution space and determines the global optimum in a faster manner. The performance of the proposed algorithm is evaluated by considering two scenarios. One is the optimization of 23 benchmark functions and the second is the problem of power allocation in wireless networks. The results show that the proposed scheme enhances the performance of the basic BO method by increasing the robustness and providing a better solution quality. [ABSTRACT FROM AUTHOR]

The paper deals with the approximation and numerical realization of the Stokes system in 3D with Coulomb's slip boundary conditions. The weak velocity–pressure formulation leads to an implicit inequality type problem which is discretized by the P1+bubble/P1 elements. To regularize the discrete non-smooth slip term and to release the discrete impermeability condition the duality approach is used. For numerical realization of the resulting saddle-point problem two strategies are proposed, namely (i) its fixed-point formulation solved by the method of successive approximations (i i) the direct numerical solution of the saddle-point problem. The semi-smooth Newton method is used to solve non-smooth equations appearing in both these approaches. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation of the spectral conjugate directions formulation for optimizing unconstrained problems. A novel modified algorithm is proposed based on the conjugate gradient coefficient method. The algorithm employs the Wolfe inexact line search conditions to determine the optimum step length at each iteration and selects the appropriate conjugate gradient coefficient accordingly. The algorithm is evaluated through several numerical experiments using various unconstrained functions. The results indicate that the algorithm is highly stable, regardless of the starting point, and has better convergence rates and efficiency compared to classical methods in certain cases. Overall, this research provides a promising approach to solving unconstrained optimization problems. [ABSTRACT FROM AUTHOR]

This paper appends three proposed heuristic algorithms, viz. Initialization Algorithm, Fraction Repair Algorithm and Negative Repair Algorithm, to Particle Swarm Optimization (PSO) and extends its application to Pure Integer Linear Solid Transportation Problem (STP). The chief contribution of the paper is that the proposed Hybrid Particle Swarm Optimization (HPSO) algorithm discretizes the continuous search space of PSO so that it can operate in the discrete solution space of STP with any of the valid parameter settings. The Initialization Algorithm is developed to generate the sufficient number of random solutions for initiating HPSO with a diverse population of given size. Whereas Fraction Repair and Negative Repair Algorithms are developed to ensure that each successive population obtained with HPSO remains in the solution space of STP. The validity of HPSO is examined and illustrated by solving a numerical problem with certain parameter settings. Further, the HPSO demonstrates its ability to obtain an optimal or near optimal solution along with the alternate optimal solution, if it exists. It searches for the solutions even without adhering to the rigid conditions of traditional methods that every solution of STP must have a fixed number of non-zero decision variables. Moreover, the performance of HPSO is tested with three different parameter settings and compared amongst each other to analyze their significance in solving the problem. The performance of HPSO and the variants of parameters are statistically validated through an extensive experimental design. [ABSTRACT FROM AUTHOR]

In this paper, an enhanced hybrid chameleon swarm algorithm (CSA) is proposed and applied to the degree reduction problem of disk Wang–Ball (DWB) curve. CSA is a novel population-based algorithm inspired by the hunting behavior of chameleons, its simplicity and easy implementation make it applied to different fields. However, it suffers from premature convergence and easy to fall into local optimum, especially in the face of complex optimization problems. Therefore, this paper proposes an enhanced hybrid CSA (CCECSA, for short). Compared with the classic CSA, the proposed CCECSA mainly introduces three improvements: (1) The crisscross optimization algorithm is mixed to avoid premature convergence, in which the horizontal and vertical crossover can generate moderation solutions to increase the diversity of the population. (2) Elite guidance mechanism is introduced to speed up the convergence. (3) Competitive substitution mechanism is added to replace the worst individual, and an interference strategy is set to prevent the algorithm from falling into a local optimum. The efficiency and robustness of the proposed CCECSA are demonstrated by the comparison results with some advanced meta-heuristic algorithms on CEC2014, CEC2017, and 4 engineering design examples. In addition, for the degree reduction problem of DWB curves, the multi-degree reduction optimization models of its center curve and radius function are established respectively. At the same time, the optimal center curve and radius function of the approximating DWB curves of lower degree are obtained by the proposed CCECSA. The experimental results show that the proposed CCECSA achieves the optimal solution with better convergence and robustness. The source code of CCECSA is publicly available in the supplementary material related to this article. [ABSTRACT FROM AUTHOR]

This paper proposes an improved iterative algorithm based on a Newton iterative algorithm, which is used to research the stochastic linear quadratic optimal tracking (SLQT) control for stochastic continuous-time systems. Firstly, a Newton iterative algorithm for solving stochastic algebraic Riccati equations (SAREs) is derived based on the Frechet derivative. Secondly, an improved iterative algorithm in an incremental form for indirectly solving SAREs is presented by combining the numerical iterative method with the incremental Newton iterative (INI) algorithm and introducing a tuning parameter. Under a suitable initial condition, the convergence of the improved iterative algorithm is talked over. Finally, numerical simulation experiments are carried out to compare our proposed improved iterative algorithm with some known works. The results show that the improved iterative algorithm has a faster convergence rate. [ABSTRACT FROM AUTHOR]

Whale optimization algorithm (WOA), as an advanced optimization algorithm with simple structure, has been favored by various fields. However, there are some disadvantages of WOA, such as slow convergence speed, low precision and falling into local optimal value easily. In this paper, a novel improved whale optimization algorithm (IWOA) with multi-strategy and hybrid algorithm is proposed to overcome above shortcomings. Firstly, IWOA initializes the population by chaotic mapping to avoid the initial population distribution of WOA deviating from the optimal value. Secondly, IWOA combines the pheromone of the black widow algorithm and the opposition-based learning strategy to modify the population, which improves the convergence speed and the global performance of WOA respectively. Finally, the adaptive coefficients and the new update modes replace the original update modes, which makes the structure of WOA simpler and more accurate. In addition, the convergence of IWOA is also proved in this paper. On the one hand, to demonstrate the effectiveness of IWOA, 23 benchmark functions are used to test various performance of the algorithm. On the other hand, in order to prove the superiority of IWOA, the experimental results are compared and analyzed with other optimization algorithms. Simulation results show that IWOA proposed in this paper owns excellent performance in convergence speed, stability, accuracy and global performance, compared with other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a novel algorithm for anti-diagonalization of skew symmetric matrices via using orthogonal similarity transformations has been introduced. The theory and algorithm about the anti-triangular factorization of skew-symmetric matrices are proved. In the case of skew-symmetric matrices, we prove that the anti-diagonal form is always obtained, resulting in developing a new factorization scheme. Moreover, a theoretical algorithm is given based on the theory of double eigenvector system, which provides all the information for the factorization of arbitrary matrices. Finally, the proposed algorithm is verified effective and efficient through the numerical experiments of anti-diagonalization of matrices over a general number field. [ABSTRACT FROM AUTHOR]

Meta-heuristic algorithms have been widely used to solve different optimization problems. There have always been ongoing efforts to develop new and efficient algorithms. In this paper, the Orchard Algorithm (OA) is designed and introduced, inspired by fruit gardening. In this process, various actions such as irrigation, fertilization, trimming, and grafting lead to a fruit orchard where most trees grow and produce fruit adequately. In OA, both explorations of the search space and exploitation of the best solutions are achieved using personal and social behavior. By introducing various operators such as annual growth, screening, and grafting, the algorithm can efficiently search and explore the search space. The performance of the proposed OA algorithm was evaluated on CEC2005, IEEE CEC06 2019,test functions, and five real-world engineering problems compared with 13 widely used and competitive algorithms. Thirty benchmark functions were used to compare the capabilities of the OA algorithm with other research. The OA yields far better results in many aspects than the other algorithms. The results show the OA's superiority and this algorithm's capability in solving optimization problems. • We proposed new meta-heuristic algorithm for solving optimization problems. • The orchard algorithm is introduced, which is inspired by fruit gardening process. • In OA, using personal and social behavior, exploration and exploitation are achieved. • At 60 test functions, OA performed better than other algorithms. • The orchard algorithm performed very well in five engineering benchmark problems. [ABSTRACT FROM AUTHOR]

In this paper, the identification of a time delay Hammerstein system is considered. Based on a normalized Gaussian white input, a cross-correlation function increment method is investigated to estimate the time delay without the parameter estimates. The integer delay is obtained directly, not by rounding a decimal delay estimate. To identify the parameters, a novel multi-error information gradient algorithm with variable stacking length is proposed. In the parameter identification algorithm, the slow stochastic information gradient algorithm is accelerated by a stacked error named multi-error and the variable stacking length is determined by a loss function descent criterion. Several simulation experiments validate the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic strategy-based quadratic opposition-based learning adaptive variable-speed whale optimization algorithm is proposed. The improved algorithm is used to solve the problems that the whale optimization algorithm's convergence accuracy and convergence speed are insufficient. Firstly, the proposed algorithm is initialized by a method based on chaotic maps and quadratic opposition-based learning strategy to obtain a population with better ergodicity. Secondly, by introducing an adaptive variable speed adjustment factor, each search link unites to form a negative feedback regulation network, thereby effectively balancing the algorithm's exploration ability and exploitation ability. Finally, 20 benchmark test functions and 3 complex constrained engineering optimization problems were used to conduct extensive tests on the improved algorithm. The results show that the improved algorithm has better performance than others in terms of convergence speed and convergence accuracy in a majority of cases, and can effectively jump out of the local optimum. [Display omitted] • Firstly, this paper proposed a quadratic Opposition-Base Learning strategy based on Bernoulli map, and successfully obtained a higher quality initial whale population. • Secondly, this paper proposed a new variable speed adjustment factor and a cooperative convergence factor, and combine them with individual fitness to form a negative feedback adjustment network. Experiments show that the algorithm has good self-adjusting ability. • Finally, the range of some of the original random numbers in whale optimization algorithm has been changed. This adjustment allows the algorithm to have a more variable search range. [ABSTRACT FROM AUTHOR]

More and more privacy-sensitive images have been produced daily. Chaotic encryption guarantees that only the targeted receiver can obtain the raw image. Many works perform encryption on bit-level for better permutation but incur an unbearable time consumption caused by generating additional 3D coordinates. High-dimensional chaotic system, suitable for encrypting images, needs to iterate repeatedly for several rounds, resulting in low encrypting efficiency. This paper proposes a parallel image encryption algorithm using intra bitplane scrambling. Four threads are utilized to encrypt the images in bit-level during the permutation, where each thread scrambles two bitplanes. In diffusion, we build multiple threads to generate keystream segments to reduce encryption time. We make cryptographic analyses and compare the encryption speed with the advanced works, demonstrating that our scheme is secure and efficient. • The proposed parallel bit-level permutation algorithm offers a good trade-off between efficiency and effect. • To accelerate the keystreams generation in diffusion stage, multi-threading technology is used to generate them in parallel. • The results of security analyses show the proposed algorithm has high efficiency compared with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

For the operation of the salp swarm algorithm(SSA), the leaders fall into local optimum, which leads to the population falling into local optimum problem. In this paper, a salp swarm algorithm based on Harris Eagle foraging strategy is proposed(ISSAHF). Harris hawk optimization algorithms of four types of feeding mechanism are integrated into salp location update process optimization algorithm follower. To strengthen the exploitation of potential areas, complemented by a multi-point leadership crossover strategy to maintain a balance between exploitation and exploration. The performance of the proposed ISSAHF was compared, and Wilcoxon's statistical analysis was performed on 20 benchmark functions including unimodal, multimodal, and partial CEC2014. Finally, ISSAHF is applied to three practical engineering optimization problems to evaluate its optimization performance further. [ABSTRACT FROM AUTHOR]

This paper suggests a new hybrid algorithm by integrating two population-based algorithms: Whale Optimization Algorithm (WOA) and Flower Pollination Algorithm (FPA), to solve complex nonlinear systems and unconstrained optimization problems. WOFPA denotes the suggested algorithm, a hybrid Whale Optimization Algorithm and Flower Pollination Algorithm. Nonlinear systems can be cast into unconstrained optimization problems, called merit functions, where the optimal solutions for the merit functions are equivalent to the solutions of nonlinear systems. WOFPA aims to decrease the execution time and the complexity of WOA and FPA. WOFPA has the advantages of WOA and FPA; WOFPA is a high-quality algorithm to solve both problems, nonlinear systems and unconstrained optimization problems. For example, FPA may have a premature convergence in the local optima, and WOFPA subdues the disadvantage of FPA. Numerical experiments of 14 benchmarks nonlinear systems and 30 CEC 2014 benchmarks unconstrained optimization functions with various dimensions are employed to test the performance of WOFPA. To have a further investigation for the performance of WOFPA, WOFPA is compared with WOA, FPA, and other existing algorithms from the literature. Two non-parametric statistical tests, Wilcoxon statistical test and the Friedman test, are conducted for this study to check the performance of the proposed algorithms and other compared algorithms and the significance of our results. The experiment results demonstrate that WOFPA performs better than other algorithms in the literature by getting the optimum solutions for most nonlinear systems and optimization problems and proves its efficiency compared with other existing algorithms. • This paper proposes a new hybridization Whale Optimization Algorithm and Flower Pollination Algorithm. • We solve system of nonlinear equations and unconstrained optimization problem. • The efficiency and effectiveness of our algorithm are provided. • Experimental results prove the superiority of our algorithm over the state-of-the-arts. [ABSTRACT FROM AUTHOR]

In a previous paper based on the interpolation finite difference method, a calculation system was shown for calculating 1D (one-dimensional) Laplace's equation and Poisson's equation using high-order difference schemes. Finite difference schemes, from the usual second-order to tenth-order differences, including odd number order differences, were systematically and instantaneously derived over equally/unequally spaced grid points based on the Lagrange interpolation function. Using the direct method with the band diagonal matrix algorithm, 1D Poisson equations were numerically calculated under double precision floating arithmetic, but it became clear that high accurate calculations could not be secured in high-order differences because "digit-loss errors" caused by the finite precision of computations occurred in the calculations when using the high-order differences. The double precision calculation corresponds to 15 (significant) digit calculation. In this paper, we systematically investigate how the calculation accuracy changes by high precision calculations (30-digit, and 45-digit calculations). Under 45-digit calculation, where the digit-loss error can be almost ignored, the high-order differences enable extremely high-accurate calculations. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a specific type of quasilinear boundary value problem with Dirichlet boundary conditions and with p -Laplacian. We show two ways of proving the existence of nontrivial weak solutions. The first one uses the mountain pass theorem, the other one is based on our new minimax theorem. This method is novel even for p = 2. In the paper, we also present a numerical algorithm based on the introduced approach. The suggested algorithm is illustrated on numerical examples and compared with a current approach to demonstrate its efficiency. [ABSTRACT FROM AUTHOR]

A recently developed metaheuristic optimization algorithm, Salp Swarm Algorithm (SSA), has manifested its capability in solving various optimization problems and many real-life applications. SSA is based on salps' swarming behaviour when finding their way and searching for food in the oceans. Nonetheless, like most metaheuristic algorithms, SSA experiences low convergence and stagnation in local optima and rate. There is a need to enhance SSA to speed its convergence and effectiveness to solve complex problems. In the present study, we will introduce chaos into SSA (CSSA) to increase its global search mobility for robust global optimization. Detailed studies are carried out on real-world nonlinear benchmark systems and CEC 2013 benchmark functions with chaotic map (Tent). Here, the algorithm utilizes a Tent map to tune the salp leaders' attractive movement around food sources. The experimental results, considering both convergence and accuracy simultaneously, demonstrate the effectiveness of CSSA for 12 nonlinear systems and 28 unconstrained optimization problems CEC 2013. Two nonparametric statistical tests, the Friedman test and Wilcoxon Signed-Rank Test, are conducted to show the superiority of CSCA over other states of the art algorithms and our results' significance. • This paper introduces chaos into Salp Swarm Algorithm. • Solve 28 unconstrained optimization problems, CEC and 12 nonlinear systems. • The effectiveness and efficiency of our algorithm are provided. • Experimental results prove superiority of our algorithm over the state-of-the-arts. [ABSTRACT FROM AUTHOR]

In this paper, a kinetic equation of Euler–Bernoulli beam is established with variable order fractional viscoelastic model. An effective numerical algorithm is proposed. This method uses a combination of shifted Bernstein polynomial and Legendre polynomial to approximate the numerical solution. The effectiveness of the algorithm is tested and verified by mathematical examples. The dynamic behavior of viscoelastic beams made of two materials under various loading conditions is studied. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to solve the two-dimensional nonlinear fractional partial integro-differential equation (PIDE) with a weakly singular kernel by using the time two-grid finite difference (FD) algorithm. The second-order backward difference formula (BDF) and L1 scheme are used in time. The time two-grid algorithm is constructed to improve the solving efficiency of nonlinear systems. The Newton iteration is used to solve nonlinear discrete system on the coarse grid, and then we apply Lagrangian linear interpolation to attain the function value used in constructing the difference scheme on the fine grid. The second-order finite difference method (FDM) is used in space. The unconditional stability and convergence are attained for the two-grid fully discrete system. Numerical experiments show that the used CPU time for the presented two-grid numerical algorithm is lower than the general finite difference method for solving the nonlinear system. [ABSTRACT FROM AUTHOR]

Due to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal-polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation and pixel diffusion operation with the proposed SPCCS. The detailed simulation results verify superiority and effectiveness of the proposed image encryption algorithm. [ABSTRACT FROM AUTHOR]

The paper offers a novel technique for resolving the multi-robot cooperation for stick carrying applications. The problem addresses the computation of a collision-free optimal path from a predefined initial position to target position during transportation of stick or object cooperatively by robot pair in the multi-robot environment. The stick carrying application has been resolved by embedding the modified Q-learning into the hybrid process of an improved version of particle swarm optimization and intelligent water drop algorithm. In the present context, modified Q-learning generates the best solution for particle swarm optimization and particle swarm optimization is upgraded through the perception of cubic spline and generate the optimal position in the successive iteration using intelligent water drop algorithm and also enhances the intensification and diversification capability of particle swarm optimization. The proposed hybrid algorithm computes the collision-free subsequent position for each robot pair by avoiding the obstacles in its path, avoiding the trapping at the local optima, improving the convergence speed, optimizing the path distance for every pair of robots, energy usage and path smoothness both in the static and dynamic environment's. The validation of the proposed hybrid algorithm has been verified and checked the robustness of the algorithm through computer simulation and real robots through Webots simulator. Further, the efficiency of the proposed algorithm has been verified by comparing the result obtained proposed algorithm and its competitor algorithms and comparing the result of the proposed algorithm with the existing state-of arts. The comparison result shows that the proposed algorithm is superior to its competitor algorithms and state of arts for different matrices. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic adaptive firefly algorithm to overcome the disadvantages of the standard firefly algorithm, to improve the convergence rate and solution precision, and to avoid the premature algorithm trapping at the local extreme. It has a global-oriented moving mechanism and can dynamically adjust the step size and attractiveness. First, through the adaptive deviation degree strategy of optimal distance combining with the Gaussian distribution, it optimizes the fixed step-factor to balance the exploration and excavation capabilities of the algorithm and improves the diversity of the population. Second, minimum attractiveness is introduced to the algorithm, and is adaptively changed with the number of iterations, which can avoid random walk due to lack of traction between fireflies. Finally, this paper improves the mobility mechanism based on the position of the current optimal firefly. It enables firefly move with global orientation and also expands the sharing of information between fireflies to improve the overall evolutionary optimization performance of the algorithm. Theoretical analysis proves the convergence and time complexity of the improved algorithm. The simulation results of several test functions and engineering constraint optimization problems show that the improved algorithm has better solution performance, and clearly improves the convergence speed and solution accuracy. [ABSTRACT FROM AUTHOR]

This paper introduces a 3-layer feed-forward neuronet model, trained by novel beetle antennae search weights-and-structure-determination (BASWASD) algorithm. On the one hand, the beetle antennae search (BAS) algorithm is a memetic meta-heuristic optimization algorithm capable of solving combinatorial optimization problems. On the other hand, neuronets trained by a weights-and-structure-determination (WASD) algorithm are known to resolve the shortcomings of traditional back-propagation neuronets, including slow speed of training and local minimum. Combining the BAS and WASD algorithms, a novel BASWASD algorithm is created for training neuronets, and a multi-input BASWASD neuronet (MI-BASWASDN) model is introduced. Using a power sigmoid activation function and while managing the model fitting and validation, the BASWASD algorithm finds the optimal weights and structure of the MI-BASWASDN. Four financial datasets, taken from the European Central Bank publications, validate and demonstrate the MI-BASWASDN model's outstanding learning and predicting performance. Also included is a comparison of the MI-BASWASDN model to three other well-performing neural network models, as well as a MATLAB kit that is publicly available on GitHub to promote and support this research. [ABSTRACT FROM AUTHOR]

In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. [ABSTRACT FROM AUTHOR]

In this paper, we first build a model for a complicated newsvendor problem, which is involved with optimization to preseason production quantity with random yields and outsourcing quantity with supplier quantity discounts. Different from the existing models, a two-stage decision-making strategy is proposed for the retailer such that the possible loss, caused by the uncertainty of production, is reduced in virtue of dynamically choosing the outsourcing quantities and sales prices. Additionally, the cross-elasticity of prices is incorporated into formulating the random and price-dependent demand function in our model. Consequently, the mathematical model is expressed by a parameterized optimization problem, and a cyclic coordinate descent algorithm (CCD), combined with a feasible direction method and a parameters-choosing procedure, is developed to obtain optimal solutions of the original problem. Both substitute and complementary scenarios for different products are further investigated by numerical simulation. Main managerial implications are summarized as follows: (1) The two-stage policy of decision-making brings more benefits than a static policy for the complicated newsvendor problems. (2) The budget available is a critical constraint for the small-and-medium sized business, the maximum expected profit increases as the budget becomes greater, but remains at the same level after it reaches a threshold value. (3) The cross elasticity relationship between the products plays a critical role in choosing optimal quantities of preseason production, sales prices and outsourcing quantities. [ABSTRACT FROM AUTHOR]

In this paper we considers the Caputo fractional semi linear control systems, then we obtain sufficient conditions for regional boundary controllability of a board class of considered system with order (0 < α ≤ 1). The conditions are obtained using fractional calculus and Schauder's fixed point theorem, that leads to an important approach based on a link between internal and boundary controllability which will be summarized as an algorithm. At the end, some simulations are given to show the application of our result. [ABSTRACT FROM AUTHOR]

An effective numerical algorithm is presented to analyze the fractional viscoelastic plate in the time domain for the first time in this paper. The viscoelastic behavior of the plate is described with fractional Kelvin–Voigt (FKV) constitutive model in three-dimensional space. A governing equation with three independent variables is established. Ternary unknown function in the governing equation is solved by deriving integer and fractional order differential operational matrices of the shifted Legendre polynomials. Error analysis and mathematical example are presented to verify the effectiveness and accuracy of proposed algorithm. Finally, numerical analysis of the plate under different loading conditions is carried out. Effects of the damping coefficient on vibration amplitude of the viscoelastic plate are studied. The results obtained are consistent with the current reference and actual situation. It shows that shifted Legendre polynomials algorithm is suitable for numerical analysis of fractional viscoelastic plates. • The fractional order governing equation of a viscoelastic plate is established. • Shifted Legendre polynomials algorithm is used to solve the governing equation. • The feasibility and efficiency of the proposed algorithm are verified. • Transverse displacements of viscoelastic plate are calculated directly in the time domain. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the decentralized proportional–integral–derivative (PID) output-feedback control problem for a class of discrete-time uncertain large-scale systems with delayed interconnections. The robust finite time stabilization of the addressed uncertain large-scale system is attained via the feedback control with the prescribed extended passive performance index. Specifically, by using an appropriate Lyapunov–Krasovskii functional, a new set of sufficient conditions is derived on the basis of linear matrix inequality which ensures the finite-time boundedness of the augmented closed-loop uncertain large-scale systems. Furthermore, cone complementarity linearization (CCL) algorithm is developed to obtain the control gain parameters. Finally, a numerical example is provided to illustrate the effectiveness of proposed control design. [ABSTRACT FROM AUTHOR]

In this paper, we present a direct parallel block W Z algorithm, named DPBWZA, for the solution of block tridiagonal toeplitz–block–toeplitz (TBT) linear system A x = f. The algorithm is based on the proposed block W Z factorization of the coefficient matrix A. Existence of the block W Z factorization for block tridiagonal TBT block diagonally dominant matrix is proved. Error analysis of the parallel algorithm DPBWZA is presented and numerical stability of the algorithm is established. Numerical experiments are conducted to demonstrate the efficiency, stability and accuracy of the Direct Parallel Block W Z Algorithm on GPU platform. Forward and backward errors are computed and DPBWZA is found to be highly accurate, numerically stable and as efficient as the subroutine csrlsvlu of GPU accelerated cuSolverSP library. • A direct parallel block WZ algorithm for block tridiagonal toeplitz–block–toeplitz linear systems. • The present parallel algorithm is accurate and numerically stable. • As efficient as the subroutine csrlsvlu of GPU accelerated cuSolverSP library. [ABSTRACT FROM AUTHOR]

In this paper, we develop a branch and bounds algorithm to solve bound-construction bi-objective optimization problem. The proposed algorithm allows to determine an approximation of the Pareto optimal solutions sets in both spaces: decisions and objectives ones. By running α -dense space filling curves, we convert a multidimensional bi-objective optimization problem into a one-dimensional one. Hence it gets possible the implementation of the proposed algorithm when objectives depend on more than one decision variable. The proposed algorithm was applied on an engineering problem to find the working space of a robotic manipulator and the obtained results are promising. [ABSTRACT FROM AUTHOR]

This paper introduces the energy-preserving scheme for the nonlinear fractional Klein–Gordon Schrödinger equation, which uses the scalar auxiliary variable approach. By a scalar variable, the system is transformed into a new equivalent system. Then applying the extrapolated Crank–Nicolson method on the temporal direction and Fourier pseudospectral method on space direction, we give a linear implicit energy-preserving scheme. Moreover, it proved that at each discrete time the scheme preserves the corresponding discrete mass and energy. The unique solvability and convergence of the numerical solution are also investigated. In particular, it shows the method has the second-order accuracy in time and the spectral accuracy in space. Finally, it gives the algorithm implementation. Several numerical examples illustrate the efficiency and accuracy of the numerical scheme. [ABSTRACT FROM AUTHOR]

Using chaotic system for image encryption is a feasible and popular research interest. In this paper, a compound Sine-Piecewise Linear Chaotic Map is proposed to improve the chaotic characteristics of the original chaotic map. Compared with the original chaotic system, the proposed compound chaotic system has better dynamics performances, larger parameter space, which is more suitable for cryptographic applications. Furthermore, an image encryption algorithm based on this chaotic model and varying DNA coding is proposed. In this encryption algorithm, a novel method is provided to convert decimal numbers to binary numbers. Several numerical experiments show that the proposed encryption algorithm has good security performances, and is competitive with other chaos-based image encryption algorithms. [ABSTRACT FROM AUTHOR]

The usual classical polynomials-based spectral Galerkin and Petrov–Galerkin methods enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and fidelity can be deteriorated when the solutions exhibit weakly singular behaviors and this issue becomes much more severe for polynomial-based spectral methods. The eigenfunctions of the Sturm–Liouville problems of fractional order serve as basis functions for constructing efficient spectral approximations for fractional differential models with nonsmooth solutions. In this paper, the Petrov–Galerkin spectral method is adopted to deal with the initial singularity in the temporal direction in which the first kind Jacobi poly-fractonomials are utilized as temporal trial functions and the second kind Jacobi poly-fractonomials as temporal test functions. Along the spatial direction, the Galerkin spectral method is adopted for the first time to deal with the boundary singularity in the spatial direction in which weighted Jacobi functions are utilized as bases in multi-dimensions. Various numerical experiments are provided to demonstrate the performance of the proposed schemes. [ABSTRACT FROM AUTHOR]

This paper proposes an accurate numerical method, the direct flux method (DFM), to solve fluxes directly for Poisson's equation. In DFM, fluxes are the variables to be solved in the system equations, where a flux is defined as an integral of the flux density across a certain finite-sized cross section. The system equation of the DFM is derived from two equations: an integral form of Poisson's equation obtained by using Gauss's divergence theorem and an integral form of the rotation-free nature of any scalar field from Stokes' theorem. In the numerical approach, no discretization error arises from Gauss's divergence theorem because it is represented as a sum of fluxes. Therefore, the discretization error is caused only by the integral form of the rotation-free nature. From the comparison between DFM, the finite difference method (FDM), and the finite volume method (FVM), we show that the accuracy of DFM is superior to that of FDM and FVM. However, DFM generally requires larger computational resources than other methods because the number of equations in DFM is more than that in other methods. To overcome this drawback, we also propose a faster algorithm than DFM, called FastDFM, which can reduce the number of equations without changing the accuracy. Hence, the proposed FastDFM produces results with the same accuracy as the DFM and with computation time almost the same as that of FDM and FVM. • Proposed DFM can solve fluxes with high accuracy. • Proposed FastDFM makes DFM faster by reducing variables. • DFM is slower than FDM and FVM but more accurate. • FastDFM solves fluxes as accurately as DFM and almost as fast as FDM and FVM. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to derive cubature formulas using bivariate degree-graded alternative shifted Jacobi polynomials and present some of their applications through a method for fast and explicit construction of operational integration matrices in this polynomial basis. First, we take the non-degree-graded alternative shifted Jacobi polynomial basis over the interval [ 0 , 1 ] and introduce a corresponding degree-graded polynomial basis. We then construct sparse and well-structured operational integration matrices in that basis. The main advantage of the proposed idea is the low computational complexity which is derived through vector–matrix multiplications without change of bases. As an application, a fast and accurate numerical algorithm based on the obtained cubature formula is developed for the approximate solution of nonlinear multi-dimensional integral equations which arise in the theory of nonlinear parabolic boundary value problems as well as the mathematical modeling of the spatio-temporal development of an epidemic. It is shown that such a matrix representation of cubature formula in terms of the bivariate degree-graded basis gives an approximate solution with a higher order accuracy. The experimental results also illustrate that smaller size and lower orders of the operational matrix and basis functions can obtain a favorable approximate solution. [ABSTRACT FROM AUTHOR]

In this paper, wave propagation in a two-layer composite strip is investigated analytically and numerically. The strip is loaded by a very short transverse stress pulse. Three cases of the strip problem are assumed: (i) isotropic aluminum Al strip and two-layer strips made of (ii) Al and the ceramics Al 2 O 3 and (iii) the ceramics Al 2 O 3 and Al. The analytical method is based on Laplace and Fourier transform. The in-house finite element algorithm and thermodynamic consistent finite volume scheme are employed for computations, while the explicit time stepping procedure is used in both cases. The comparison of analytical and numerical results determines the degree of the accuracy of calculations, which is important for simulation of complex wave propagation problems in general heterogeneous media. [ABSTRACT FROM AUTHOR]

As a popular sampling tool used for Monte Carlo computing, importance sampling (IS) has been used in a wide variety of application areas recently. In large-scale survey data such as Chinese General Social Survey (CGSS), missing data, a high level of skewness and heteroscedastic variances commonly occur. Most of the existing literatures on survey data analysis focused on modeling the conditional mean without deep investigation about missing data. In this paper, we study an IS imputation algorithm and its modified algorithm with inverse probability weighting arrangement in quantile regression with missing covariates. We make full use of the observed data compared with the existing complete cases analysis and inverse probability weighting method, and also improve the computational efficiency of multiple imputation and EM-based algorithms. The quantile regression framework allows us to obtain an overall picture of covariates' effects, highlights the changing relationships according to the explored quantile of interest, and solves the problems of skewness and heterogeneity. Through simulation studies, we investigate the performances of both IS and ISW with other existing algorithms. Finally, we apply our algorithms to part of annual income data from CGSS in 2010. We build three kinds of quantile regression models based on all the subjects, urban areas subjects and rural areas subjects, respectively. [ABSTRACT FROM AUTHOR]

In this paper, a comparison between three small-world algorithms is performed. Fixed-size complex networks are used to investigate efficiency of small-world property promoting synchronization. Cooperative behavior is determined through its transition point to the synchronized state. The presence of different types of synchronization characterizes the efficiency of the algorithms. Non-linear systems that exhibit chaos are used to compose the complex networks. • Determining efficiency of small-world algorithms achieving synchronization in a complex network. • The small-world property is effectively used to promote tendency of a network to achieve synchrony. • Transition point to the synchronized state was found. • Three different types of synchronization were identified. • Discovery that synchronization process goes from less restrictive to the most restrictive type. [ABSTRACT FROM AUTHOR]

This paper proposes a new three-dimensional bit-level image encryption scheme with Rubik's cube method (3D-BERC). In the permutation process, the Rubik's cube method and bit-level encryption principle are combined to realize the image scrambling operation in three-dimensional space. Through the contraction mapping principle, the ascending and reducing dimension operation can be implemented effectively. In the diffusion process, we design an improved two-dimensional diffusion structure, which can spread slight change in plain image to the whole cipher image. Experimental results and simulation analysis illustrate the security and the validity of the proposed scheme. [ABSTRACT FROM AUTHOR]

In the paper, we aim to develop a class of high-order structure-preserving algorithms, which are built upon the idea of the newly introduced scalar auxiliary variable approach, for the multi-dimensional space fractional nonlinear Schrödinger equation. First, we reformulate the equation as an infinite-dimension canonical Hamiltonian system, and obtain an equivalent system with a modified energy conservation law by using the scalar auxiliary variable approach. Then, the new system is discretized by Gauss collocation methods to arrive at semi-discrete conservative systems. Subsequently, the Fourier pseudo-spectral method is applied for semi-discrete systems to obtain high-order fully-discrete schemes, which can both preserve the mass and the modified energy exactly in discrete scene. Finally, numerical experiments are provided to demonstrate the conservation and accuracy of the proposed schemes. • We derive the Hamiltonian formulation of the fractional nonlinear Schrödinger equation. • A class of high-order conservative schemes are devedloped for the equation. • Remarkable performances in the energy preservation and accuracy are obtained with the schemes. [ABSTRACT FROM AUTHOR]

The paper deals with an engineering application of the inverse magnetostrictive Villari effect. This effect is usually modeled through multi-variate relationships, strongly non linear and with hysteresis. Here, the task is to provide a suitable formulation of those relationships aiming at a device able to measure mechanical force profiles with good accuracy. The device is analyzed and modeled by a mapping function, resulting in an algorithm that reconstructs the time profile of the applied force. A preliminary calibration characterization is carried out on a concept device that exploits Galfenol as magnetostrictive material. Finally, some tests performed with the aim of validating the algorithm and to estimate its performance are presented. [ABSTRACT FROM AUTHOR]

In the current paper, for the time fractional diffusion equation with an exponential tempering, we propose a numerical algorithm based on the Lagrange-quadratic spline interpolations and the optimal technique. The discretized linear systems and some properties are investigated in detail. By using these properties, the coefficient matrix and the right-hand term at each time step are given to analyze the computational cost. Theoretical analyses show that this proposed method enjoys both stability and convergence order of O (τ 2 + h 4). Some numerical examples are provided to verify the practical feasibility and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract The increasing railway traffic and the environmental issue demand to find new solutions to provide energy to autonomous train (train with embedded energy sources such as diesel power supply). Using hybrid diesel train with embedded storage elements is an interesting technical solution but this kind of multisource system presents new scientific and methodology challenges. Thus, in the paper, the problematic focus on the design and the energy management of the different sources for this system. Moreover, these two fields are linked to each other. Indeed, there is a strong influence of the sizing on the energy management but the reverse is also true. The paper deals with a new optimization approach to perform the design of both the hybrid sources sizing and their energy management. The multi-sources system is represented by a power flow model and the energy management strategy is based on a frequency approach and on dynamic programming. This direct optimization problem is solved by the Sequential Quadratic Programming (SQP) algorithm. Thus, in the paper, this optimization approach is applied to a real railway study case. A comparison is made between two cases with different energy management methods. [ABSTRACT FROM AUTHOR]

Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy-tailed distributions and distributions with analytically intractable densities turns out to be rather problematic. In this paper, we propose a novel approach towards the use of MCMC algorithms for distributions with analytically known Fourier transforms and, in particular, heavy-tailed distributions. The main idea of the proposed approach is to use MCMC methods in Fourier domain to sample from a density proportional to the absolute value of the underlying characteristic function. A subsequent application of the Parseval's formula leads to an efficient algorithm for the computation of integrals with respect to the underlying density. We show that the resulting Markov chain in Fourier domain may be geometrically ergodic even in the case of heavy-tailed original distributions. We illustrate our approach by several numerical examples including multivariate elliptically contoured stable distributions. [ABSTRACT FROM AUTHOR]

In this paper, on the basis of information theory measures (statistical complexity and normalized Shannon entropy), the dynamical complexity of FitzHugh–Nagumo (FHN) neuron model under the co-excitation of Lévy noise and Gaussian white noise is studied. Because the potential function of the neuron system is asymmetric, we consider not only the total residence time interval of the system, but also the residence time interval of the left and right potential wells respectively. Here, we use Bandt–Pompe algorithm to calculate the three interval sequences, and obtain the statistical complexity and normalized Shannon entropy of the total system as well as the left and right potential wells. Finally, the effects of additive noise intensity, multiplicative noise intensity and system parameter on complexity of system are analyzed. We find that the total dynamical complexity of the system is obviously different from that of a single potential well. In addition, Gaussian white noise and Lévy noise have different effects on the complexity of the system. [ABSTRACT FROM AUTHOR]

In this paper, we consider a fast algorithm to calculate a two-dimensional nonlinear time distributed-order and space fractional diffusion equation, which is called the time two-mesh (TT-M) finite element (FE) method. In time, the TT-M algorithm combined with both the implicit second-order σ backward difference formula and Crank–Nicolson scheme for computing the numerical solution at time t 1 is used to speed up the calculation. At the same time, the spatial direction is approximated by the FE method. The detailed analyses of stability and error are also given, and the second-order time convergence accuracy can be arrived at. Finally, some numerical examples are shown to illustrate the effectiveness of our numerical method. [ABSTRACT FROM AUTHOR]

In this paper, we study the centralized fusion (CF) and weighted measurement fusion (WMF) robust steady-state Kalman filtering problem for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, two-step random delays, missing measurements, and uncertain noise variances. By using a model transformation approach consisting of augmented approach, de-randomization approach and fictitious noise approach, the original multisensor system under study is converted into a multi-model multisensor system with only uncertain noise variances. By introducing an augmented state vector, and applying the weighted least squares (WLS) algorithm, the CF and WMF systems are obtained. According to the minimax robust estimation principle, based on the worst-case fusion systems with conservative upper bounds of uncertain noise variances, the CF and WMF robust steady-state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using a combination method consisting of augmented noise approach, matrix representation approach of quadratic form, and Lyapunov equation approach, the so-called robustness is concerned with the design of a filter such that for all admissible uncertainties, the actual fused steady-state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady-state Kalman estimators are proved. An example with application to autoregressive (AR) signal processing is proposed, which shows that the robust fusion signal estimation problems can be solved by the robust fusion state estimation method. Simulation example shows the effectiveness and correctness of the proposed method. [ABSTRACT FROM AUTHOR]

Particle Swarm Optimization (PSO) algorithm is a nature-inspired meta-heuristic that has been utilized as a powerful optimization tool in a wide range of applications since its inception in 1995. Due to the flexibility of its parameters and concepts, PSO has appeared in many variants, probably more than any other meta-heuristic algorithm. This paper introduces the Generalized Particle Swarm Optimization (GEPSO) algorithm as a new version of the PSO algorithm for continuous space optimization, which enriches the original PSO by incorporating two new terms into the velocity updating equation. These terms aim to deepen the interrelations of particles and their knowledge sharing, increase variety in the swarm, and provide a better search in unexplored areas of the search space. Moreover, a novel procedure is utilized for dynamic updating of the particles' inertia weights, which controls the convergence of the swarm towards a solution. Also, since parameters of heuristic and meta-heuristic algorithms have a significant influence on their performance, a comprehensive guideline for parameter tuning of the GEPSO is developed. The computational results of solving numerous well-known benchmark functions by the GEPSO, original PSO, Repulsive PSO (REPSO), PSO with Passive Congregation (PSOPC), Negative PSO (NPSO), Deterministic PSO (DPSO), and Line Search-Based Derivative-Free PSO (LS-DF-PSO) approaches showed that the GEPSO outperformed the compared methods in terms of mean and standard deviation of fitness function values and runtimes. • Presenting a more robust interrelation between particles in the proposed algorithm. • Introducing a more efficient exploration way in the search space. • Presenting a stronger mechanism to update velocity and position of the proposed algorithm compared to the original PSO algorithm. • Proposing a dynamic inertial weight adjustment mechanism. • Confirming efficacy of the performance of the proposed algorithm in comparison to other variants of the PSO. [ABSTRACT FROM AUTHOR]