Search

Abstract: This work presents a proof of convergence of a discrete solution to a continuous one. At first, the continuous problem is stated as a system of equations which describe the filtration process in the pressing section of a paper machine. Two flow regimes appear in the modeling of this problem. The model for the saturated flow is presented by the Darcy’s law and the mass conservation. The second regime is described by the Richards’ approach together with a dynamic capillary pressure model. The finite volume method is used to approximate the system of PDEs. Then, the existence of a discrete solution to the proposed finite difference scheme is proven. Compactness of the set of all discrete solutions for different mesh sizes is proven. The main theorem shows that the discrete solution converges to the solution of the continuous problem. At the end we present numerical studies for the rate of convergence. [Copyright &y& Elsevier]

Abstract: In this note, we point out an error in the recently published article [R.K. Mohanty, M.K. Jain, D. Dhall, A cubic spline approximation and application of TAGE iterative method for the solution of two-point boundary value problems with forcing function in integral form, Appl. Math. Model. 35 (2011) 3036–3047] and then correct it. [Copyright &y& Elsevier]

Abstract: In a recent paper by Jin Erdong and Sun Zhaowei [Robust controllers design with finite time convergence for rigid spacecraft attitude tracking control, Aerospace Science and Technology 12 (2008) 324–330], a terminal sliding mode control technique has been applied to the attitude control problem of rigid spacecraft. Unfortunately, the controller has singularity problem which will cause the instability of the closed-loop system of attitude tracking errors. In this article, a nonsingular terminal sliding mode controller is presented to overcome this problem. [Copyright &y& Elsevier]

In designing the extended state observer (ESO), one of the most challenging issues is its performance improvement. In this paper, a simple fuzzy system is proposed to improve the performance of ESO and changes this observer into fuzzy extended state observer (FESO). This FESO is an intelligent linear form of the ESO. The fuzzy system, which is applied to tune the observer gains in an intelligent manner, directs the observer to deliver an appropriate estimation performance. To design this fuzzy system, a simple input–output form is applied to reduce the number of fuzzy rules. The linear form of FESO simplifies the convergence analysis of this observer, which is analyzed through a Lyapunov function. The performance of FESO in the fields of fault diagnosis and active disturbance rejection control (ADRC) are shown by simulation examples and compared with traditional forms of ESO. In this paper, it is revealed that this new proposed ESO embodies advantages of the simple linear structure and provides a good performance, confirmed by its results. • A fuzzy extended state observer (FESO) is designed to obtain a good estimation performance. • A simple SISO form of the fuzzy system is introduced to tune the observer gains. • The FESO performance is investigated in the fields of fault diagnosis and ADRC. [ABSTRACT FROM AUTHOR]

Highlights • Sampling-based algorithms are commonly used in motion planning problems. • The RRT* algorithm incrementally builds a tree of motion to find a solution. • Taking a shortcut to the ancestry increases the convergence rate to the optimal. • Combination with sampling strategies further improves the performance. Abstract The Rapidly-exploring Random Tree (RRT) algorithm is a popular algorithm in motion planning problems. The optimal RRT (RRT*) is an extended algorithm of RRT, which provides asymptotic optimality. This paper proposes Quick-RRT* (Q-RRT*), a modified RRT* algorithm that generates a better initial solution and converges to the optimal faster than RRT*. Q-RRT* enlarges the set of possible parent vertices by considering not only a set of vertices contained in a hypersphere, as in RRT*, but also their ancestry up to a user-defined parameter, thus, resulting in paths with less cost than those of RRT*. It also applies a similar technique to the rewiring procedure resulting in acceleration of the tendency that near vertices share common parents. Since the algorithm proposed in this paper is a tree extending algorithm, it can be combined with other sampling strategies and graph-pruning algorithms. The effectiveness of Q-RRT* is demonstrated by comparing the algorithm with existing algorithms through numerical simulations. It is also verified that the performance can be further enhanced when combined with other sampling strategies. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the superconvergence properties of the quadratic finite volume method (FVM) on triangular meshes for elliptic equations. We proved the 3rd order superconvergence rate of the gradient approximation ‖ u h − u I ‖ 1 = O (h 3) and the 4th order superconvergence rate of the function value approximation ‖ u h − u I ‖ 0 = O (h 4) for the quadratic FVM on triangular meshes. Here u h is the FVM solution and u I is the piecewise quadratic Lagrange interpolation of the exact solution. It should be pointed out that the superconvergence phenomena of FVM strongly depends on the construction of dual mesh. Specially for quadratic FVMs, the scheme presented in this paper is the unique scheme which holds superconvergence. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose a Strongly Stable generalized finite element method (SSGFEM) for a non-smooth interface problem, where the interface has a corner. The SSGFEM employs enrichments of 2 types: the nodes in a neighborhood of the corner are enriched by singular functions characterizing the singularity of the unknown solution, while the nodes close to the interface are enriched by a distance based function characterizing the jump in the gradient of the unknown solution along the interface. Thus nodes in the neighborhood of the corner and close to the interface are enriched with two enrichment functions. Both types of enrichments have been modified by a simple local procedure of "subtracting the interpolant." A simple local orthogonalization technique (LOT) also has been used at the nodes enriched with both enrichment functions. We prove that the SSGFEM yields the optimal order of convergence. The numerical experiments presented in this paper indicate that the conditioning of the SSGFEM is not worse than that of the standard finite element method, and the conditioning is robust with respect to the position of the mesh relative to the interface. Highlights • GFEM for 2D non-smooth interface problem. • Singular enrichment functions in addition to distance based enrichment functions. • Proof of optimal convergence of the GFEM. • Experimental study of conditioning and robustness of GFEM. • The notion of Strongly Stable GFEM (SSGFEM). [ABSTRACT FROM AUTHOR]

Abstract We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. Such multimesh finite element methods are particularly well suited to problems in which the computational domain undergoes large deformations as a result of the relative motion of the separate components of a multi-body system. In the present paper, we formulate the multimesh finite element method for the Poisson equation. Numerical examples demonstrate the optimal order convergence, the numerical robustness of the formulation and implementation in the face of thin intersections and rounding errors, as well as the applicability of the methodology. In the accompanying paper (Johansson et al., 2018), we analyze the proposed method and prove optimal order convergence and stability. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with diffusion control problem of a tempered anomalous diffusion system based on fractional-order PI controllers. The contribution of this paper is to introduce fractional-order PI controllers into the tempered anomalous diffusion system for mobile actuators motion and spraying control. For the proposed control force, convergence analysis of the system described by mobile actuator dynamical equations is presented based on Lyapunov stability arguments. Moreover, a new Centroidal Voronoi Tessellation (CVT) algorithm based on fractional-order PI controllers, henceforth called FOPI-based CVT algorithm, is provided together with a modified simulation platform called Fractional-Order Diffusion Mobile Actuator-Sensor 2-Dimension Fractional-Order Proportional Integral (FO-Diff-MAS2D-FOPI). Finally, extensive numerical simulations for the tempered anomalous diffusion process are presented to verify the effectiveness of our proposed fractional-order PI controllers. [ABSTRACT FROM AUTHOR]

This paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The AMGe coarse spaces with approximation properties used in this work enable us to overcome the difficulties in evaluating the nonlinear coarse operators and the degradation in convergence rates that characterized previous attempts to extend FAS to algebraic multilevel hierarchies on general unstructured grids. Specifically, the AMGe technique employed in this paper allows to derive stable and accurate coarse discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow applications. Our approach outperforms – both in terms of number of iterations and computational time – traditional methods in all the experiments. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) is a frontier analysis procedure for evaluating the relative performance of decision making units (DMUs) with multiple inputs and multiple outputs. To improve its discrimination power, an important extension is proposed as cross-efficiency, which uses peer DMUs’ optimal relative weights to evaluate the relative performance. However, the existing cross-efficiency methods show an inconsistent and unbalanced evaluation standard, since each DMU might determine a different total (or mean) efficiency value across all DMUs. The different values imply that the DMUs that have assigned larger cross-efficiency scores will have a larger effect in aggregating the ultimate cross-efficiency scores and different DMUs’ effects are unbalanced in cross-efficiency methods. In this paper, we will deal with this unbalanced cross-efficiency evaluation problem. To this end, we first suggest a practical adjustment measure to rectify the traditional cross-efficiency, which will provide a common evaluation standard for all DMUs and make each DMU dispatch an identical total efficiency score across all DMUs. Further, we propose a game-like iterative procedure to obtain the optimal balanced cross-efficiency. Finally, we present both a numerical example and an empirical study derived from the literature and a real-world problem to demonstrate the usefulness and efficacy of the new balanced cross-efficiency evaluation approach. The work presented in this paper can extend the traditional cross-efficiency approaches to situations involving unbalanced evaluation standards, and make the evaluation results more practical significance. [ABSTRACT FROM AUTHOR]

In this paper, we propose Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis functions within GMsFEM framework such that the convergence of method is independent of the contrast and linearly decreases with respect to mesh size if oversampling size is appropriately chosen. We would like to show a mesh-dependent convergence with a minimal number of basis functions. Our construction starts with an auxiliary multiscale space by solving local spectral problems. In auxiliary multiscale space, we select the basis functions that correspond to small (contrast-dependent) eigenvalues. These basis functions represent the channels (high-contrast features that connect the boundaries of the coarse block). Using the auxiliary space, we propose a constraint energy minimization to construct multiscale spaces. The minimization is performed in the oversampling domain, which is larger than the target coarse block. The constraints allow handling non-decaying components of the local minimizers. If the auxiliary space is correctly chosen, we show that the convergence rate is independent of the contrast (because the basis representing the channels are included in the auxiliary space) and is proportional to the coarse-mesh size (because the constraints handle non-decaying components of the local minimizers). The oversampling size weakly depends on the contrast as our analysis shows. The convergence theorem requires that channels are not aligned with the coarse edges, which hold in many applications, where the channels are oblique with respect to the coarse-mesh geometry. The numerical results confirm our theoretical results. In particular, we show that if the oversampling domain size is not sufficiently large, the errors are large. To remove the contrast-dependence of the oversampling size, we propose a modified construction for basis functions and present numerical results and the analysis. [ABSTRACT FROM AUTHOR]

Highlights • This paper proposes a two stage method for identification of multiple-input single-output Hammerstein model with time delay. • The nonlinear part of Hammerstein model is approximated by the means of Radial Basis Function Neural Network. • The fractional order transfer function is applied to estimate the linear part of Hammerstein model. • The identification method is based on a hybrid scheme, including a novel evolutionary algorithm called Modified Genetic Algorithm (MGA) and the Recursive Least Squares method. • The MGA is inspired from the artificial genetic operation in some agronomic products. Abstract This paper deals with identification of the continuous-time Hammerstein systems with time delay using Genetic Algorithm (GA) combined with the Recursive Least-Squares (RLS) method. This model consists of the Radial Basis Function Neural Network (RBFNN) as its nonlinear static part and fractional order transfer function as its dynamic linear part. The fractional orders are identified by GA with an innovative strategy called Modified Genetic Algorithm (MGA). The main innovative idea is the selection and transferring the best characteristics or properties to the next generation. On the other hand, the centers and widths and the weighting parameters of the RBFNN and the transfer function coefficients of the linear dynamic part are updated by the RLS method. Simulation results are applied to illustrate the proposed method accuracy. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • In this paper, a modified BCO (MBCO) approach is proposed for data clustering. In the proposed MBCO, cloning and fairness concepts are used to improve the quality of clustering solution. • For every stage of allocation only data points which are unallocated in the previous stages of allocation are considered. • To obtain more diverse solution, a probability based selection ( Pbselection ) approach is proposed to assign the unallocated data to clusters in each iteration. • Next, to improve the convergence time, the current solution (centroid values) is always compared with the previous best solution. • In order to get global optimal and diverse solution, two hybridized approaches, i.e. MKCLUST and KMCLUST are proposed. Abstract Among the nature inspired heuristic or meta-heuristic optimization algorithms, Bee Colony Optimization (BCO) algorithms are widely used to solve clustering problem. In this paper, a modified BCO (MBCO) approach is proposed for data clustering. In the proposed MBCO, the forgiveness characteristics of bees and giving a fair chance to both trustworthy and untrustworthy bees are being taken care of. A probability based selection ( Pbselection ) approach is introduced in the proposed MBCO for assigning unallocated data points in every iteration. The result shows that, the proposed method gives faster convergence as compared to the existing well known algorithms. In order to improve the performance of MBCO further and to obtain global optimal and diverse solution, the proposed MBCO is hybridized with k -means algorithm. In average, the hybridized MKCLUST and KMCLUST give same or better result than the proposed MBCO. To validate the proposed algorithms, seven standard data sets are considered. From classification error percentages calculation, it is observed that the proposed algorithms perform better compared to some existing algorithms. The simulation results infer that the proposed algorithms can be efficiently used for data clustering. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • This paper proposed an improved version of fruit fly optimization (FOA). • Mutation adaptation mechanism is adopted to enhance the balance of FOA in terms of the exploitation and exploration ability. • The phase angle-based encoded strategy helps to achieve the high convergence performance. • The proposed method is used to find the optimal UAV path in the 3D environments. • Numerical experiments results show the proposed method is superior to several existing state-of-the-art optimization algorithms. Abstract This paper proposed an improved version of fruit fly optimization (FOA) to solve the unmanned aerial vehicle (UAV) path planning problem. The improved algorithm combines the phase angle-encoded and mutation adaptation mechanisms into the basic FOA and is referred to as θ-MAFOA. Mutation adaptation mechanism is adopted to enhance the balance of FOA in terms of the exploitation and exploration ability, while phase angle-based encoded strategy for fruit fly locations helps to achieve the high performance in the convergence process. Then, the proposed θ-MAFOA is used to find the optimal flight path for UAV in the complex three-dimensional (3D) terrain environments with various ground defense weapons. B-Spline curve that connects the start and target points is employed to represent a smooth path. Several performance criteria and constraints are taken into consideration to evaluate the cost of UAV paths. Numerical experiments are carried out on various test scenarios and the results show the proposed θ-MAFOA is superior to the basic and other two modified versions of FOA, and also more powerful than several existing state-of-the-art optimization algorithms. [ABSTRACT FROM AUTHOR]

Recently, Mao (2015) developed a new explicit method, called the truncated Euler–Maruyama (EM) method, for the nonlinear SDE and established the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. In his another follow-up paper (Mao, 2016), he discussed the rates of L q -convergence of the truncated EM method for q ≥ 2 and showed that the order of L q -convergence can be arbitrarily close to q ∕ 2 under some additional conditions. However, there are some restrictions on the truncation functions and these restrictions sometimes might force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is to establish the convergence rate without these restrictions. The other aim is to study the stability of the truncated EM method. The advantages of our new results will be highlighted by the comparisons with the results in Mao (2015, 2016) as well as others on the tamed EM and implicit methods. [ABSTRACT FROM AUTHOR]

This paper aims to provide a novel metaheuristic algorithm motivated from quantum motion entitled Multi-scale Quantum Harmonic Oscillator Algorithm (MQHOA). The calculation accuracy of MQHOA is adjustable. The physical model and mathematical analysis of the proposed algorithm are detailed and well interpreted in this paper. The structure of MQHOA is very simple, including merely two phases, the quantum harmonic oscillator process (QHO process) and multi-scale process (M process). Experiments are carried out to validate the effectiveness and efficiency of MQHOA by applying it to 30 well defined benchmark functions. We also compare MQHOA with several well-known metaheuristic algorithms, such as genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO) and quantum particle swarm optimization (QPSO). The comparative results indicate the competitive and superior performance of the proposed algorithm in both convergence speed and optimal solution accuracy. [ABSTRACT FROM AUTHOR]

In this paper we consider a family of high-order iterative methods which is more efficient than the Newton method to approximate a solution of symmetric algebraic Riccati equations. In fact, this paper is devoted to the convergence study of a k -steps iterative scheme with low operational cost and high order of convergence. We analyze their accessibility and computational efficiency. We also obtain results about the existence and localization of solution. Numerical experiments confirm the advantageous performance of the iterative scheme analyzed. [ABSTRACT FROM AUTHOR]

This paper examines convergence and stability of the two classes of theta-Milstein schemes for stochastic differential equations (SDEs) with non-global Lipschitz continuous coefficients: the split-step theta-Milstein (SSTM) scheme and the stochastic theta-Milstein (STM) scheme. For θ ∈ [ 1 ∕ 2 , 1 ] , this paper concludes that the two classes of theta-Milstein schemes converge strongly to the exact solution with the order 1. For θ ∈ [ 0 , 1 ∕ 2 ] , under the additional linear growth condition for the drift coefficient, these two classes of the theta-Milstein schemes are also strongly convergent with the standard order. This paper also investigates exponential mean-square stability of these two classes of the theta-Milstein schemes. For θ ∈ ( 1 ∕ 2 , 1 ] , these two theta-Milstein schemes can share the exponential mean-square stability of the exact solution. For θ ∈ [ 0 , 1 ∕ 2 ] , similar to the convergence, under the additional linear growth condition, these two theta-Milstein schemes can also reproduce the exponential mean-square stability of the exact solution. [ABSTRACT FROM AUTHOR]

For a Tychonoff space X , C p ( X ) is the space of all real-valued continuous functions with the topology of pointwise convergence. A subset A ⊂ X is said to be sequentially dense in X if every point of X is the limit of a convergent sequence in A . In this paper, the following 8 properties for C p ( X ) are considered. S 1 ( S , S ) ⇒ S f i n ( S , S ) ⇒ S 1 ( S , D ) ⇒ S f i n ( S , D ) ⇑ ⇑ ⇑ ⇑ S 1 ( D , S ) ⇒ S f i n ( D , S ) ⇒ S 1 ( D , D ) ⇒ S f i n ( D , D ) For example, a space X satisfies S 1 ( D , S ) (resp., S f i n ( D , S ) ) if whenever { D n : n ∈ N } is a sequence of dense subsets of X , one can take points x n ∈ D n (resp., finite F n ⊂ D n ) such that { x n : n ∈ N } (resp., ⋃ { F n : n ∈ N } ) is sequentially dense in X . Other properties are defined similarly. S 1 ( D , D ) (= R -separability) and S f i n ( D , D ) (= M -separability) for C p ( X ) were already investigated by several authors. In this paper, we have gave characterizations for C p ( X ) to satisfy other 6 properties above. [ABSTRACT FROM AUTHOR]

This paper presents a robust finite-time guidance (RFTG) law to a short-range interception problem. The main challenge is that the evasive strategy of the target is unpredictable because it is determined not only by the states of both the interceptor and the target, but also by external un-modeled factors. By robustly stabilizing a line-of-sight rate, this paper proposes an integrated continuous finite-time disturbance observer/bounded continuous finite-time stabilizer strategy. The design of this integrated strategy has two points: 1) effect of a target maneuver is modeled as disturbance and then is estimated by the second-order homogeneous observer; 2) the finite-time stabilizer is actively coupled with the observer. Based on homogeneity technique, the local finite-time input-to-state stability is established for the closed-loop guidance system, thus implying the proposed RFTG law can quickly render the LOS rate within a bounded error throughout intercept. Moreover, convergence properties of the LOS rate in the presence of control saturation are discussed. Numerical comparison studies demonstrate the guidance performance. [ABSTRACT FROM AUTHOR]

Nowadays, most of real world problems are complex and hence they cannot be solved by exact methods. So generally, we have to utilize approximate methods such as metaheuristics. So far, a significant amount of metaheuristic algorithms are proposed which are different with together in algorithm motivation and steps. Similarly, this paper presents the Tree Growth Algorithm (TGA) as a novel method with different approach to address optimization tasks. The proposed algorithm is inspired by trees competition for acquiring light and foods. Diversification and intensification phases and their tradeoff are detailed in the paper. Besides, the proposed algorithm is verified by using both mathematical and engineering benchmarks commonly used in this research area. This new approach in metaheuristic is compared and studied with well-known optimization algorithms and the comparison of TGA with standard versions of these employed algorithms showed the superiority of TGA in these problems. Also, convergence analysis and significance tests via some nonparametric technique are employed to confirm efficiency and robustness of the TGA. According to the results of conducted tests, the TGA can be considered as a successful metaheuristic and suitable for optimization problems. Therefore, the main purpose of providing this algorithm is achieving to better results, especially in continuous problems, due to the natural behavior inspired by trees. [ABSTRACT FROM AUTHOR]

This paper is devoted to studies of I wQN-spaces and some of their cardinal characteristics. Recently, Šupina in [32] proved that I is not a weak P-ideal if and only if any topological space is an I QN-space. Moreover, under p = c he constructed a maximal ideal I (which is not a weak P-ideal) for which the notions of I QN-space and QN-space do not coincide. In this paper we show that, consistently, there is an ideal I (which is not a weak P-ideal) for which the notions of I wQN-space and wQN-space do not coincide. This is a partial solution to [6, Problem 3.7] . We also prove that for this ideal the ideal version of Scheepers Conjecture does not hold (this is the first known example of such weak P-ideal). We obtain a strictly combinatorial characterization of non ( I wQN-space ) similar to the one given in [32] by Šupina in the case of non ( I QN-space ) . We calculate non ( I QN-space ) and non ( I wQN-space ) for some weak P-ideals. Namely, we show that b ≤ non ( I QN-space ) ≤ non ( I wQN-space ) ≤ d for every weak P-ideal I and that non ( I QN-space ) = non ( I wQN-space ) = b for every F σ ideal I as well as for every analytic P-ideal I generated by an unbounded submeasure (this establishes some new bounds for b ( I , I , Fin ) introduced in [31] ). As a consequence, we obtain some bounds for add ( I QN-space ) . In particular, we get add ( I QN-space ) = b for analytic P-ideals I generated by unbounded submeasures. By a result of Bukovský, Das and Šupina from [6] it is known that in the case of tall ideals I the notions of I QN-space ( I wQN-space) and QN-space (wQN-space) cannot be distinguished. Answering [6, Problem 3.2] , we prove that if I is a tall ideal and X is a topological space of cardinality less than co v ⁎ ( I ) , then X is an I wQN-space if and only if it is a wQN-space. [ABSTRACT FROM AUTHOR]

Motivated by truncated Euler–Maruyama (EM) method introduced by Mao (2015), a new explicit numerical method named modified truncated Euler–Maruyama method is developed in this paper. Strong convergence rates of the given numerical scheme to the exact solutions to stochastic differential equations are investigated under given conditions in this paper. Compared with truncated EM method, the given numerical simulation strongly converges to the exact solution at fixed time T and over a time interval [ 0 , T ] under weaker sufficient conditions. Meanwhile, the convergence rates are also obtained for both cases. Two examples are provided to support our conclusions. [ABSTRACT FROM AUTHOR]

This paper presents a new quantum chaotic cuckoo search algorithm (QCCS) for data clustering. Recent researches show the superiority of cuckoo search (CS) over traditional meta-heuristic algorithms for clustering problems. Unfortunately, all the cuckoos have identical search behaviours that may lead the algorithm to converge to local optima. Also, the convergence rate is sensitive to initial centroids seeds that are randomly generated. Therefore, the main contribution of this paper is to extend the CS capabilities using nonhomogeneous update inspired by the quantum theory in order to tackle the cuckoo search clustering problem in terms of global search ability. Also, the randomness at the beginning step is replaced by the chaotic map in order to make the search procedure more efficient and improve the convergence speed. In addition, an effective strategy is developed to well manage the boundaries. The experimental results on six famous real-life datasets show the significant superiority of the proposed QCCS over eight recent well known algorithms including, genetic quantum cuckoo search, hybrid cuckoo search and differential evolution, hybrid K-means and improved cuckoo search, standard cuckoo search, quantum particle swarm optimization, differential evolution, hybrid K-means chaotic particle swarm optimization and genetic algorithm for all benchmark datasets in terms of internal and external clustering quality. [ABSTRACT FROM AUTHOR]

Travelling salesman problem is a combinatorial optimization problem with wide application background and important theoretical value. The traditional method is only suitable for solving small scale travelling salesman problems, thus limiting the application and popularization of such methods. Based on genetic algorithm, the paper proposes an improved strategy combining random crossover and dynamic mutation to increase population diversity and optimize mutation characters. The simulation results show the convergence rate and the optimal solution of the improved algorithm in the paper are obviously superior to the traditional genetic algorithm, the adaptive crossover probability genetic algorithm and the improved selection genetic algorithm, and it provides a new method for the travelling salesman problem. [ABSTRACT FROM AUTHOR]

In the genetic algorithms, both crossover and mutation operators need one or more solutions from the population as inputs to be operated. Selection strategy decides which solutions should be selected as inputs of these operators. When a new solution is produced after applying one of these operators, the replacement strategy decides that is the new solution satiable to be inserted into the population, and if the answer is positive, then which of solutions in the population should be removed. The replacement plays a direct role in maintaining the diversity of the population, which is critical to avoid premature convergence problem. The selection effects on exploitation ability, which is vital to obtain high quality solutions. Where many of recent methods for the replacement and selection are time consuming or need complicated structures for the population, this paper proposes simple algorithms for the selection and the replacement, which are based on similarity between a pair of solutions. Result of experiments show how using the proposed strategies increases performance of genetic algorithm in terms of accuracy, on function optimization datasets. In addition, the proposed algorithms in this paper can be easily applied to different types of the population-based evolutionary algorithms. Results of experiments show how the proposed algorithms improve the performance of differential evolutionary algorithm in terms of accuracy, on variety of datasets including CEC-2015 Black Box Optimization. [ABSTRACT FROM AUTHOR]

In this paper, a modified weak Galerkin method is proposed for the Stokes problem. The numerical scheme is based on a novel variational form of the Stokes problem. The degree of freedoms in the modified weak Galerkin method is less than that in the original weak Galerkin method, while the accuracy stays the same. In this paper, the optimal convergence orders are given and some numerical experiments are presented to verify the theory. [ABSTRACT FROM AUTHOR]

In this paper, meshless weak form techniques are applied to find the numerical solution of nonlinear biharmonic Sivashinsky equation arising in the alloy solidification problem. Stability and convergence analysis of time-discrete scheme are proved. An error analysis of meshless global weak form method based on radial point interpolation technique is proposed for this nonlinear biharmonic equation. In addition, a comparison between meshless global and local weak form methods is done from the perspective of accuracy and efficiency. The main purpose of this paper is to show that the meshless weak form techniques can be used for solving the nonlinear biharmonic partial differential equations especially Sivashinsky equation. The numerical results confirm the good efficiency of the proposed methods for solving this nonlinear biharmonic model. [ABSTRACT FROM AUTHOR]

We further develop the Multivariate Decomposition Method (MDM) for the Lebesgue integration of functions of infinitely many variables x 1 , x 2 , x 3 , … with respect to a corresponding product of a one dimensional probability measure. The method is designed for functions that admit a dominantly convergent decomposition f = ∑ u f u , where u runs over all finite subsets of positive integers, and for each u = { i 1 , … , i k } the function f u depends only on x i 1 , … , x i k . Although a number of concepts of infinite-dimensional integrals have been used in the literature, questions of uniqueness and compatibility have mostly not been studied. We show that, under appropriate convergence conditions, the Lebesgue integral equals the ‘anchored’ integral, independently of the anchor. For approximating the integral, the MDM assumes that point values of f u are available for important subsets u , at some known cost. In this paper, we introduce a new setting, in which it is assumed that each f u belongs to a normed space F u , and that bounds B u on ‖ f u ‖ F u are known. This contrasts with the assumption in many papers that weights γ u , appearing in the norm of the infinite-dimensional function space, are somehow known. Often such weights γ u were determined by minimizing an error bound depending on the B u , the γ u and the chosen algorithm, resulting in weights that depend on the algorithm. In contrast, in this paper, only the bounds B u are assumed to be known. We give two examples in which we specialize the MDM: in the first case, F u is the | u | -fold tensor product of an anchored reproducing kernel Hilbert space; in the second case, it is a particular non-Hilbert space for integration over an unbounded domain. [ABSTRACT FROM AUTHOR]

When solving constrained multi-objective optimization problems (CMOPs), keeping infeasible individuals with good objective values and small constraint violations in the population can improve the performance of the algorithms, since they provide the information about the optimal direction towards Pareto front. By taking the constraint violation as an objective, we propose a novel constraint-handling technique based on directed weights to deal with CMOPs. This paper adopts two types of weights, i.e. feasible and infeasible weights distributing on feasible and infeasible regions respectively, to guide the search to the promising region. To utilize the useful information contained in infeasible individuals, this paper uses infeasible weights to maintain a number of well-diversified infeasible individuals. Meanwhile, they are dynamically changed along with the evolution to prefer infeasible individuals with better objective values and smaller constraint violations. Furthermore, 18 test instances and 2 engineering design problems are used to evaluate the effectiveness of the proposed algorithm. Several numerical experiments indicate that the proposed algorithm outperforms four compared algorithms in terms of finding a set of well-distributed non-domination solutions. [ABSTRACT FROM AUTHOR]

Over the last four decades, Environmental Accounting tools have been developed to conceptualise and quantify the direct and indirect effects of human activity on the environment, to enable decision-makers to track and measure progress towards sustainability outcomes and goals. These environmental accounting methods range from ecological footprinting, carbon footprinting, energy analysis, emergy analysis, ecological pricing and life cycle assessment to environmental input-output analysis. Regrettably, the contemporaneous development of these tools has frequently occurred in isolation from each other, even though they often seek to serve common analytical and evaluative purposes, as well as serving similar communities of interest. It is the central argument of this paper that, in spite of this isolation, the environmental accounting methods have a number of common features − that is, they can be mathematically reduced to similar analytics, and they often confront the same methodological issues − e.g., joint production (co-products) problem, weighting, commensuration, double counting and boundary setting. In this regard the paper reviews how the various environmental accounting tools can ‘learn’ from each other − e.g., how the mathematics of ecological pricing can address the joint production problem in a number of the other environmental accounting methods; and how the insights from input-output analysis can be used in system boundary setting. The paper concludes by agreeing with previous authors, that a better understanding of any given environmental issue is likely to be achieved by using a mix of these environmental accounting tools, rather than relying on just one tool, one perspective or one criterion. [ABSTRACT FROM AUTHOR]

In the current paper, an efficient numerical method based on two-dimensional hybrid of block-pulse functions and Legendre polynomials is developed to approximate the solutions of two-dimensional nonlinear Fredholm, Volterra and Volterra–Fredholm integral equations of the second kind. The main idea of the presented method is based upon some of the important benefits of the hybrid functions such as high accuracy, wide applicability and adjustability of the orders of block-pulse functions and Legendre polynomials to achieve highly accurate numerical solutions. By using the numerical integration and collocation method, two-dimensional nonlinear integral equations are reduced to a system of nonlinear algebraic equations. The focus of this paper is to obtain an error estimate and to show the convergence analysis for the numerical approach under the L 2 -norm. Numerical results are presented and compared with the results from other existing methods to illustrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Full waveform inversion (FWI) entails the ill-posed reconstruction of material parameters (such as sound speed and attenuation) from measurements of complete wave fields (full seismograms). In this paper we present a novel framework for FWI in the visco-acoustic regime. The new framework is based on a new elegant derivation of the system of state and adjoint PDEs which are approximated by the discontinuous Galerkin (DG) method. The inverse problem is then solved by the well established regularization scheme CG-REGINN which has not yet been applied in the context of FWI. For the DG discretization we provide a preconditioner for the efficient computation of the time steps by GMRES which yields optimal convergence estimates in space and time and which is confirmed by numerical tests. The inverse solver expresses the required Fréchet derivative and its adjoint in the DG setting. Successful reconstructions in a simplified cross-well setting serve as a proof of concept for our framework and demonstrate the applicability of our new combination of DG method and inverse solver. Some of the inversion experiments use seismograms generated by an independent finite difference time domain forward solver to avoid inverse crime. [ABSTRACT FROM AUTHOR]

This paper proposes the introduction of a connectivity constraint in the Bi-directional Evolutionary Structural Optimisation (BESO) method, which avoids the possibility of arriving at highly non-optimal local optima. By developing a constraint that looks at the usefulness of complete members, rather than just elements, local optima are shown to be avoided. This problem, which affects both evolutionary and discrete optimisation techniques, has divided the optimisation community and resulted in significant discussion. This discussion has led to the development of what is now known in the literature as the Zhou-Rozvany (Z-R) problem. After analysing previous attempts at solving this problem, an updated formulation for the convergence criteria of the proposed BESO algorithm is presented. The convergence of the sequence is calculated by the structure's ability to safely carry the applied loads without breaking the constraints. The Z-R problem is solved for both stress minimisation and minimum compliance, further highlighting the flexibility of the proposed formulation. Finally, this paper aims to give some new insights into the uniqueness of the Z-R problem and to discuss the reasons for which discrete methods struggle to find suitable global optima. [ABSTRACT FROM AUTHOR]

There are many dynamic multi-objective optimization problems (DMOPs) in real-life engineering applications whose objectives change over time. After an environmental change occurs, prediction strategies are commonly used in dynamic multi-objective optimization algorithms to find the new Pareto optimal set (POS). Being able to make more accurate prediction means the algorithm requires fewer computational resources to make the population approximate to the Pareto optimal front (POF). This paper proposes a hybrid diversity maintenance method to improve prediction accuracy. The method consists of three steps, which are implemented after an environmental change. The first step, based on the moving direction of the center points, uses the prediction to relocate a number of solutions close to the new Pareto front. On the basis of self-defined minimum and maximum points of the POS in this paper, the second step applies the gradual search to produce some well-distributed solutions in the decision space so as to compensate for the inaccuracy of the first step, simultaneously and further enhancing the convergence and diversity of the population. In the third step, some diverse individuals are randomly generated within the region of next probable POS, which prompts the diversity of the population. Eventually the prediction becomes more accurate as the solutions with good convergence and diversity are selected after the non-dominated sort [1] on the combined solutions generated by the three steps. Compared with three other prediction methods on a series of test instances, our method is very competitive in convergence and diversity as well as the speed at which it responds to environmental changes. [ABSTRACT FROM AUTHOR]

This paper proposes several novel hybrid ant colony optimization (ACO)-based algorithms to resolve multi-objective job-shop scheduling problem with equal-size lot splitting. The main issue discussed in this paper is lot-splitting of jobs and tradeoff between lot-splitting costs and makespan. One of the disadvantages of ACO is its uncertainty on time of convergence. In order to enrich search patterns of ACO and improve its performance, five enhancements are made in the proposed algorithms including: A new type of pheromone and greedy heuristic function; Three new functions of state transition rules; A nimble local search algorithm for the improvements of solution quality; Mutation mechanism for divisive searching; A particle swarm optimization (PSO)-based algorithm for adaptive tuning of parameters. The objectives that are used to measure the quality of the generated schedules are weighted-sum of makespan, tardiness of jobs and lot-splitting cost. The developed algorithms are analyzed extensively on real-world data obtained from a printing company and simulated data. A mathematical programming model is developed and paired-samples t -tests are performed between obtained solutions of mathematical programming model and proposed algorithms in order to verify effectiveness of proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time synchronization issue of time-varying delayed neural networks (DNNs) with discontinuous activations. Based on master-slave concept, several sufficient conditions are given to guarantee the finite-time synchronization of discontinuous DNNs. In order to control the synchronization error to converge zero in a finite time, we design three classes of novel switching state-feedback controllers which involve time-delays and discontinuous factors. The analysis in this paper employs the extended differential inclusion theory, the famous finite-time stability theorem, inequality techniques and generalized Lyapunov approach. Moreover, the upper bounds of the settling time of synchronization are estimated. Finally, the validity of proposed design method and theoretical results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents an iterative convex programming algorithm for the complex ascent trajectory planning problem. Due to the nonlinear dynamics and constraints, ascent trajectory planning problems are always difficult to be solved rapidly. With deterministic convergence, convex programming is becoming increasingly attractive to such problems. In this paper, first, path constraints (dynamic pressure, load and bending moment) are convexified by a change of variables and a reasonable approximation. Then, based on the Newton–Kantorovich/Pseudospectral (N–K/PS) approach, the dynamic equations are transcribed into linearized algebraic equality constraints with a given initial guess, and the ascent trajectory planning problem is formulated as a convex programming problem. At last, by iteratively solving the convex programming problem with readily available convex optimization methods and successively updating the initial guess with the Newton–Kantorovich iteration, the trajectory planning problem can be solved accurately and rapidly. The convergence of the proposed iterative convex programming method is proved theoretically, and numerical simulations show that the method proposed can potentially be implemented onboard a launch vehicle for real-time applications. [ABSTRACT FROM AUTHOR]

In this paper a new semi-analytical solution for the moving mass problem is presented. Firstly, the problem of a mass traversing a finite beam on an elastic foundation is reviewed and some new aspects are added. Then, the new semi-analytical solution is deduced for an infinite beam. The semi-analytical solution of the displacement under the mass is derived with the help of integral transforms and the full deflection shape is obtained by linking together two semi-infinite beams. An iterative procedure is suggested for the determination of the frequency of the oscillation induced by the moving mass. Results deduced for infinite beams are confirmed by analysis of long finite beams, with the help of derivations given in the first part of this paper. Convergence analysis on finite beams is also presented, and, in addition, the effects of the normal force, of the harmonic component of the vertical force and of the foundation damping are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we modify the general iterative method to approximate a common element of the set of solutions of split variational inclusion problem and the set of common fixed points of a finite family of k -strictly pseudo-contractive nonself mappings. Strong convergence theorem is established under some suitable conditions in a real Hilbert space, which also solves some variational inequality problems. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors. Finally, some examples to study the rate of convergence and some illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

We extend in this paper an optimal family of three-step eighth-order methods developed by Džunić et al. (2011) with higher-order weight functions employed in the second and third sub-steps and investigate their dynamics under the relevant extraneous fixed points among which purely imaginary ones are specially treated for the analysis of the rich dynamics. Their theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence and the asymptotic error constant as well as proper choices of special cases. A wide variety of relevant numerical examples are illustrated to confirm the underlying theoretical development. In addition, this paper investigates the dynamics of selected existing optimal eighth-order iterative maps with the help of illustrative basins of attraction for various polynomials. [ABSTRACT FROM AUTHOR]

This paper uses a divergence-conforming B-spline fluid discretization to address the long-standing issue of poor mass conservation in immersed methods for computational fluid–structure interaction (FSI) that represent the influence of the structure as a forcing term in the fluid subproblem. We focus, in particular, on the immersogeometric method developed in our earlier work, analyze its convergence for linear model problems, then apply it to FSI analysis of heart valves, using divergence-conforming B-splines to discretize the fluid subproblem. Poor mass conservation can manifest as effective leakage of fluid through thin solid barriers. This leakage disrupts the qualitative behavior of FSI systems such as heart valves, which exist specifically to block flow. Divergence-conforming discretizations can enforce mass conservation exactly, avoiding this problem. To demonstrate the practical utility of immersogeometric FSI analysis with divergence-conforming B-splines, we use the methods described in this paper to construct and evaluate a computational model of an in vitro experiment that pumps water through an artificial valve. [ABSTRACT FROM AUTHOR]

This paper introduces a new method for the integration of localized surface geometry with fully parameterized absolute nodal coordinate formulation (ANCF) finite elements. In this investigation, ANCF finite elements are used to create the global geometry and perform the finite element (FE)/multibody system (MBS) analysis of deformable bodies. The localized surface geometry details can be described on ANCF element surfaces without the need for mesh refinement. The localized surface is represented using a standard computational geometry method, Non-uniform rational B-spline surface (NURBS), which can describe both conic surface and freeform surface efficiently and accurately. The basic idea of the integration of localized surface geometry with ANCF elements lies in the inclusion of such detail in the element mass matrix and forces. The integration can be implemented by overlapping the localized surface geometry on the original ANCF element or by directly trimming the ANCF element domain to fit the required shape. During the integration process, a mapping between ANCF local coordinates and NURBS localized geometric parameters is used for a consistent implementation of the overlapping and trimming methods. Additionally, two numerical integration methods are compared for the rate of convergence. The results show that the proposed subdomain integration method is better, since it is optimized for dealing with complex geometry. The proposed subdomain method can be used with any fully parameterized ANCF element. In order to analyze the accuracy of the proposed method, a cantilever plate example with localized surface geometry is used, and the simulation results with the proposed method are compared with the simulation results obtained using a commercial FE code. Two other examples that include contact with ground and localized surface geometry are also provided. These examples are a simple plate structure with surface geometry and a tire with tread details. The incompressible hyperelastic Mooney–Rivlin material model is used to describe the material used in the tire tread. It is shown through the tire contact patch that the proposed method can successfully capture the effect of the tread grooves. The rate of convergence and locking of fully parameterized ANCF elements are also discussed in this paper. [ABSTRACT FROM AUTHOR]

Since contours of multi-dimensional depth functions often characterize the distribution, it has become of interest to consider structural properties and limit theorems for the sample contours (see Zuo and Serfling (2000)). For finite dimensional data Massé and Theodorescu (1994) [14] and Kong and Mizera (2012) have made connections of directional quantile envelopes to level sets of half-space (Tukey) depth. In the recent paper (Kuelbs and Zinn, 2014) we showed that half-space depth regions determined by evaluation maps of a stochastic process are not only uniquely determined by related upper and lower quantile functions for the process, but limit theorems have also been obtained. In this paper we study the consequences of these results when applied to finite dimensional data in greater detail. The methods we employ here are based on Kuelbs and Zinn (2015) and Kuelbs and Zinn (2013). [ABSTRACT FROM AUTHOR]