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This paper intends to develop a new integral filled function method with four properties. First, the proposed filled function is non-exponential and non-logarithmic. This property is aimed at avoiding the overflow effect during the computational stage. Second, our method does not contain parameters, so the possibility of non-converging iterations can be prevented. Third, the filled function proposed in this paper is continuously differentiable. By this property, any local minimization procedures can be applied. Finally, the suggested filled function is dependent on the objective function, and thus it can provide any information for locating a minimum of the filled function. To show that the proposed method is competitive, a comparison has been made with one of the deterministic approaches, namely the DIRECT method. [ABSTRACT FROM AUTHOR]

We improve the approximated solution for the inventory model with a linear trend in demand such that there is no necessary to adjust the last or the first time interval. Our formula is easier to compute. We estimate our approximated result to the optimal solution of the equal time interval constraint, then our result is measured with an error of less than two-thirds. For the second inventory system examined in this paper, we consider an inventory system with two retailers and a manufacturer. Through the algebraic process, we obtain the optimal profit that is missing in the previously published paper. We show the elegant character of the algebraic process. [ABSTRACT FROM AUTHOR]

This paper proposes a predictive control algorithm for the speed and displacement tracking of urban rail trains. Firstly, the train dynamics model is constructed considering the resistance existing in the actual operational scenarios. Secondly, based on the model predictive control (MPC) framework, a control objective function for tracking the desired speed and displacement and the stable change of control quantities is designed. Finally, combined with constraints of the train operation, the proposed MPC algorithm for the train tracking control problem is transformed into quadratic programming with inequality constraints, thereby facilitating a solution with the commonly-used solvers. Experimental results demonstrate that the proposed algorithm can effectively enhance the speed and displacement control performance while improving energy efficiency, ensuring the safety, stability, and riding comfort of the train. [ABSTRACT FROM AUTHOR]

The progressive iterative approximation (PIA) is a versatile method for interpolating or fitting a given data set. The convergence behavior of PIA plays a pivotal role in determining the computational efficiency of data interpolation or fitting. This paper introduces an accelerated iterative approach, GS-PIA, derived from the Gauss-Seidel splitting, specifically designed for interpolating data points. The convergence and computational cost of the proposed iterative method are discussed. Numerical results underscore the superiority of GS-PIA in data interpolation when compared to other existing methods. [ABSTRACT FROM AUTHOR]

This paper presents a decision-making approach grounded in rough set theory and evidential reasoning to address the demand for expert decision-making in greenhouse environmental control systems. Furthermore, a decision-making model is developed by integrating the D-S evidence theory with an expert knowledge table for greenhouse environmental control systems. The model's reasoning process encompasses continuous attribute discretization, expert decision table formation, attribute reduction, and evidence combination reasoning. Firstly, the fuzzy C-means clustering algorithm is employed to discretize the original environmental data and cluster it. Subsequently, an attribute reduction algorithm based on information entropy is utilized to optimize the decision table by eliminating unnecessary conditional attributes in expert knowledge. The reduced indicators are then combined using evidential theory. Finally, suitable greenhouse control methods are determined by the confidence decision proposed by the D-S evidence theory. To assess the efficacy of this intelligent decision-making algorithm based on rough set and D-S evidence theory, its performance is compared with traditional SVM algorithms and small-shot learning algorithms. The results indicate that this proposed method significantly enhances the credibility of control decision-making processes, with an average running time of 0.002378s for the fusion decision algorithm and 0.017939s for the support vector machine (SVM) algorithm, respectively. The SVM accuracy rate after testing and training stands at 90.34%. Moreover, retraining based on information entropy attribute reduction leads to a correct decision rate increase of up to 100%. This method notably improves confidence levels in decision-making processes while reducing uncertainty and demonstrates reliability when applied in making decisions regarding greenhouse environments. [ABSTRACT FROM AUTHOR]

Person Re-Identification falls within the scope of computer vision, acting a technique to ascertain the presence of a specified pedestrian within a video or image library. The related research is of great significance in real-world environments such as criminal investigation and statistical analysis of commercial foot traffic and has received extensive attention from the academic community. However, traditional methods such as manual extraction cannot adapt to largescale data volumes, and deep learning-based methods at this stage suffer from interference in complex environments such as similar costumes, perspective changes, and occlusion. Therefore, in this paper, we investigate the above problems. Firstly, we expand the dataset by introducing random erasure-based preprocessing of pedestrian images to enhancing the robustness and generalization capability of neural networks. Secondly, a composite attention mechanism is introduced after the network residual layer to enhance the spatial information capability and feature expression. Finally, the union loss composed of Circle Loss, Ternary Loss, and Cross Entropy Loss was chosen for network training in the loss optimization phase. Findings from the experiments reveal that the improved method proposed in this experiment achieves 96.0%Rank-1 and 88.3%mAP in Market1501, which reflects the validity of the approach proposed in this manuscript, and provides valuable reference suggestions for Person Re-Identification related research. [ABSTRACT FROM AUTHOR]

In recent years, there is massive development of new metaheuristics as stochastic methods. Meanwhile, there is not any metaheuristics is powerful to handle all problems as stated in the no-free-lunch (NFL) theory. Based on this circumstance, this paper introduces a new swarm-based metaheuristics with the main strategy moving toward the resultant of better swarm members and avoiding the resultant of worse swarm members called group better-worse algorithm (GBWA). It consists of five searches: moving toward the best swarm member, moving toward the resultant of better swarm members, moving away from the resultant of worse swarm members, searching locally, and jumping to the opposite area. GBWA is then evaluated in three ways. The first evaluation is a comparative evaluation where GBWA is compared to five recent metaheuristics: coati optimization algorithm (COA), average and subtraction-based optimization (ASBO), clouded leopard optimization (CLO), total interaction algorithm (TIA), and osprey optimization algorithm (OOA). The second evaluation is the individual search evaluation. The third evaluation is hyperparameter test. The collection of 23 classic functions is chosen as the use case in all evaluations. The result of the first evaluation shows that GBWA is better than COA, ASBO, CLO, TIA, and OOA in 20, 21, 20, 21, and 21 functions consecutively. Meanwhile, the result of the second evaluation shows the equal contribution between the motion toward the best swarm member and the motion toward the resultant of better swarm members. [ABSTRACT FROM AUTHOR]

A new swarm-based metaheuristic, namely the enriched coati osprey algorithm (ECOA), is proposed in this paper. As its name suggests, ECOA hybridizes two new metaheuristics, the coati optimization algorithm (COA) and the osprey optimization algorithm (OOA). ECOA is constructed by five searches performed sequentially by the swarm members. The first three are directed searches, while the last two are neighborhood searches. All three directed searches are adopted from COA and OOA. Meanwhile, the four-bordered neighborhood search is developed based on a new approach. During the assessment, ECOA was challenged to overcome the set of 23 functions and contended with five new metaheuristics: total interaction algorithm (TIA), golden search optimization (GSO), average and subtraction-based optimization (ASBO), COA, and OOA. The result shows that ECOA outperforms TIA, GSO, ASBO, COA, and OOA in 16, 23, 18, 21, and 21 functions. Meanwhile, the individual search test result shows that the directed searches perform better than the neighborhood searches. Moreover, the directed search toward the best member becomes the most dominant search. [ABSTRACT FROM AUTHOR]

This paper proposes a robust identification and control-based on a neural network method for a Twin Rotor Multivariable System (TRMS) using a recursive adaptive training algorithm. The algorithm is based on a recursive least squares approach with an additional steepest descent stage. An Adaline neural network is used for modeling the system, and a robust structure is selected based on a linear auto-regressive structure with exogenous inputs (ARX) related to the estimation error. The identification is performed online and the system is controlled under a polynomial structure by pole placement with a dead-beat strategy. The method is evaluated in terms of estimation and tracking error in the presence of external additive disturbances, parametric disturbances, and sinusoidal reference signals. The Root-Mean Square Error (RMSE) is used to evaluate the estimation performance and the Integral-Time Absolute Error (ITAE) is used to evaluate the tracking performance. As a result, a novel robust controller based on a neural network is designed where the best results are obtained for a training recursive least squares algorithm with an additional steepest descent stage. [ABSTRACT FROM AUTHOR]

Machine learning (ML) is evolving rapidly and has made many theoretical breakthroughs while widely applied in various fields. ML allows systems the ability to access data and use it to enable computers to execute cognitive processes such as learning and improving from previous experiences and solving complicated issues. Many first-order stochastic optimization methods have been used to solve the optimization model of ML. These algorithms adopt Barzilai-Borwein (BB) step size instead of fixed or diminishing step size to improve performance. However, the BB step size format involves fractional calculation, which inevitably leads to a zero denominator, especially when the objective function is non-convex. The BB technique will be violated if the denominator is near 0 or even negative. To improve the computation of the step size, a Positive Defined Stabilized Barzilai-Borwein (PDSBB) approach is introduced in this paper. Integrating PDSBB with the stochastic variance reduced gradient (SVRG) approach, a new method SVRG-PDSBB is proposed. Numerical experiments have shown that the new algorithm has stabilized the performance of the new step size, which successfully avoiding zero denominators and effectively solving the common problems in machine learning. The convergence of SVRG-PDSBB is theoretically and numerically proven, and the effectiveness of the new algorithm is shown by comparison with other algorithms. [ABSTRACT FROM AUTHOR]

The Lotka-Volterra competition model consisting of two equations is studied. The existence and uniqueness of solutions on an infinite interval are proved by using the Schauder fixed point theorem, Gronwall’s inequality and some special analytical techniques. Some conditions of existence for positive solutions are obtained. Iterative algorithms and error estimations for solving this model are established. The results of this paper can be generalized to the cases consisting of more than two equations. [ABSTRACT FROM AUTHOR]

Multi-objective problems have gained much attention during the last decade. To balance the diversity and the convergence of the multi-objective differential evolution algorithm (MODE), an improved MODE is proposed based on the affinity propagation clustering (APC) and the non-dominated count approach in this paper. The proposed algorithm is referred to as AP-MODE, which improves the search efficiency by utilizing the affinity propagation approach to find out the population distribution structure for guiding search. In addition, mating restriction probability is used to select parent individuals for recombination from the neighborhoods or the whole population. Meanwhile, the mating restriction probability is updated according to the non-dominated count approach at each generation. This proposed algorithm is verified by comparing it with some state-of-the-art multi-objective evolutionary algorithms, and the simulation results on DTLZ test problems indicate that AP-MODE can efficiently achieve two goals of multi-objective optimization, i.e., the convergence to actual Pareto front and uniform spread of individuals along Pareto front. [ABSTRACT FROM AUTHOR]

The optimal configuration problem of distributed generators (DGs) and shunt capacitors (SCs) in a radial distributed network (RDN) is to find the best installation locations and optimal capacities of DGs and SCs for optimizing a certain performance indicator. The discontinuity characteristic and huge computation of optimizing DGs and SCs in RDN make it no longer applicable by traditional methods. In this paper, a new bus processing method and an improved butterfly algorithm are proposed to solve the optimal configuration of DGs and SCs. The method of processing nodes considers not only the power loss index (PLI) but also the voltage amplitude of the original system, forming a sequence of candidate nodes to guide algorithm to optimizing, which can simplify the algorithm search space and improve search efficiency. Meanwhile, the butterfly algorithm with constriction factor (BF-CF) combines the inertia coefficient to introduce a constriction factor, improves the speed update model and the local search pattern, and overcomes the disadvantages of the original butterfly algorithm which is easy to fall into the local optimum and the precision of result is not high. To verify the performance of the proposed method, minimizing the active power loss and voltage deviation are selected as the objective function and reactive power loss and the worst voltage are taken as reference targets, which are performed in three standard test systems of 33-bus, 69-bus and 119-bus, respectively. The simulation results illustrate that, compared with the original butterfly algorithm and other intelligent algorithms, the method proposed in this paper has more obvious advantages and performance in solving the configuration problem of DGs and SCs in systems of various scales. [ABSTRACT FROM AUTHOR]

In this paper, a modified and hybrid flower pollination algorithms (MHFPA) is proposed for dealing with the multi-objective optimal power flow (MOOPF) problem with conflictive objectives. The algorithm combines the mutation and crossover process in the differential evolution (DE) algorithm, introduces the sinusoidal nonlinear dynamic switching probability (SNDSP) and the elite strategy of elder generation (ESEG), which can improve the shortcomings of the original pollen algorithm that it is easy to fall into the local optimum and the diversity is insufficient. A screening approach with Pareto-dominant rule (SAPR) is proposed to ensure that the state variable can satisfy the inequality constraints of the power system. A uniformly distributed Pareto optimal set (POS) is obtained by the non-dominant sorting with elite strategy (NSES) based on Rank and Density estimation, and the best trade-off solution (BTS) is determined from the POS obtained by the fuzzy affiliation theory. For practicality, the total fuel cost, active power loss, emissions and voltage deviation are selected as objective functions. Due to the limitations of the actual power system, the valve point effect is also considered. The IEEE30-, 57- and IEEE118-bus test systems are used to verify the performance of the proposed MHFPA. In addition, two performance indicators, Hypervolume (HV) and Spacing (SP), quantitatively evaluate the diversity and uniformity of the POS obtained by MHFPA. The simulation results show that, compared with the classic MOPSO and NSGA-II algorithms, the method proposed in this paper shows a greater competitive advantage in dealing with different scales and non-convex optimization problems. [ABSTRACT FROM AUTHOR]

Trapdoor functions contributed since their announcement in the evolvement cryptography as we know it, especially the lossy mode, by helping reduce the residual leakage for an optimal rate, but to make it more resilient cryptographically: generic constructions were made based on graph isomorphism, or other NP-hard problems defended by the zero-knowledge proof, such were used in Indistinguishability under Chosen-Plaintext Attack (IND-CPA), Computationnal Diffie-Hellman (CDH), or Decisional Diffie-Hellman (DDH). Once schemes like Indistinguishability under Chosen- Ciphertext Attack (IND-CCA) were adopted it became clear it cannot simulate a decryption using Lossy Trapdoor Functions (LTF); the problem with existing trapdoor functions in general is partial information leakage, lack of randomness and multiple messages insecurity. In the light of the following issues came the idea to present through this paper a simple but important fix, in the note of randomness a new Variate of the Engel expansion (VEE) is chosen, providing a pseudo-random bit sequence as an output, the reason being to recover the seed of the algorithm for an attacker, it is considered a hard number theory problem, and surely after the new construction in this paper, another NP-complete problem emerging from tensors the scheme is more secure. As for the strenghtening evidence of how it can be trusted, it seems more robust to supply a proof of its ergodicity as being done in this article, instead of semantic security analysis, to prove the efficiency of the new construction resolving the issues surrounding multi-challenge using a lossy trapdoor function. [ABSTRACT FROM AUTHOR]

Distributed generators (DGs) are recognized as an effective method for controlling the power loss, voltage stability, etc.. In this paper, a novel hybrid algorithm of beetle antennae search (BAS) and particle swarm optimization (PSO) is presented for optimal allocation of DGs in radial distribution network. The BAS describes the beetle's individual search by smell, PSO describes the group search of birds by location. The proposed algorithm combines their advantages, proceeds with individual optimization while conducting group optimization. Therefore, the proposed algorithm searches widely, and converges fast. In this paper, a series of improvement measures are proposed to deal with the shortcoming of PSO-BAS which is easy to fall into local optimum. These methods include equal interval initialization, cross mutation, and non-linear learning factor. This paper will show the comparison results of PSO-BAS and IPSO-BAS in the six confessed test functions to prove the necessity of the improved methods. Simultaneously, in order to verify the feasibility and effectiveness of this proposed algorithm in terms of practical application, it is tested on the standard IEEE 33-bus, IEEE 69-bus and IEEE 119-bus systems. The results of active power loss and voltage stability show that proposed algorithm is more effective and more suitable for the power distribution system than other algorithms. At the same time, this article also explores the impact of new energy sources on the annual network loss. Besides, a method for optimizing the annual network loss is proposed. Here, the IPSO-BAS algorithm is used to adjust the size of multiple biomass energy sources within 24 hours to optimize the network loss, and a comparison plan is designed to verify the feasibility of the proposed method. According to the final result, this proposed method can greatly reduce the annual network loss. [ABSTRACT FROM AUTHOR]

To effectively handle the many-objective optimal power flow (MOOPF) problems considering the simultaneous reduction of power loss, emission and fuel cost, an improved NSGA-Ⅲ (INSGA-Ⅲ) algorithm is put forward in this paper. In detail, the proposed INSGA-Ⅲ algorithm adopts the competitive solutions preliminarily optimized by traditional NSGA-Ⅲ method as the initial population and integrates the novel adaptive dominant (NAD) strategy. Comparing with the original NSGA-Ⅲ algorithm, INSGA-Ⅲ obtains the more preferable Pareto front (PF) with uniform distribution. More significantly, an entirely new BP fuel-cost prediction network is proposed to explore the potential elite power flow (EPL) solutions. These EPL solutions determined around the best compromise solution (BCS) of INSGA-Ⅲ algorithm provide decision-makers with more and better scheduling schemes. The effectiveness and superiorities of proposed INSGA-Ⅲ algorithm and BP fuel-cost prediction model are verified by both dual-objective and triple-objective MOOPF simulation experiments. In general, this paper presents an innovative way to solve the complex engineering problems by computer technologies represented by intelligent algorithms and neural networks. [ABSTRACT FROM AUTHOR]

G(V, E) represents the basic chart without circle, if existing a one-to-one mapping f:E(G) → {1,2,...,|E|}, for any two vertices in the diagram, in the event that d(u)= d(v). S(u)=S(v), where S(u)= Σuw∈E(G)f(uw), d(u) represents the degree of the vertex u, then call the mapping f: Adjacent Vertex Reducible Edge Labeling (alluded as AVREL). In graph theory, graph coloring and graph labeling are two research directions of graph theory, and there is little correlation between the two in previous research results. In the process of researching the concept of Adjacent Reducible Edge Coloring proposed by Professor Zhang Zhongfu, we found that there are several graph classes whose coloring number reaches the sum of the number of vertices and edges, so we propose a new concept of Adjacent Reducible Edge Labeling. In the transportation network, the edge weight represents the transportation capacity, and the node transportation capacity is represented by the sum of its associated edges. Two nodes with the same degree of adjacency require the transportation capacity to be as equal as possible, which can be described by the Adjacent Vertex Reducible Edge Coloring model. when the road diversity reaches the extreme value, it can be described by the Adjacent Vertex Reducible Edge Labeling model. In this paper, designing and using Adjacent Vertex Reducible Edge Labeling algorithm (abbreviation: AVREL algorithm). The algorithm recursively looks through the arrangement space of the Adjacent Reducible Edge Label through the underlying label of the edge, lastly sifts through the graph book fulfilling the edge label and results as a label matrix. In the wake of examining the algorithm results, some special graphs such as Petersen-pyramid graphs, Möbius ladder graphs, bicyclic graphs, and some joint graphs in various situations are summed up, the proofs and conjectures are given. [ABSTRACT FROM AUTHOR]

In this paper, a algorithm of the partial derivatives of the generalized hypergeometric function pFq ( ã; ˜b; z ) is obtained, where ã = {a1, a2, . . ., ap}, ˜b = {b1, b2, . . ., bq}. Moreover, we compare some algorithms of calculating the partial derivatives of pFq ( ã; ˜b; z ) . Numerical examples show the algorithm given in this paper improves the precision and accelerates the calculation of partial derivatives of the generalized hypergeometric function. Furthermore, we obtain some applications of the partial derivatives of the generalized hypergeometric function in calculating improper integrals and the derivative of the special function, such as the derivatives with respect to the order of Bessel function etc. The accuracy and the speed of calculating the improper integrals are improved by numerical examples. [ABSTRACT FROM AUTHOR]

Multi-objective reactive power optimization (MORPO) is a high-dimensional, nonlinear, multi-constraint problem. To solve this problem, an improved multi-objective honey badger algorithm (MOIHBA) is proposed. To address the shortcomings of the original algorithm, such as easy falling into local optimum and insufficient population diversity, the improved algorithm introduces a sine chaotic mapping strategy to expand the population diversity, a backward learning mechanism to narrow the range of high-quality solution sets, and a cross-learning mechanism to improve the precision of the algorithm optimization process. In addition, in order to obtain the pareto optimal set (POS), a method based on calculating individual rank and crowding distance is proposed to sort the non-inferior solution, and the best compromise solution (BCS) is obtained by using a fuzzy theory strategy. By introducing three objective functions of active power loss, voltage stability index, and voltage deviation, the multi-objective reactive power optimization is established. To investigate the robustness of the introduced improved algorithm and its ability to solve the MORPO problem, this paper uses IEEE30, IEEE57, and IEEE118 as test systems that optimize the dual objective and triple objective simultaneously. In order to study the comprehensive performance of the improved algorithm, the algorithm time complexity, GD index, and HV index are adopted for evaluation. The simulation results and performance index results show that compared with other algorithms, MOIHBA has better BCS and pareto fronts (PFs) with the best uniformity and convergence. Therefore, the MOIHBA algorithm has a greater competitive advantage in solving the MORPO problem. [ABSTRACT FROM AUTHOR]

This paper proposes an improved novel bionic intelligent Moth-Flame Optimization (MFO) algorithm optimized linear active disturbance rejection control (LADRC) strategy for automatic generation control (AGC) problems. LADRC is a control strategy that combines linear extended state observer (LESO) and traditional proportional-derivative (PD) control, with the advantages of its resistance to disturbance and simplicity. The three-order LADRC controller is designed in load frequency control (LFC) system. The Improved MFO (IMFO) algorithm is proposed by Cauchy mutation strategy and self-adaptive weight to overcome the weaknesses in easily falling into local optima and poor optimization search accuracy, and the IMFO algorithm is employed for tuning the parameters of LADRC. Besides, an objective function takes account of the performance index integral-time-multiplied-AE (ITAE) with dynamic indicators, which is used to improve the effectiveness of LADRC. The proposed control strategy is tested for robustness in a two-area non-reheat thermal system and compared with recent control methods published in the literature. As a result, its superiority is demonstrated for the lowest cost function values of ITAE = 0.0036, ITSE = 1.24E-05, ISE = 6.81E-05 and IAE= 0.0086. To further explore the potential of the LADRC controller based on the IMFO algorithm, it is also extended to a two-area nonlinear system and an unequal three-area reheat system. The performance indicator functions and dynamic performance indicators are analyzed qualitatively in the meantime. [ABSTRACT FROM AUTHOR]

In this paper, an improved marine predators algorithm (IMPA) is proposed to solve the short-term hydrothermal scheduling (STHS) problem. The marine predators algorithm (MPA) owns low diversity of the initial population and is easy to fall into local optima in the optimization process. Facing these challenges, three improvements are presented. Tent map is applied to initialize the population, which makes the population more uniformly distributed. An average fitness preferential strategy is adopted to improve the quality of population, which provides more possibility for MPA to find better solutions. By segmenting the probability factor in fish aggregating devices (FADs) effect on the optimization process, the premature convergence of MPA is improved. Moreover, a selective repair strategy and an economic priority strategy are proposed to handle dynamic water balance of reservoirs and the power balance, respectively. Three hydrothermal test cases are employed to verify the feasibility and effectiveness of the proposed method, and the results show that IMPA can obtain solutions of high quality. Compared with other methods, IMPA can get better results, which reflects its strong competitiveness in tackling the STHS problem. [ABSTRACT FROM AUTHOR]

A graph G(p, q) is said to have an edge-magic total labeling if there exists a bijective function f: V(G) ∪ E(G) → {1, 2, ...,p + q}, such that for any edge uv∊E(G) the condition f(u)+f(v)+f(uv)=k is satisfied, k is a constant. In this paper, a new algorithm, based on the graph generate algorithm, is designed to obtain the edge-magic total labeling of the unicyclic graphs. Some theorems about unicyclic graphs are also deduced from the algorithm's results. It's believed that the algorithm proposed is innovative and can be adopted by other researchers. [ABSTRACT FROM AUTHOR]

The discrete filled function method (DFFM) is a global optimization method for searching for the best solution amongst multiple local optima. This method consists of two phases: in the first phase, an ordinary descent method is used to find a local minimum; in the second phase, an auxiliary function, called a filled function, is introduced that has a maximizer at the current local minimum, so that minimizing the filled function leads to improved points. Once an improved point is found, it can serve as a starting point for the next local search. In this paper, we consider a standard discrete filled function algorithm in the literature and propose a modification to increase its efficiency. Three numerical examples are given to demonstrate the proposed modification's potential in solving large scale discrete optimization problems. [ABSTRACT FROM AUTHOR]

This paper proposes a node-adaptive algorithm that aims to enhance the effectiveness of the dual reciprocity boundary element method (DRBEM) for numerically solving PDEs. The adaptation algorithm allows the internal nodes to automatically adapt accordingly to a pre-defined criterion during the computing process. The multiquadric radial basis function (MQ-RBF) is used to link the supports from internal nodes to the boundary ones. The proposed adaptation scheme is driven by the local change in velocity (in both x- and ydirections) using a form of normalized error indicator. The node-adaptation manner falls into the h-type of refinement where nodes are automatically added into (or removed from) the computational domain. It is found that the numerical solutions obtained from the proposed adaptation scheme are noticeably improved for all cases under the investigation. This promising aspect certainly provides a numerical tool for better applications of DRBEM toward more complex problems. [ABSTRACT FROM AUTHOR]

Recently, intuitionistic fuzzy sets and numbers are widely interesting in the literature, and many types of Intuitionistic Fuzzy Numbers (IFN's) are studied and applied to different mathematical and real life problems. In this paper, an algorithm to approximate general IFN's by the n-Intuitionistic Polygonal Fuzzy Number (n-IPFN) is introduced. The approximation facilitates the calculations due to its linearity, not to mention its realisticity and flexibility. After that, a new method to rank IFN's is introduced and applied to the n-IPFN. Based on that, convenient arithmetic operations for n-IPFN's that preserve the ranking values are proposed and shown to satisfy the most important properties. As a result, defining a ranking equivalence relation gave a strong algebraic structure that is isomorphic to the real numbers set. Finally, some definitions are proposed for dealing with matrices, functions, equalities and inequalities with n-IPFN's. [ABSTRACT FROM AUTHOR]

Water cycle algorithm (WCA) is a heuristic algorithm proposed in recent years. To overcome the insufficiency of standard WCA algorithm in solving the non-convex optimal power flow (OPF) problems, the multi-objective novel improved water cycle algorithm (MONIWCA) is proposed in this paper. The evaporation process is improved in WCA by introducing evaporation rate and the normal distribution optimization mechanism is used to mutate the individual position. The modified WCA also adopts a constraint-based strategy to ensure zero constraint violations. In order to obtain a high-quality Pareto optimal solution set (POS) and select the best compromise solution (BCs), a global ranking strategy is proposed. The global ranking strategy includes the novel constraint handling method, the rank index calculation and the BCs on fuzzy satisfaction theory to deal with the complex constraints of the optimization problem. The MONIWCA has been simulated under the constraints of zero violations on IEEE 30, IEEE 57 and IEEE 118 standard test systems, including six dual-objective cases and one tri- objective case. The simulation results are compared with the multi-objective particle swarm optimization (MOPSO). The results show that the improved method can effectively solve the MOOPF problem, not only to obtain a uniform continuous Pareto solution set but also to achieve a better compromise solution. In addition, the two performance indicators of the generational distance (GD) and the spacing (SP) also show that the MONIWCA algorithm has uniform distribution, high convergence and strong stability. [ABSTRACT FROM AUTHOR]

Quasi-Newton method is one of the most effective methods for solving nonlinear equations. In this paper, we improve convergence results of a BFGS trust region quasi-Newton method for nonlinear equations. The global and superlinear convergence are proved under the local error bound and the Hölderian continuity conditions, which are weaker than the nonsingularity and the Lipschitz continuity, respectively. Numerical results show that the algorithm is efficient and promising. [ABSTRACT FROM AUTHOR]

In this paper, B-spline curve interpolation model by using intuitionistic fuzzy set approach is introduced. Firstly, intuitionistic fuzzy control point relation is defined based on the intuitionistic fuzzy concept. Later, the intuitionistic fuzzy control point relation is blended with B-spline basis function. Through interpolation method, intuitionistic fuzzy B-spline curve model is visualized. Finally, some numerical examples and an algorithm to generate the desired curve is shown. [ABSTRACT FROM AUTHOR]

In this paper, some fast algorithms using elliptical arc artificial boundary is designed to solve exterior anisotropic problems in concave angle domains. Some exact nonlocal boundary conditions are derived on the elliptical arc artificial boundary. Based on the above artificial boundary conditions, the Dirichlet-Neumann alternating method is presented. The convergence of this algorithm is examined. Finally, some numerical examples are given to show the effectiveness of our methods. [ABSTRACT FROM AUTHOR]

In this paper, we mainly utilize the reduced sixorder compact finite difference scheme (R-CFDS6) based on proper orthogonal decomposition (POD) and operator splitting method (R-CFDS6-OSM) to solve the two-dimensional Fisher-Kolmogorov equation and extended Fisher-Kolmogorov equation. Toward this end, the CFDS6 is built to attain high accuracy for one-dimensional extended Fisher-Kolmogorov equation. Then by means of the operator splitting method, the two-dimensional extended Fisher-Kolmogorov equation has been converted into a succession of one-dimensional equations successfully, which can be solved easily with CFDS6 compared with Alternating direction implicit method. Finally, by POD method, we develop the R-CFDS6-OSM with fewer unknowns and sufficiently high accuracy to improve the computational efficiency of CFDS6 and furnish the algorithm procedure of R-CFDS6-OSM. Some numerical examples are carried out to validate the high accuracy, effectiveness and feasibility of the R-CFDS6-OSM for the numerical solution of 2D Fisher-Kolmogorov equation. [ABSTRACT FROM AUTHOR]

A problem of practical and theoretical interest is to determine or estimate the diameter of various families of Cayley networks. The previously known estimate for the diameter of Cayley graphs generated by transposition trees is an upper bound given in the oft-cited paper of Akers and Krishnamurthy (1989). In this work, we first assess the performance of their upper bound. We show that for every n, there exists a tree on n vertices, such that the difference between the upper bound and the true diameter value is at least n - 4. Evaluating their upper bound takes time Ω(n!). In this paper, we provide an algorithm that obtains an estimate of the diameter, but which requires only time O(n²); furthermore, the value obtained by our algorithm is less than or equal to the previously known diameter upper bound. Such an improvement to polynomial time, while still performing at least as well as the previous bound, is possible because our algorithm works directly with the transposition tree on n vertices and does not require examining any of the permutations. We also provide a tree for which the value computed by our algorithm is not necessarily unique, which is an important result because such examples are quite rare. For all families of trees we have investigated so far, each of the possible values computed by our algorithm happens to also be an upper bound on the diameter. [ABSTRACT FROM AUTHOR]

The notion of the Lp-projection body was introduced by Lutwak, Yang and Zhang. Whereafter, Ludwig proposed the asymmetric Lp-projection bodies, Haberl and Schuster introduced the general Lp-projection bodies. In this paper, associated with the Lp-geominimal surface area, we study the Shephard type problems for the general Lp-projection bodies. [ABSTRACT FROM AUTHOR]

An adaptive multi-objective optimization artificial immune algorithm (AMOAIA) is presented in this paper. An innovating sorting mechanism based on its Pareto ratio is used to sort individuals in the antibody population. The selection and cloning scheme is improved by using a neighborhood-based fitness assessment. An adaptive clone selection mechanism is introduced to preserve the diversity of the antibody. A new hybrid mutation operator using chaos random series for globally optimization solution has been proposed to maintain the diversity of the antibody population. A multi-objective optimization clustering algorithm based on the distribution of distributed Pareto frontiers is proposed. In addition, the effectiveness of the proposed algorithm is verified under many difficult conditions such as local optimality, non-uniformity, discontinuity, non-convexity, high-dimension, and constraints. The comparative study shows the effectiveness of the proposed algorithm, which produces solution sets that are highly superiority in terms of global convergence, diversity and distribution. [ABSTRACT FROM AUTHOR]

In this paper we present two path planning algorithms based on Bézier curves for autonomous vehicles with waypoints and corridor constraints. Bézier curves have useful properties for the path generation problem. This paper describes how the algorithms apply these properties to generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join a set of low-degree Bézier curves segments smoothly to generate the path. Additionally, we discuss the constrained optimization problem that optimizes the resulting path for a user-defined cost function. The simulation demonstrates the improvement of trajectory generation in terms of smoother steering control and smaller cross track error compared to previous work. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the Legendre wavelets for the solution of linear and nonlinear fractional integro-differential equations. The properties of Legendre wavelets together with the fractional order operational matrix of integration are used to reduce the problem to the solution of a system of algebraic equations. Also a reliable approach for convergence of the Legendre wavelets method is discussed. Further some numerical examples are shown to illustrate the accuracy and reliability of the proposed approach and the results have been compared with the exact solution. [ABSTRACT FROM AUTHOR]

Often in nature different physical systems interact which translates to coupled mathematical models. Even if powerful solvers often already exist for problems in a single physical domain (e.g. structural or fluid problems), the development of similar tools for multi-physics problems is still ongoing. When the interaction (or coupling) between the two systems is strong, many methods still fail or are computationally very expensive. Approaches for solving these multi-physics problems can be broadly put in two categories: monolithic or partitioned. While we are not claiming that the partitioned approach is panacea for all coupled problems, here we will only focus our attention on studying methods to solve (strongly) coupled problems with a partitioned approach in which each of the physical problems is solved with a specialized code that we consider to be a black box solver and of which the Jacobian is unknown. We also assume that calling these black boxes is the most expensive part of any algorithm, so that performance is judged by the number of times these are called. Running these black boxes one after another, until convergence is reached, is a standard solution technique and can be considered as a non-linear Gauss-Seidel iteration. It is easy to implement but comes at the cost of slow or even conditional convergence. A recent interpretation of this approach as a rootfinding problem has opened the door to acceleration techniques based on quasi-Newton methods. These quasi-Newton methods can easily be "strapped onto" the original iteration loop without the need to modify the underlying code and with little extra computational cost. In this paper, we analyze the performance of ten acceleration techniques that can be applied to accelerate the convergence of a non-linear Gauss-Seidel iteration, on different multi-physics problems. [ABSTRACT FROM AUTHOR]

For globally solving sum of linear ratios problem (SLRP), this paper presents a new branch-and-bound method. In this method, a new linear relaxation technique is proposed firstly; then, the initial problem SLRP is solved by a sequence of linear programming problems. Meanwhile, to improve the convergence speed of our algorithm, two accelerating techniques are presented. The proposed algorithm is proved to be convergent, and some experiments are provided to show its feasibility and efficiency. [ABSTRACT FROM AUTHOR]

It is requisite to construct the normal extended function for a given function defined on the interface. In this paper, the extended function is compulsory to satisfy some interface conditions. Firstly, we construct a proper normal extended correction function which can transfer the interface problem to some non-interface one. The correction function is designed in the form of power series which are helpful to theoretical analysis. Open and closed interface curves are considered respectively. Secondly, a simple but efficient algorithm is presented to obtain the extended function value at any given point not only on the interface, such as some Gaussian points. Finally, we employ the extended function into some interface problems and carry on with some numerical experiments by employing the linear finite element method. Numerical results confirm the validity of normal extended correction functions and the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

The relationship between gold and US dollar series, which are non-stationary, is commonly known to be negative from a periodic perspective. Is this really the case? This paper established a combined iteration algorithm using the theory of spectral analysis after subtracting the trend using penalized B-spline functions to obtain the implicit cycles in gold and US dollar series. This algorithm accurately separates the trend terms and periodic terms of the two series to produce more precise and complete periodic information. The results show that both series share three common implicit cycles: two long periods and one short one. Both long-period terms are negatively correlated, whereas the short-period terms are positively correlated. [ABSTRACT FROM AUTHOR]

The relationship between gold and US dollar series, which are non-stationary, is commonly known to be negative from a periodic perspective. Is this really the case? This paper established a combined iteration algorithm using the theory of spectral analysis after subtracting the trend using penalized B-spline functions to obtain the implicit cycles in gold and US dollar series. This algorithm accurately separates the trend terms and periodic terms of the two series to produce more precise and complete periodic information. The results show that both series share three common implicit cycles: two long periods and one short one. Both long-period terms are negatively correlated, whereas the short-period terms are positively correlated. [ABSTRACT FROM AUTHOR]

The IDRStab method, which combines the Induced Dimension Reduction (IDR) (s) method with higher-order stabilizing polynomials, is an effective method for solving large nonsymmetric linear systems. IDRStab can be implemented using different algorithms which are mathematically equivalent. In this paper, we illustrate preconditioned algorithms for three variants of IDRStab and describe their advantages. Numerical experiments show the differences in the convergence of the variants of IDRStab with preconditioning. [ABSTRACT FROM AUTHOR]

Different regularities can be used to identify the sequence among other sequences. Regularities allow us to infer an information about the evolution of the sequence. Tandem repeats are the most frequent in the genomes of eukaryotes. Extraction of regularities is a widely studied problem. However, searching for exact tandem repeats can be too restrictive. So, a natural extension of the repetition is to allow errors. In this paper, we consider the approximate period problem. In particular, we consider an explicit reduction from the approximate period problem to the satisfiability problem and present experimental results for different satisfiability algorithms. Also, we consider the approximate period problem for sequences of motor primitives of robots. In particular, we use the approximate period problem to obtain some meta-parameters that adapt the global motion behavior. We try to use such meta-parameters for learning to generalize motor primitives to a different behavior by trial and error without re-learning the task. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study weak and strong convergence of a two-step implicit algorithm for a finite family of asymptotically quasi-nonexpansive maps in a uniformly convex Banach space. The results are proved for a more general implicit algorithm under weaker assumptions on the control sequences of parameters. Our results are generalizations of several well-known results in the current literature. [ABSTRACT FROM AUTHOR]

The pricing of mortgages in the context of stochastic interest rate plays an important role for financial management. The contributing factors impacting the mortgage contract value have been explored by abundant literatures. However, the market players anticipate a systematic but low-cost approach to minimize the net present value of the payment streams by taking advantage of refinancing, for instance. This paper focuses on finding a desirable refinancing time for mortgage borrowers to minimize the total payment in a stochastic interest rate environment. The underlying interest rate is assumed to follow a stochastic process with mean-reverting property, the setting of which is broad enough to accommodate a large spectrum of market realities. Two types of commonly adopted mortgage balance settlement schemes are analyzed and compared to ensure the applicability of our study. Our numerical algorithm is validated with with varying samplings, leading to several interesting characteristics pertaining to the optimal mortgage refinancing period. As one of the applications, we obtain the optimal boundary conditions for the value of the mortgage contract for all time before the expiry of the contract. Our approach and algorithm provide cost effective and easy to use financial tools for both institutional and individual property investors. [ABSTRACT FROM AUTHOR]

Despite all the progress in filtering algorithms for state estimation in very high dimensional systems, the technology is delicate and sometimes difficult to apply. Good initialization of filter gain, appropriate choice of tuning parameters and their optimization are the key factors to achieve robust high-performance filtering algorithms. In this paper the authors propose a method for properly initializing the filter gain, and for efficient optimization of the filter performance. Numerical experiments will be given to illustrate the algorithm and to demonstrate the efficiency of the proposed filter for state estimation problems in classical low dimensional as well as in very high dimensional systems. [ABSTRACT FROM AUTHOR]

This paper proposes a exact solution algorithm to explicitly obtain the exact optimal solution of a second-order cone programming problem with box constraints of decision variables. The proposed solution algorithm is based on a parametric solution approach to determine the optimal strict region of parameters, and the main procedures are to perform deterministic equivalent transformations for the main problem and to solve the KKT condition of auxiliary problem without the loss of optimality. [ABSTRACT FROM AUTHOR]

In this paper, we focus on hierarchical multiobjective linear programming problems where multiple decision makers in a hierarchical organization have their own multiple objective linear functions together with common linear constraints, and propose an interactive decision making method to obtain a satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers but also their own preferences for their membership functions. In the proposed method, instead of Pareto optimal concept, a generalized Λ-extreme point concept is introduced. In order to obtain a satisfactory solution from among a generalized Λ-extreme point set, an interactive algorithm based on linear programming is proposed, and an interactive processes are demonstrated by means of an illustrative numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm of the homotopy analysis method (HAM) to obtain symbolic approximate solutions for linear and nonlinear differential equations of fractional order. We show that the HAM is different from all analytical methods; it provides us with a simple way to adjust and control the convergence region of the series solution by introducing the auxiliary parameter ħ, the auxiliary function H(t) , the initial guess y0(t) and the auxiliary linear operator ... . Three examples, the fractional oscillation equation, the fractional Riccati equation and the fractional Lane-Emden equation, are tested using the modified algorithm. The obtained results show that the Adomain decomposition method, Variational iteration method and homotopy perturbation method are special cases of homotopy analysis method. The modified algorithm can be widely implemented to solve both ordinary and partial differential equations of fractional order. [ABSTRACT FROM AUTHOR]

High precision multi region FDM calculations require the use of accurate algorithms not only for general mesh points of the net but also for points one unit from a metal surface. This paper corrects and extends a theory previously presented by including the possibility of a non constant tangential flux near the surface. Comparison of these results with the general meshpoint algorithm for the two tube lens shows that the two have similar precisions. [ABSTRACT FROM AUTHOR]