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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]

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]

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 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]

• 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]

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]

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]

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]

This paper proposes a distributed model predictive control (MPC) approach for a family of discrete-time linear systems with local (uncoupled) and global (coupled) constraints. The proposed approach is based on the dual problem of an overall MPC optimization problem involving all systems, which is then solved distributively using a modified distributed Nesterov-accelerated-gradient algorithm. To further reduce the computational requirement, this approach allows for early termination of the distributed gradient algorithm. This is made possible via a consensus algorithm that determines the satisfaction of the termination condition and by appropriate tightening of the coupled constraints. Under reasonable assumptions, the approach is able to produce a suboptimal solution as long as the network of the systems is connected while ensuring recursive feasibility and exponential stability of the closed-loop system. The performance of the proposed approach is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

Several optimization-based control design techniques can be cast in the form of parametric optimization problems. The multiparametric quadratic programming (mpQP) represents a popular class often related to the control of constrained linear systems. The complete solution to mpQP takes the form of explicit feedback functions with a piecewise affine structure, valid in polyhedral partitions of the feasible parameter space known as critical regions. The recently proposed combinatorial approach for solving mpQP has shown better efficiency than geometric approaches in finding the complete solution to problems with high dimensions of the parameter vectors. The drawback of this method, on the other hand, is that it tends to become very slow as the number of constraints increases in the problem. This paper presents an alternative method for enumerating all optimal active sets in an mpQP based on theoretical properties of adjacent critical regions and their corresponding optimal active sets. Consequently, it results in excluding a noticeable number of feasible but not optimal candidate active sets from investigation. Therefore, the number of linear programs that should be solved decreases noticeably and the algorithm becomes faster. Simulation results confirm the reliability of the suggested method in finding the complete solution to the mpQPs while decreasing the computational time compared favorably with the best alternative approaches. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has recently become a very popular unsupervised learning method because of its representational properties of factors and simple multiplicative update algorithms for solving the NMF. However, for the common NMF approach of minimizing the Euclidean distance between approximate and true values, the convergence of multiplicative update algorithms has not been well resolved. This paper first discusses the convergence of existing multiplicative update algorithms. We then propose a new multiplicative update algorithm for minimizing the Euclidean distance between approximate and true values. Based on the optimization principle and the auxiliary function method, we prove that our new algorithm not only converges to a stationary point, but also does faster than existing ones. To verify our theoretical results, the experiments on three data sets have been conducted by comparing our proposed algorithm with other existing methods. [ABSTRACT FROM AUTHOR]

Distributed optimization algorithms have the advantages of privacy protection and parallel computing. However, the distributed nature of these algorithms makes the system vulnerable to external attacks. This paper presents two penalty function based resilient algorithms for constrained distributed optimization under static and dynamic attacks. The objective function of the optimization problem is extended to nonsmooth ones and the convergence of the proposed algorithms in this case are proved under some mild conditions. Simulation experiments are performed and compared with some existing resilient primal-dual optimization algorithms using median-based mean estimator. For static attack, the proposed algorithm has better performance and faster convergence rate in the simulation experiments. For dynamic attack, the proposed algorithm has better performance and robustness in the simulation experiments, which illustrate that the proposed algorithms are more effective. [ABSTRACT FROM AUTHOR]

Data clustering is one of the most common and challenging problems in the machine learning domain. It requires an efficient method to be addressed. This paper proposed a new version of the Flow Direction Algorithm (FDA) to solve various optimization problems. The proposed method is called FDAOA, which enhanced the performance of the original Flow Direction Algorithm by the arithmetic operators that have been used in the Arithmetic Optimization Algorithm (AOA). The main aim of the proposed FDAOA is to avoid the recognized weaknesses in the original methods; stuck in the local area, premature convergence, and weak equilibrium between the exploration and exploitation search mechanisms. The proposed method is tested on two sets of various problems to validate its performance. In the first set, twenty-three benchmark functions are used, which belong to three categories; seven unimodal functions, six multimodal functions, and ten fixed dimension functions. In the second set, eight common data clustering problems are used to prove the ability of the proposed FDAOA to deal with real-world optimization problems. The results of the proposed method are compared with other well-established methods, and the proposed FDAOA achieved promising output compared to the other methods on various tested problems. The proposed method got the optimal clustering solutions almost in all the tested data clustering problems with clear significant improvements against the other comparative methods. [ABSTRACT FROM AUTHOR]

Purpose The aim of this paper is to explore the potential of particle swarm optimization (PSO) algorithm to solve an electromagnetic inverse problem.Design/methodology/approach A modified PSO algorithm is designed.Findings The modified PSO algorithm is a more stable, robust and efficient global optimizer for solving the well-known benchmark optimization problems. The new mutation approach preserves the diversity of the population, whereas the proposed dynamic and adaptive parameters maintain a good balance between the exploration and exploitation searches. The numerically experimental results of two case studies demonstrate the merits of the proposed algorithm.Originality/value Some improvements, such as the design of a new global mutation mechanism and introducing a novel strategy for learning and control parameters, are proposed. [ABSTRACT FROM AUTHOR]

In conventional sparse Space-Time Adaptive Processing (STAP) algorithms, the l 0 -norm is often used instead of the l 1 -norm to relax convexity constraints. The approach presented in this paper can be mathematically reformulated as a linear problem, which can be efficiently solved using various convex optimization techniques. While this method effectively circumvents the NP-Hard complexity associated with the l 0 -norm, it does come with certain potential challenges. For example, the observation matrix must meet the criteria of the Restricted Isometry Property (RIP) and other stringent conditions. In this research, a novel STAP algorithm is introduced, which is based on a non-convex penalty function. This innovative algorithm substitutes the traditional l 0 -norm with a custom-designed non-convex penalty function and is applied to the Direct Filter Processor (DFP), solved using the recursive least squares (RLS) algorithm. The resulting algorithm, known as g p -RLS, is demonstrated through Monte Carlo simulations to outperform other l 1 -based and reduced-rank STAP algorithms in terms of faster convergence, improved signal-to-clutter-plus-noise ratio (SCNR), and enhanced target detection performance. [ABSTRACT FROM AUTHOR]

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

• A supervised multi-view model is proposed to realize a block-based feature selection. • The proposed model is composed of all sharing sub-models in each class. • The sparse regularizer can enhance the sparsity of blocks from features and views. • The proposed algorithm can realize the block separation and independent solution. • Numerical experiments show the effectiveness of our method on large-scale datasets. With the increasing scale of obtained multi-view data, how to deal with large-scale multi-view data quickly and efficiently is a significant problem. In this paper, a novel supervised multi-view feature selection method based on locally sparse regularization and block computing is proposed to solve the problem. Specifically, the multi-view dataset is firstly divided into sub-blocks according to classes and views. Then with the aid of the Alternating Direction Method of Multipliers (ADMM), a sharing sub-model is proposed to perform feature selection on each class by integrating each view's locally sparse regularizers and shared loss that makes all views share a common penalty and regresses samples to their labels. Finally, all the sharing sub-models are fused to form the final general additive feature selection model, in which each sub-block adjusts its corresponding variables to perform block-based feature selection. In the optimization process, the proposed model can be decomposed into multiple separate subproblems, and an efficient optimization algorithm is proposed to solve them quickly. The comparison experiments with several state-of-the-art feature selection methods show that the proposed method is superior in classification accuracy and training speed. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) is a population-based random-search optimization technique that has become an increasingly important branch of swarm intelligence studies. Population diversity is an effective measurement that shows the distribution of particles in a search space. In this paper, we propose a diversity-based PSO algorithm that is combined with multiple techniques, and population diversity is used as a search-strategy selection criterion for particles. When diversity is high, we suggest implementing a search strategy that has a strong exploration ability. When diversity is low, we suggest implementing a search strategy that has a strong exploitation ability. In addition to our diversity-based method, we introduce a gradient-based local-search technique, multi-crossover operation, and disturbance strategy to help improve the performance of the proposed algorithm. In the experiments, we compare the proposed algorithm with 10 advanced PSO variants based on 40 widely used benchmark functions, including the CEC2017 benchmark. The results indicate that the proposed algorithm yields a better solution accuracy and convergence speed than those of other PSO variants. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the online convex optimization (OCO) with long-term constraints which is widely used in various resource allocations and recommendation systems. Different from the most existing works, our work adopts a dynamic benchmark to analyze the optimization performance since the dynamic benchmark is more common than the static benchmark in practical applications. Moreover, compared with many constrained OCO works ignoring the Slater condition, we study the effect of the Slater condition on the constraint violation bounds and obtain the better performance of the constraint violations when the Slater condition holds. More importantly, we propose a novel iterative optimization algorithm based on the virtual queues to achieve sublinear regret and constraint violations. Finally, we apply our dynamic OCO model to a resource allocation problem in cloud computing and the results of the experiments validate the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

• The concept and verification method of affine invariance are presented. • Six algorithms are employed to analyze their affine invariances. • PSO, OFA and DE are affine invariant, GWO, SCA and BOA are not affine invariant. • Multiple experimental comparisons are executed to verify algorithms' affine invariance. An algorithm whose performance depends on the objective function being aligned with a privileged coordinate system is a poor choice in general because it is unlikely that the optimal orientation will be known in advance. In this paper, a property of meta -heuristic algorithms, named affine invariance, is introduced to verify whether the algorithm is depended on the privileged coordinate system or not. The concept of affine invariance is described in detail, and some classical algorithms, efficient in most test and actual problems, are proved to be affine invariant. While some recent algorithms in the literature are proved to be not affine invariant. As a conclusion, particle swarm optimization (PSO), differential evolution (DE) and optimal foraging algorithm (OFA) are affine invariant, while grey wolf optimizer (GWO), sine cosine algorithm (SCA) and butterfly optimization algorithm (BOA) are not affine invariant. Furthermore, comparison tests are designed to support the theoretical analysis results. In these tests, same random numbers and initial population are used to avoid the influence of randomness, thus, the conclusion is reliable. [ABSTRACT FROM AUTHOR]

• A new algorithm, called BTLBO, is proposed to balance between exploration and exploitation. • A new Tutoring Phase is added to TLBO to accelerate the convergence to the global optimum. • A new Restarting Phase is added to TLBO to promote convergence to the global optimum. • Control parameters are self-adaptively tuned. • The superiority of BTLBO is verified by solving standard benchmarks and real world optimization problems. Teaching-learning-based optimization (TLBO) is a population-based metaheuristic algorithm which simulates the teaching and learning mechanisms in a classroom. The TLBO algorithm has emerged as one of the most efficient and attractive optimization techniques. Even though the TLBO algorithm has an acceptable exploration capability and fast convergence speed, there may be a possibility to converge into a local optimum during solving complex optimization problems and there is a need to keep a balance between exploration and exploitation capabilities. Hence, a Balanced Teaching-Learning-Based Optimization (BTLBO) algorithm is proposed in this paper. The proposed BTLBO algorithm is a modification of the TLBO algorithm and it consists of four phases: (1) Teacher Phase in which a weighted mean is used instead of a mean value for keeping the diversity, (2) Learner Phase, which is same as the learner phase of basic TLBO algorithm, (3) Tutoring Phase, which is a powerful local search for exploiting the regions around the best ever found solution, and (4) Restarting Phase, which improves exploration capability by replacing inactive learners with new randomly initialized learners. An acceptable balance between the exploration and exploitation capabilities is achieved by the proposed BTLBO algorithm. To evaluate the performance of BTLBO algorithm, several experimental studies are conducted on standard benchmark suits and the results are compared with several TLBO variants and state-of-the-art population-based optimization algorithms. The results are in excellent agreement and confirm the efficiency of BTLBO algorithm with accelerated exploitation and exploration capabilities with an appropriate balance between such criteria for solving complex optimization problems. [ABSTRACT FROM AUTHOR]

For many-objective problems, how to maintain the diversity and convergence of the distribution of the solution set over Pareto front (PF) has always been the research emphasis. In the iteration process, the state of population is critical to improve the level of evolution. Therefore, this paper will use two convergence and diversity indicators to further strengthen the usage of evolutionary state information and propose a dynamic learning strategy. In addition, a dynamic learning strategy based many-objective evolutionary algorithm (MaOEA) is proposed, called dynamic learning evolution algorithm (DLEA), which continuously changes the direction of learning: convergence and diversity in the iteration process. The purpose is to make the algorithm prefer to convergence in the early iteration and prefer to diversity when it is close to PF in the late iteration, so that the convergence and diversity of the final solution set can be well maintained. And then, the performance of DLEA is measured by two indicators. Meanwhile, DLEA will be compared with four state-of-the-art algorithms on the DTLZ and MaF, and its performance will be verified on a many-objective combinatorial problem. And the experimental results and Friedman test show that DLEA has great advantages. [ABSTRACT FROM AUTHOR]

In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. The objective is to minimize the sum of local time-varying cost functions, each of which is known to only an individual agent, through local interaction. Here, the optimal point is time varying and creates an optimal trajectory. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. In both cases, a centralized approach is first introduced to solve the optimization problem. Then, this problem is solved in a distributed manner and a discontinuous algorithm based on the signum function is proposed in each case. In the case of single-integrator (respectively, double-integrator) dynamics, each agent relies only on its own position and the relative positions (respectively, positions and velocities) between itself and its neighbors. A gain adaption scheme is introduced in both algorithms to eliminate certain global information requirement. To relax the restricted assumption imposed on feasible cost functions, an estimator based algorithm using the signum function is proposed, where each agent uses dynamic average tracking as a tool to estimate the centralized control input. As a tradeoff, the estimator-based algorithm necessitates communication between neighbors. Then, in the case of double-integrator dynamics, the proposed algorithms are further extended. Two continuous algorithms based on, respectively, a time-varying and a fixed boundary layer are proposed as continuous approximations of the signum function. To account for interagent collision for physical agents, a distributed convex optimization problem with swarm tracking behavior is introduced for both single-integrator and double-integrator dynamics. It is shown that the center of the agents tracks the optimal trajectory, the connectivity of the agents is maintained, and interagent collision is avoided. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) are difficult to handle because objectives and constraints need to be considered simultaneously, especially when the constraints are extremely complex. Some recent algorithms work well when dealing with CMOPs with a simple feasible region; however, the effectiveness of most algorithms degrades considerably for CMOPs with complex feasible regions. To address this issue, this paper proposes a multi-stage evolutionary algorithm, where constraints are added one after the other and handled in different stages of evolution. Specifically, in the early stages, the algorithm only considers a small number of constraints, which can make the population efficiently converge to the potential feasible region with good diversity. As the algorithm moves to the later stages, more constraints are considered to search the optimal solutions based on the solutions obtained in the previous stages. Furthermore, a strategy for sorting the constraint-handling priority according to the impact on the unconstrained Pareto front is proposed, which can accelerate the convergence of the algorithm. Experimental results on five benchmark suites and three real-world applications showed that the proposed algorithm outperforms several state-of-the-art constraint multi-objective evolutionary algorithms when dealing with CMOPs, especially for problems with complex constraints. [ABSTRACT FROM AUTHOR]

This paper presents a new fractal search space decomposition-based algorithm to address the issue of scaling up the divide and conquer approach to deal with large scale problems (up to 50 continuous decision variables). The proposed algorithm, called polyFrac, fractally decomposes the search space using hyper-polytopes. It allows moving throughout different granularity levels by only computing the average of vertices of a hyper-polytope to obtain the coordinates of the centroids. Only the most promising hyper-polytopes are decomposed into child-polytopes. Then, a simple deterministic local search (single solution-based metaheuristic) is used to perform the intensification process to find the best solution within the selected lowest hyper-polytope. The proposed algorithm performance is evaluated on the well-known SOCO 2011, CEC 2013, and CEC 2017 benchmarks and compared with 26 states of the art algorithms. A real-world optimization problem is also used to calibrate its performance. The obtained results show that polyFrac outperforms all the algorithms. Moreover, experimental results and analysis suggest that polyFrac is a highly competitive optimization algorithm for solving large-scale and complex optimization problems. [ABSTRACT FROM AUTHOR]