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Purpose - The purpose of this paper is to present results concerning resource distribution problems for a class of production systems composed of production operations described by relations with uncertain parameters - for newly considered serial-parallel and parallel-serial structures. Design/methodology/approach - The resource distribution problems are formulated. For the typical mathematical model of a single production operation, the resource distribution algorithms are derived analytically or, when that is impossible, numerical procedures for finding solutions to distribution problems are suggested. Findings - The uncertain variables have been proved as a convenient tool for solving specific optimization problems in production management based on relational knowledge representation with unknown parameters. Originality/value - The paper presents analytical resource distribution and numerical algorithms for determining the optimal resource distribution, which may be applied in knowledge-based management-level decision systems for serial-parallel and parallel-serial structures of production systems. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a new assessment system module for handling the comprehensive answers written through the answer interface. Design/methodology/approach: The working principle is under three major phases: Preliminary semantic processing: In the pre-processing work, the keywords are extracted for each answer given by the course instructor. In fact, this answer is actually considered as the key to evaluating the answers written by the e-learners. Keyword and semantic processing of e-learners for hierarchical clustering-based ontology construction: For each answer given by each student, the keywords and the semantic information are extracted and clustered (hierarchical clustering) using a new improved rider optimization algorithm known as Rider with Randomized Overtaker Update (RR-OU). Ontology matching evaluation: Once the ontology structures are completed, a new alignment procedure is used to find out the similarity between two different documents. Moreover, the objects defined in this work focuses on "how exactly the matching process is done for evaluating the document." Finally, the e-learners are classified based on their grades. Findings: On observing the outcomes, the proposed model shows less relative mean squared error measure when weights were (0.5, 0, 0.5), and it was 71.78% and 16.92% better than the error values attained for (0, 0.5, 0.5) and (0.5, 0.5, 0). On examining the outcomes, the values of error attained for (1, 0, 0) were found to be lower than the values when weights were (0, 0, 1) and (0, 1, 0). Here, the mean absolute error (MAE) measure for weight (1, 0, 0) was 33.99% and 51.52% better than the MAE value for weights (0, 0, 1) and (0, 1, 0). On analyzing the overall error analysis, the mean absolute percentage error of the implemented RR-OU model was 3.74% and 56.53% better than k-means and collaborative filtering + Onto + sequential pattern mining models, respectively. Originality/value: This paper adopts the latest optimization algorithm called RR-OU for proposing a new assessment system module for handling the comprehensive answers written through the answer interface. To the best of the authors' knowledge, this is the first work that uses RR-OU-based optimization for developing a new ontology alignment-based online assessment of e-learners. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to apply grey wolf optimizer (GWO) algorithm for steady state analysis of self-excited induction generators (SEIGs) supplying isolated loads. Design/methodology/approach: Taking the equivalent circuit of SEIG, the impedances representing the stator, rotor and the connected load are reduced to a single loop impedance in terms of the unknown frequency, magnetizing reactance and core loss resistance for the given rotor speed. This loop impedance is taken as the objective function and minimized using GWO to solve for the unknown parameters. By including the value of the desired voltage as a constraint, the formulated objective function is also extended for estimating the required excitation capacitance. Findings: The experimental results obtained on a three phase 415 V, 3.5 kW SEIG and the corresponding predetermined performance characteristics agree closely, thereby validating the proposed GWO method. Moreover, a comparative study of GWO with genetic algorithm and particle swarm optimization techniques reveals that GWO exhibits much quicker convergence of the objective function. Originality/value: The important contributions of this paper are as follows: for the first time, GWO has been introduced for the SEIG performance predetermination and computation of the excitation capacitance for attaining the desired terminal voltage for the given load and speed; the predicted performance accuracy is improved by considering the variable core loss of the SEIG; and GWO does not require derivations of lengthy equations for calculating the SEIG performance. [ABSTRACT FROM AUTHOR]

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

Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions. We further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters. For problems that satisfy the assumptions, we show how to select step-size and metric for the algorithm that optimize the derived convergence rate bounds. For problems with a similar structure that do not satisfy the assumptions, we present heuristic step-size and metric selection methods. [ABSTRACT FROM PUBLISHER]

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

Purpose – When facing a clouded global economy, many countries would increase their gold reserves. On the other hand, oil supply and demand depends on the political and economic situations of oil producing countries and their production technologies. Both oil and gold reserve play important roles in the economic development of a country. The paper aims to discuss this issue. Design/methodology/approach – This paper uses the historical data of oil and gold prices as research data, and uses the historical price tendency charts of oil and gold, as well as cluster analysis, to discuss the correlation between the historical data of oil and gold prices. By referring to the technical index equation of stocks, the technical indices of oil and gold prices are calculated as the independent variable and the closing price as the dependent variable of the forecasting model. Findings – The findings indicate that there is no obvious correlation between the price tendencies of oil and gold. According to five evaluating indicators, the MFOAGRNN forecast model has better forecast ability than the other three forecasting models. Originality/value – This paper explored the correlation between oil and gold prices, and built oil and gold prices forecasting models. In addition, this paper proposes a modified FOA (MFOA), where an escape parameter Δ is added to Si. The findings showed that the forecasting model that combines MFOA and GRNN has the best ability to forecast the closing price of oil and gold. [ABSTRACT FROM AUTHOR]

Reducing address arithmetic operations by optimization of address offset assignment greatly improves the performance of digital signal processor (DSP) applications. However, minimizing address operations alone may not directly reduce code size and schedule length for DSPs with multiple functional units. Little research work has been conducted on loop optimization with address offset assignment problem for architectures with multiple functional units. In this paper, we combine loop scheduling, array interleaving, and address assignment to minimize the schedule length and the number of address operations for loops on DSP architectures with multiple functional units. Array interleaving is applied to optimize address assignment for arrays in loop scheduling process. An algorithm, Address Operation Reduction Rotation Scheduling (AORRS), is proposed. The algorithm minimizes both schedule length and the number of address operations. with to list scheduling, AORRS shows an average reduction of 38.4% in schedule length and an average reduction of 31.7% in the number of address operations. Compared with rotation scheduling, AORRS shows an average reduction of 15.9% in schedule length and 33.6% in the number of address operations. [ABSTRACT FROM AUTHOR]

In model predictive control (MPC), the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem at each sample in the control loop. The main computational effort when solving the CFTOC problem using an active-set (AS) method is often spent on computing the search directions, which in MPC corresponds to solving unconstrained finite-time optimal control (UFTOC) problems. This is commonly performed using Riccati recursions or generic sparsity exploiting algorithms. In this paper, the focus is efficient search direction computations for AS type methods. The system of equations to be solved at each AS iteration is changed only by a low-rank modification of the previous one, and exploiting this structured change is important for the performance of AS-type solvers. In this paper, theory for how to exploit these low-rank changes by modifying the Riccati factorization between AS iterations in a structured way is presented. A numerical evaluation of the proposed algorithm shows that the computation time can be significantly reduced by modifying, instead of re-computing, the Riccati factorization. This speedup can be important for AS-type solvers used for linear, nonlinear, and hybrid MPC. [ABSTRACT FROM PUBLISHER]

Finding the optimal solution to the constrained l0 -norm minimization problems in the recovery of compressive sensed signals is an NP-hard problem and it usually requires intractable combinatorial searching operations for getting the global optimal solution, unless using other objective functions (e.g., the l1 norm or lp norm) for approximate solutions or using greedy search methods for locally optimal solutions (e.g., the orthogonal matching pursuit type algorithms). In this paper, a neurodynamic optimization method is proposed to solve the l0 -norm minimization problems for obtaining the global optimum using a recurrent neural network (RNN) model. For the RNN model, a group of modified Gaussian functions are constructed and their sum is taken as the objective function for approximating the l0 norm and for optimization. The constructed objective function sets up a convexity condition under which the neurodynamic system is guaranteed to obtain the globally convergent optimal solution. An adaptive adjustment scheme is developed for improving the performance of the optimization algorithm further. Extensive experiments are conducted to test the proposed approach in this paper and the output results validate the effectiveness of the new method. [ABSTRACT FROM PUBLISHER]

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

Purpose – The key control characteristics (KCCs) are very important to control dimensional quality of the final product. The purpose of this paper is to propose optimization algorithm and rules of design KCCs by optimizing KCCs of 2D and 3D workpieces based on equations and candidate locating points. Design/methodology/approach – This paper analyzes optimization process of 2D and 3D rectangle workpieces based on equations and candidate locating points by using fruit fly optimization algorithm (FOA). For decreasing variables of the algorithm, the improved fruit fly optimization algorithm (IFOA) is presented. Moreover, the Euclidean norm of inverse Jacobian is used as the objective function of optimizing KCCs by comparing different objective functions. Finally, a case of side frame assembly is presented to illustrate design and optimization of KCCs through IFOA, and results show that the method proposed in this paper is efficient and precise. Findings – The paper provides some reasonable conclusions for the design and optimization of KCCs. Originality/value – This paper designs and optimizes KCCs of fixtures and parts to improve dimensional quality of the final product. [ABSTRACT FROM AUTHOR]

Purpose – For many optimization problems such as optimal techniques, compositions, producing process, the optimizing objectives in systems are complex relations with respect to a great deal of parameters. Generally, the objective function is hardly obtained, even the searching objective is unquantifiable. So it is difficult to model and optimize the complex systems to some extent. Design/methodology/approach – To the above purpose, a novel approach is presented in this paper. It firstly utilizes the excellent fitting performance of neural network (NN) combined with expert knowledge (EK) to obtain the objective function, and secondly searches the optimal influential parameters with genetic algorithm (GA). Findings – Peaks function inside Matlab and the acural application of comprehensive performance optimization in analog PID control system are studied, respectively. The results of simulation and the actual experiment both show that the modeling and optimizing method presented in the paper are effective. Research limitations/implications – Expert knowledge is needed for the fuzzy/unquantifiable objective. Practical implications – The paper presents a useful way to model and optimize complex systems. Originality/value – The combined approach based on NN, EK and GA is firstly presented and is effectively used in modeling and optimizing complex systems. [ABSTRACT FROM AUTHOR]

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the computational task, instead of using a single centralized processor to obtain a “global solution” of the scenario problem (SP), we resort to multiple interconnected processors that are distributed among different nodes of a network to simultaneously solve the SP. Then, we propose a primal-dual subgradient algorithm and a random projection algorithm to distributedly solve the SP over undirected and directed graphs, respectively. Both algorithms are given in an explicit recursive form with simple iterations, which are especially suited for processors with limited computational capability. We show that, if the underlying graph is strongly connected, each node asymptotically computes a common optimal solution to the SP with a convergence rate $O(1/(\sum _{t=1}^k\zeta ^t))$ , where $\lbrace \zeta ^t\rbrace$ is a sequence of appropriately decreasing stepsizes. That is, the RCO is effectively solved in a distributed way. The relations with the existing literature on robust convex programs are thoroughly discussed and an example of robust system identification is included to validate the effectiveness of our distributed algorithms. [ABSTRACT FROM AUTHOR]

A reduction of a source distribution is a collection of smaller sized distributions that are collectively equivalent to the source distribution with respect to the property of decomposability. That is, an arbitrary language is decomposable with respect to the source distribution if and only if it is decomposable with respect to each smaller sized distribution (in the reduction). The notion of reduction of distributions has previously been proposed to improve the complexity of decomposability verification. In this paper, we address the problem of generating (optimal) reductions of distributions automatically. A (partial) solution to this problem is provided, which consists of an incremental algorithm for the production of candidate reductions and a reduction validation procedure. In the incremental production stage, backtracking is applied whenever a candidate reduction that cannot be validated is produced. A strengthened substitution-based proof technique is used for reduction validation, while a fixed template of candidate counter examples is used for reduction refutation; put together, they constitute our (partial) solution to the reduction verification problem. In addition, we show that a recursive approach for the generation of (small) reductions is easily supported. [ABSTRACT FROM AUTHOR]

This paper is concerned with a general class of distributed constrained optimization problems over a multiagent network, where the global objective function is represented by the sum of all local objective functions. Each agent in the network only knows its own local objective function, and is restricted to a global nonempty closed convex set. We discuss the scenario where the communication of the whole multiagent network is expressed as a sequence of time-varying general unbalanced directed graphs. The directed graphs are required to be uniformly jointly strongly connected and the weight matrices are only row-stochastic. To collaboratively deal with the optimization problems, existing distributed methods mostly require the communication graph to be fixed or balanced, which is impractical and hardly inevitable. In contrast, we propose a new distributed projection subgradient algorithm which is applicable to the time-varying general unbalanced directed graphs and does not need each agent to know its in-neighbors’ out-degree. When the objective functions are convex and Lipschitz continuous, it is proved that the proposed algorithm exactly converges to the optimal solution. Simulation results on a numerical experiment are shown to substantiate feasibility of the proposed algorithm and correctness of the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper presents a discrete-time distributed and noncooperative routing algorithm, which is proved, via Lyapunov arguments, to asymptotically converge to a specific equilibrium condition among the traffic flows over the network paths, known as Wardrop equilibrium. This convergence result improves the discrete-time algorithms in the literature, which achieve approximate convergence to the Wardrop equilibrium. Numerical simulations show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper discusses the computation of matrix chain products of the form M1 X M2 X ... X Mn where Mi's are matrices. The order in which the matrices are computed affects the number of operations. A sufficient condition about the association of the matrices in the optimal order is presented. An O( n) algorithm to find an order of computation which takes less than 25 percent longer than the optimal time Topt is also presented. In most cases, the algorithm yields the optimal order or an order which takes only a few percent longer than Topt (less than I percent on the average). [ABSTRACT FROM AUTHOR]

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

Purpose – The purpose of this paper is to solve the problem that the standard particle swarm optimization (PSO) algorithm has a low success rate when applied to the optimization of multi-dimensional and multi-extreme value functions, the authors would introduce the extended memory factor to the PSO algorithm. Furthermore, the paper aims to improve the convergence rate and precision of basic artificial fish swarm algorithm (FSA), a novel FSA optimized by PSO algorithm with extended memory (PSOEM-FSA) is proposed. Design/methodology/approach – In PSOEM-FSA, the extended memory for PSO is introduced to store each particle’ historical information comprising of recent places, personal best positions and global best positions, and a parameter called extended memory effective factor is employed to describe the importance of extended memory. Then, stability region of its deterministic version in a dynamic environment is analyzed by means of the classic discrete control theory. Furthermore, the extended memory factor is applied to five kinds of behavior pattern for FSA, including swarming, following, remembering, communicating and searching. Findings – The paper proposes a new intelligent algorithm. On the one hand, this algorithm makes the fish swimming have the characteristics of the speed of inertia; on the other hand, it expands behavior patterns for the fish to choose in the search process and achieves higher accuracy and convergence rate than PSO-FSA, owning to extended memory beneficial to direction and purpose during search. Simulation results verify that these improvements can reduce the blindness of fish search process, improve optimization performance of the algorithm. Research limitations/implications – Because of the chosen research approach, the research results may lack persuasion. In the future study, the authors will conduct more experiments to understand the behavior of PSOEM-FSA. In addition, there are mainly two aspects that the performance of this algorithm could be further improved. Practical implications – The proposed algorithm can be used to many practical engineering problems such as tracking problems. Social implications – The authors hope that the PSOEM-FSA can increase a branch of FSA algorithm, and enrich the content of the intelligent algorithms to some extent. Originality/value – The novel optimized FSA algorithm proposed in this paper improves the convergence speed and searching precision of the ordinary FSA to some degree. [ABSTRACT FROM AUTHOR]

Purpose – For one thing, despite the fact that it is popular to research the minimization of the power losses in power systems, the optimization of single objective seems insufficient to fully improve the performance of power systems. Multi-objective VAR Dispatch (MVARD) generally minimizes two objectives simultaneously: power losses and voltage deviation. The purpose of this paper is to propose Multi-Objective Enhanced PSO (MOEPSO) algorithm that achieves a good performance when applied to solve MVARD problem. Thus, the new algorithm is worthwhile to be known by the public. Design/methodology/approach – Motivated by differential evolution algorithm, cross-over operator is introduced to increase particle diversity and reinforce global searching capacity in conventional PSO. In addition to that, a constraint-handling approach considering Constrain-prior Pareto-Dominance (CPD) is presented to handle the inequality constraints on dependent variables. Constrain-prior Nondominated Sorting (CNS) and crowding distance methods are considered to maintain well-distributed Pareto optimal solutions. The method combining CPD approach, CNS technique, and cross-over operator is called the MOEPSO method. Findings – The IEEE 30 node and IEEE 57 node on power systems have been used to examine and test the presented method. The simulation results show the MOEPSO method can achieve lower power losses, smaller voltage deviation, and better-distributed Pareto optimal solutions comparing with the Multi-Objective PSO approach. Originality/value – The most original parts include: the presented MOEPSO algorithm, the CPD approach that is used to handle constraints on dependent variables, and the CNS method which is considered to maintain a well-distributed Pareto optimal solutions. The performance of the proposed algorithm successfully reflects the value of this paper. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to perform an optimal design of a single-phase permanent magnet brushless DC motor (SPBLDCM) by using efficiency of the motor as an objective function. In the design procedure of the motor, a cuckoo search (CS) algorithm is used as an optimization tool.Design/methodology/approach For the purpose of this research work, a computer program for optimal design of electrical machines based on the CS optimization has been developed. Based on the design characteristics of SPBLDCM, some of the motor parameters are chosen to be constant and others variable. A comparative analysis of the initial motor model and the CS model based on the value of the objective function, as well as the values of the optimization parameters, is performed and presented.Findings Based on the comparative data analysis of both motor models, it can be concluded that the main objective of the optimization is realized, and it is achieved by an improvement of the efficiency of the motor.Practical implications The optimal design approach of SPBLDCM presented in this research work can be also implemented on other electrical machines and devices using the same or even other objective functions.Originality/value An optimization technique using CS as an optimization tool has been developed and applied in the design procedure of SPBLDCM. According to the results, it can be concluded that the CS algorithm is a suitable tool for design optimization of SPBLDCM and electromagnetic devices in general. The quality of the CS model has been proved through the data analysis of the initial and optimized solution. The quality of the CS solution has been also proved by comparative analysis of the two motor models using FEM as a performance analysis tool. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of distributed control for network systems aiming to achieve optimal steady-state performance. Motivated by recent research on reengineering cyber-physical systems, such as power systems and the Internet, we propose a two-step control retrofit procedure. First, we reformulate the dynamical system as an optimization algorithm to solve a certain optimization problem. Second, we combine a predefined steady-state optimization problem and the reformulated problem to systematically (re)design the control. As a result, the system automatically tracks the optimal solution of the predefined steady-state optimization problem and the control scheme can be implemented in a distributed and closed-loop manner. In order to investigate how general this framework is, we establish necessary and sufficient conditions under which a linear dynamical system can be viewed as an optimization algorithm. These conditions are characterized using properties of system matrices and related linear matrix inequalities. A practical example of frequency control in power systems shows the effectiveness of the proposed framework. [ABSTRACT FROM PUBLISHER]

Purpose: Purpose of this paper are Real power loss reduction, voltage stability enhancement and minimization of Voltage deviation. Design/methodology/approach: In HLG approach as per Henry gas law sum of gas dissolved in the liquid is directly proportional to the partial pressure on above the liquid. Gas dissolving in the liquid which based on Henry gas law is main concept to formulate the proposed algorithm. Populations are divided into groups and all the groups possess the similar Henry constant value. Exploration and exploitation has been balanced effectively. Ranking and position of the worst agents is done in order to avoid the local optima. Then in this work Mobula alfredi optimization (MAO) algorithm is projected to solve optimal reactive power problem. Foraging actions of Mobula alfredi has been imitated to design the algorithm. String foraging, twister foraging and backward roll foraging are mathematically formulated to solve the problem. In the entire exploration space the Mobula alfredi has been forced to discover new regions by assigning capricious position. Through this approach, exploration competence of the algorithm has been improved. In all iterations, the position of the Mobula alfredi has been updated and replaced with the most excellent solution found so far. Exploration and exploitation capabilities have been maintained sequentially. Then in this work balanced condition algorithm (BCA) is projected to solve optimal reactive power problem. Proposed BCA approach based on the conception in physics- on the subject of the mass; incoming, exit and producing in the control volume. Preliminary population has been created based on the dimensions and number of particles and it initialized capriciously in the exploration space with minimum and maximum concentration. Production control parameter and Production probability utilized to control the exploration and exploitation. Findings: Proposed Henry's Law based -soluble gas optimization (HLG) algorithm, Mobula alfredi optimization (MAO) algorithm and BCA are evaluated in IEEE 30 bus system with L-index (Voltage stability) and also tested in standard IEEE 14, 30, 57, 118, 300 bus test systems without L- index. Real power loss minimization, voltage deviation minimization, and voltage stability index enhancement has been attained. Originality/value: For the first time Henry's Law based -soluble gas optimization (HLG) algorithm, Mobula alfredi optimization (MAO) algorithm and BCA is projected to solve the power loss reduction problem. [ABSTRACT FROM AUTHOR]

Several sparsity-constrained algorithms, such as orthogonal matching pursuit (OMP) or the Frank–Wolfe (FW) algorithm, with sparsity constraints work by iteratively selecting a novel atom to add to the current nonzero set of variables. This selection step is usually performed by computing the gradient and then by looking for the gradient component with maximal absolute entry. This step can be computationally expensive especially for large-scale and high-dimensional data. In this paper, we aim at accelerating these sparsity-constrained optimization algorithms by exploiting the key observation that, for these algorithms to work, one only needs the coordinate of the gradient’s top entry. Hence, we introduce algorithms based on greedy methods and randomization approaches that aim at cheaply estimating the gradient and its top entry. Another of our contribution is to cast the problem of finding the best gradient entry as a best-arm identification in a multiarmed bandit problem. Owing to this novel insight, we are able to provide a bandit-based algorithm that directly estimates the top entry in a very efficient way. Theoretical observations stating that the resulting inexact FW or OMP algorithms act, with high probability, similar to their exact versions are also given. We have carried out several experiments showing that the greedy deterministic and the bandit approaches we propose can achieve an acceleration of an order of magnitude while being as efficient as the exact gradient when used in algorithms, such as OMP, FW, or CoSaMP. [ABSTRACT FROM PUBLISHER]

Purpose – The purpose of this paper is to propose a hybrid-simulated annealing algorithm to address the lacunas in production logistics. The primary focus is laid on the basic understanding of the critical quandary occurring in production logistics, and subsequently research attempts are undertaken to resolve the issue by developing a hybrid algorithm. A logistics problem associated with a flow shop (FS) having a string of jobs which need to be scheduled on m number of machines is considered. Design/methodology/approach – An attempt is made here to introduce and further establish a hybrid-simulated annealing algorithm (NEHSAO) with a new scheme for neighbourhood solutions generation, outside inverse (OINV). The competence in terms of performance of the proposed algorithm is enhanced by incorporating a fast polynomial algorithm, NEH, which provides the initial seed. Additionally, a new cooling scheme (Ex-Log) is employed to enhance the capacity of the algorithm. The algorithm is tested on the benchmark problems of Carlier and Reeves and subsequently validated against other algorithms reported in related literature. Findings – It is clearly observed that the performance of the proposed algorithm is far superior in most of the cases when compared to the other conventionally used algorithms. The proposed algorithm is then employed to a FS under dynamic conditions of machine breakdown, followed by formulation of three cases and finally identification of the best condition for scheduling under dynamic conditions. Originality/value – This paper proposes an hybrid algorithm to reduce makespan. Practical implementation of this algorithm in industries would lower the makespan and help the organisation to increse their profit [ABSTRACT FROM AUTHOR]

Purpose – As arc suppression coils (ASCs), magnetically controlled reactors (MCRs) are usually operated in the single-phase mode. Due to the lack of a third order harmonic compensation circuit, the current harmonics are high. The purpose of this paper is to propose a novel structure of MCR and a genetic algorithm (GA) to determine the parameters which will result in minimum total harmonics. Design/methodology/approach – This paper proposes the structure and the working principle of the multi-valve controlled saturable reactor (MCSR). There are several sorts of magnetic valves in the iron cores of the MCSR. The saturation degree of each magnetic valve is different when the same direct component of the magnetic flux is generated in the iron core, therefore current harmonics of different phases emerging, i.e. the total harmonics can be reduced. The magnetization characteristics and the mathematical model of the current harmonics of the MCSR are presented by introducing three parameters. The optimal values of the parameters that result in the smallest total harmonic distortion in the output current are calculated by a GA. Findings – The simulation and experimental results are coincident with the theoretical analyses, which prove the effectiveness of the proposed method on harmonic suppression. Practical implications – The method proposed in this paper can successfully reduce the current harmonics of the conventional MCR, including but not limited to the ASC. A prototype MCSR (540 kVA/10 kV) has been designed and constructed. Originality/value – In this paper, a MCSR is proposed. The mathematical model of the MCSR for harmonic analysis is developed. The optimal parameters that result in the smallest THD in the output current are calculated. The mathematical model can be also used for the harmonic analysis of conventional MCRs. [ABSTRACT FROM AUTHOR]

The recent literature indicates that preserving global pairwise sample similarity is of great importance for feature selection and that many existing selection criteria essentially work in this way. In this paper, we argue that besides global pairwise sample similarity, the local geometric structure of data is also critical and that these two factors play different roles in different learning scenarios. In order to show this, we propose a global and local structure preservation framework for feature selection (GLSPFS) which integrates both global pairwise sample similarity and local geometric data structure to conduct feature selection. To demonstrate the generality of our framework, we employ methods that are well known in the literature to model the local geometric data structure and develop three specific GLSPFS-based feature selection algorithms. Also, we develop an efficient optimization algorithm with proven global convergence to solve the resulting feature selection problem. A comprehensive experimental study is then conducted in order to compare our feature selection algorithms with many state-of-the-art ones in supervised, unsupervised, and semisupervised learning scenarios. The result indicates that: 1) our framework consistently achieves statistically significant improvement in selection performance when compared with the currently used algorithms; 2) in supervised and semisupervised learning scenarios, preserving global pairwise similarity is more important than preserving local geometric data structure; 3) in the unsupervised scenario, preserving local geometric data structure becomes clearly more important; and 4) the best feature selection performance is always obtained when the two factors are appropriately integrated. In summary, this paper not only validates the advantages of the proposed GLSPFS framework but also gains more insight into the information to be preserved in different feature selection tasks. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to show with the help widely used analytical and application-oriented benchmark problems that a novel and relatively uncommon optimization method, lambda optimization, can be successfully applied to the solution of optimization problems in electromagnetics. Furthermore an improvement to the method is proposed and its effectiveness is validated. Design/methodology/approach – An adaptive probability factor is used within the framework of lambda optimization. Findings – It is shown that in the framework of lambda optimization (LO) the use of an adaptive probability factor can provide high-quality solutions with small standard deviation on the selected benchmark problem. Research limitations/implications – Although the chosen benchmarks are considered to be representative of typical electromagnetic problems, different test cases may give less satisfactory results. Practical implications – The proposed approach appears to be an efficient general purpose stochastic optimizer for electromagnetic design problems. Originality/value – This paper introduces and validates the use of adaptive probability factor in order to improve the balance between the explorative and exploitative characteristics of the LO algorithm. [ABSTRACT FROM AUTHOR]

• In this paper, proposing a novel design of DE for Knapsack problems is reported. • A dual representation of solutions in continuous and binary is introduced. • New efficient fitness evaluation and repairing method is proposed. • Results demonstrated the efficiency of Novel DE in solving Knapsack problems. • Novel DE defined new solutions, better than best-known ones for 5 large instances. The capability of the conventional differential evolution algorithm to solve optimization problems in continuous spaces has been well demonstrated and documented in the literature. However, differential evolution has been commonly considered inapplicable for several binary/permutation-based real-world problems because of its arithmetic reproduction operator. Moreover, many limitations of the standard differential evolution algorithm, such as slow convergence and becoming trapped in local optima, have been defined. In this paper, a novel technique which makes a simple differential evolution algorithm suitable and very effective for solving binary-based problems, such as binary knapsack ones, is proposed. It incorporates new components, such as representations of solutions, a mapping method and a diversity technique. Also, a new efficient fitness evaluation approach for calculating and, at the same time, repairing knapsack candidate solutions, is introduced. To assess the performance of this new algorithm, four datasets with a total of 44 instances of binary knapsack problems are considered. Its performance and those of 22 state-of-the-art algorithms are compared, with the experimental results demonstrating its superiority in terms of both the quality of solutions and computational times. It is also capable of finding new solutions which are better than the current best ones for five large knapsack problems. [ABSTRACT FROM AUTHOR]

Purpose – To improve the performance of the krill herd (KH) algorithm, in this paper, a series of chaotic particle-swarm krill herd (CPKH) algorithms are proposed for solving optimization tasks within limited time requirements. The paper aims to discuss these issues. Design/methodology/approach – In CPKH, chaos sequence is introduced into the KH algorithm so as to further enhance its global search ability. Findings – This new method can accelerate the global convergence speed while preserving the strong robustness of the basic KH. Originality/value – Here, 32 different benchmarks and a gear train design problem are applied to tune the three main movements of the krill in CPKH method. It has been demonstrated that, in most cases, CPKH with an appropriate chaotic map performs superiorly to, or at least highly competitively with, the standard KH and other population-based optimization methods. [ABSTRACT FROM AUTHOR]

Purpose – The change in the way of active power filters (APF) location can lead to overall cost reduction due to less number or less power of APFs required. The goal of this paper was to minimize the APF currents what is equivalent to solution with less apparent power of installed devices. The next step consists in development of new methods of APF optimal location. Design/methodology/approach – Some scripts integrating optimization and harmonic analysis methods in Matlab and PCFLO software environments have been developed in order to achieve the goal. Findings – Solution to the minimization problem determines the current spectrum of an APF connected to a selected system bus in accordance with some optimization strategies which among others enable minimization of THDV coefficients. Research limitations/implications – The APF control algorithm defined in the frequency domain and based on given current spectrum could lead to some problems with synchronization between APF instantaneous current and compensated current waveforms. Originality/value – There are many papers on APFs but usually systems in which an APF is connected near a nonlinear load are analyzed. Some attempts to solve the more complex problems of synchronized multipoint compensation have been already made but there is still no generally accepted and commonly used solution. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to attempt to realize the optimization of cascading failure process of urban transit network based on Load-Capacity model, for better evaluating and improving the operation of transit network. Design/methodology/approach – Robustness is an essential index of stability performance for urban transit systems. In this paper, firstly, the static robustness of transit networks is analyzed based on the complex networks theory. Aiming at random and intentional attack, a concrete algorithm process is proposed on the basis of Dijstra algorithm. Then, the dynamic robustness of the networks, namely cascading failure, is analyzed, and the algorithm process is presented based on the Load-Capacity model. Finally, the space-of-stations is adopted to build the network topology of Foshan transit network, and then the simulation analyses of static and dynamic robustness are realized. Findings – Results show that transit network is robust to random attack when considering static robustness, but somewhat vulnerable to intentional attack. For dynamic robustness analysis, a large-scale cascade of transit network may be triggered when the tolerance parameter α is less than a value, so that the robustness of transit network can be improved through some reasonable measures. Practice implications – The results of this study provide useful information for urban transit network robustness optimization. Originality/value – An effective method for analyzing the static and dynamic robustness of transit network is provided in this paper. [ABSTRACT FROM AUTHOR]

This note presents further results based on the recent paper [J. Liang, H. Chen, and J. Lam, “An improved criterion for controllability of Boolean control networks,” IEEE Trans. Autom. Control, vol. 62, no. 11, pp. 6012–6018, Nov. 2017]. After some optimizations, the conventional method can be more efficient than the method used in the above paper. We also propose an improved method via combining the well known Tarjan's algorithm and depth-first search technique for the controllability analysis of Boolean control networks (BCNs). As a result, the computational complexity will not exceed $O(N^2)$ with $N=2^n$ , where $n$ is the number of state-variables in a BCN. [ABSTRACT FROM AUTHOR]

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

Nonbinary low-density parity-check (NB-LDPC) codes constructed over GF(q) (q>2) can achieve higher coding gain than binary LDPC codes when the code length is moderate. A complete partial-parallel decoder architecture based on the Min-max algorithm is proposed for quasi-cyclic NB-LDPC codes in this paper. A novel scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In our design, layered decoding is applied and only nm

In this paper, the distributed constrained optimization problem over a directed graph is considered. We assume that the digraph has a row-stochastic adjacency matrix, which corresponds to the case when agents assign weights to the received information individually. We present an algorithm that converges to the optimal solution even with a time-varying stepsize which is not attenuated to zero. The choice of stepsizes is relatively easy. The usable type of stepsizes is added. The diminishing or constant stepsizes can be used in our algorithm. Equality constraints and set constraints are also considered in this paper. Convergence analysis of the proposed algorithm relies on a conversion theorem between column-stochastic and row-stochastic matrices. Finally, the results of the numerical simulation are provided to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a novel method to compute the distance to instability for linear time-invariant delay systems with multiple delays, subjected to combined uncertainties on the system matrices and the delay parameters. The method is able to fully exploit structure and possible interdependencies between the uncertainties affecting the coefficient matrices, the property that realistic perturbations are real valued, and the structure of the delay equation. The resulting algorithm relies on a characterization in terms of the pseudospectral abscissa and on techniques from optimization over manifolds of matrices. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push-sum algorithms to such random scenarios. Provided that an ergodicity notion, which we term the directed infinite flow property, holds and the auxiliary states of agents are uniformly bounded away from zero infinitely often, we prove the almost sure convergence of the evolutions of this class of algorithms to the average of initial states. Moreover, for a random sequence of graphs generated using a so-called time-varying $B$ -irreducible probability matrix, we establish convergence rates for the proposed push-sum algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of observers and dynamic output-feedback controllers for positive linear systems with interval uncertainties. The continuous-time case and the discrete-time case are both treated in a unified linear matrix inequality (LMI) framework. Necessary and sufficient conditions for the existence of positive observers with general structure are established, and the desired observer matrices can be constructed easily through the solutions of LMIs. An optimization algorithm to the error dynamics is also given. Furthermore, the problem of positive stabilization by dynamic output-feedback controllers is investigated. It is revealed that an unstable positive system cannot be positively stabilized by a certain dynamic output-feedback controller without taking the positivity of the error signals into account. When the positivity of the error signals is considered, an LMI-based synthesis approach is provided to design the stabilizing controllers. Unlike other conditions which may require structural decomposition of positive matrices, all proposed conditions in this paper are expressed in terms of the system matrices, and can be verified easily by effective algorithms. Two illustrative examples are provided to show the effectiveness and applicability of the theoretical results. [ABSTRACT FROM AUTHOR]

The strong γk-γcl H∞ stabilization problem is addressed in this paper. Based on the bounded real lemma, an improved sufficient condition on strong H∞, stabilization as well as its dual form is derived, which extends the ARE constraint in the former results into an inequality constraint. Two path-following algorithms are proposed to solve the associated optimization problems with BMI constraints, which lead to full order controllers. A numerical example is presented to demonstrate the effectiveness of the result. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new approach to the theory of finite multichain Markov decision processes (MDPs) with different performance optimization criteria. We first propose the concept of nth-order bias; then, using the average reward and bias difference formulas derived in this paper, we develop an optimization theory for finite MDPs that covers a complete spectrum from average optimality, bias optimality, to all high-order bias optimality, in a unified way. The approach is simple, direct, natural, and intuitive; it depends neither on Laurent series expansion nor on discounted MDPs. We also propose one-phase policy iteration algorithms for bias and high-order bias optimal policies, which are more efficient than the two-phase algorithms in the literature. Furthermore, we derive high-order bias optimality equations. This research is a part of our effort in developing sensitivity-based learning and optimization theory. [ABSTRACT FROM AUTHOR]

In this paper, a novel optimization technique is proposed to optimize filter coefficients of linear phase finite-impulse response (FIR) filter to share common subexpressions within and among coefficients. Existing approaches of common subexpression elimination optimize digital filters in two stages: first, an FIR filter is designed in a discrete space such as finite wordlength space or signed power-of-two (SPT) space to meet a given specification; in the second stage, an optimization algorithm is applied on the discrete coefficients to find and eliminate the common subexpressions. Such a two-stage optimization technique suffers from the problem that the search space in the second stage is limited by the finite wordlength or SPT coefficients obtained in the first stage optimization. The new proposed algorithm overcomes this problem by optimizing the filter coefficients directly in subexpression space for a given specification. Numerical examples of benchmark filters show that the required number of adders obtained using the proposed algorithm is much less than those obtained using two-stage optimization approaches. [ABSTRACT FROM AUTHOR]

Designing optimal Perfect reconstruction (PR) and near PR (NPR) cosine-modulated filter banks is essentially a constrained nonlinear minimization problem. This paper proposes two seconds order cone programming based algorithms for designing NPR and practically PR cosine modulated filter banks with improved performance relative to several established design methods. In essence, the design of a cosine-modulated filter bank is a nonconvex constrained optimization problem. The focus of this paper is primarily on developing two new optimization algorithms that are tailored to the time-domain formulation set forth in so as to obtain improved designs relative to several existing methods.

In evolutionary multiobjective optimization, effectiveness refers to how an evolutionary algorithm performs in terms of converging its solutions into the Pareto front and also diversifying them over the front. This is not an easy job, particularly for optimization problems with more than three objectives, dubbed many-objective optimization problems. In such problems, classic Pareto-based algorithms fail to provide sufficient selection pressure towards the Pareto front, whilst recently developed algorithms, such as decomposition-based ones, may struggle to maintain a set of well-distributed solutions on certain problems (e.g., those with irregular Pareto fronts). Another issue in some many-objective optimizers is rapidly increasing computational requirement with the number of objectives, such as hypervolume-based algorithms and shift-based density estimation (SDE) methods. In this paper, we aim to address this problem and develop an effective and efficient evolutionary algorithm (E3A) that can handle various many-objective problems. In E3A, inspired by SDE, a novel population maintenance method is proposed to select high-quality solutions in the environmental selection procedure. We conduct extensive experiments and show that E3A performs better than 11 state-of-the-art many-objective evolutionary algorithms in quickly finding a set of well-converged and well-diversified solutions. [ABSTRACT FROM AUTHOR]

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation-based dimensionality reduction method linear discriminant analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through \ell 2,1 -norm regularization to achieve feature selection, and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously. The formulation is extended to the \ell 2,p -norm regularized case, which is more likely to offer better sparsity when $0

This paper considers a class of stochastic source-seeking problems to drive a mobile robot to the minimizer of a source signal. Our approach is first analyzed in an obstacle-free scenario, where measurements of the signal at the robot location and information of a contact sensor are required. We extend our results to environments with obstacles under mild assumptions on the step size. Our approach builds on the simultaneous perturbation stochastic approximation idea to obtain information of the signal field. We prove the practical convergence of the algorithms to a ball whose size depends on the step size that contains the location of the source. The novelty relies in that we consider nondifferentiable convex functions, a fixed step size, and the environment may contain obstacles. Our proof methods employ nonsmooth Lyapunov function theory, tools from convex analysis, and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithms in a two-dimensional scenarios. [ABSTRACT FROM AUTHOR]

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch–Kuhn–Tucker condition. By using tools from nonsmooth analysis and set-valued function theory, it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper considers the problem of a leader that seeks to optimally influence the opinions of agents in a directed network through connecting with a limited number of the agents (“direct followers”), possibly in the presence of a fixed competing leader. The settings involving a single leader and two competing leaders are unified into a general combinatoric optimization problem, for which two heuristic approaches are developed. The first approach is based on a convex relaxation scheme, possibly in combination with the $\ell _1$ -norm regularization technique, and the second is based on a greedy selection strategy. The main technical novelties of this work are in the establishment of supermodularity of the objective function and convexity of its continuous relaxation. The greedy approach is guaranteed to have a lower bound on the approximation ratio sharper than $(1-1/e)$ , while the convex approach can benefit from efficient (customized) numerical solvers to have practically comparable solutions possibly with faster computation times. The two approaches can be combined to provide improved results. In numerical examples, the approximation ratio can be made to reach ${\text{90}\%}$ or higher depending on the number of direct followers. [ABSTRACT FROM AUTHOR]

Single-layer feedforward networks (SLFNs) have been proven to be a universal approximator when all the parameters are allowed to be adjustable. It is widely used in classification and regression problems. The SLFN learning involves two tasks: determining network size and training the parameters. Most current algorithms could not be satisfactory to both sides. Some algorithms focused on construction and only tuned part of the parameters, which may not be able to achieve a compact network. Other gradient-based optimization algorithms focused on parameters tuning while the network size has to be preset by the user. Therefore, trial-and-error approach has to be used to search the optimal network size. Because results of each trial cannot be reused in another trial, it costs much computation. In this paper, a hybrid constructive (HC)algorithm is proposed for SLFN learning, which can train all the parameters and determine the network size simultaneously. At first, by combining Levenberg–Marquardt algorithm and least-square method, a hybrid algorithm is presented for training SLFN with fixed network size. Then,with the hybrid algorithm, an incremental constructive scheme is proposed. A new randomly initialized neuron is added each time when the training entrapped into local minima. Because the training continued on previous results after adding new neurons, the proposed HC algorithm works efficiently. Several practical problems were given for comparison with other popular algorithms. The experimental results demonstrated that the HC algorithm worked more efficiently than those optimization methods with trial and error, and could achieve much more compact SLFN than those construction algorithms. [ABSTRACT FROM PUBLISHER]