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This paper proposes a novel adaptive range composite differential evolution (ARCoDE) algorithm to efficiently and accurately solve optimal reactive power dispatch (ORPD) problem. Because of a novel adaptive range strategy for control parameters, the proposed ARCoDE possesses superior exploration and exploitation capabilities that can efficiently handle the ORPD problem involving complicated constraints and discrete and continuous variables. This has been demonstrated in case studies using the IEEE optimal power flow testbeds considering complex wind and demand scenarios. The superior performance of ARCoDE has been further validated through comparisons with several award-winning algorithms in 2014 IEEE Competition on “Application of Modern Heuristic Optimization Algorithms for Solving Optimal Power Flow Problems”, given limited iterations of in evolutionary optimization process. Energy Market Authority (EMA) Published version This work was supported in part by the National Key Research and Development Program of China under Grant 2019YFB1505400, and inpart by the Energy Market Authority and National Science Foundation Singapore under Grant NRF2017EWT-EP003-038.

Differential evolution (DE) algorithm has some excellent attributes including strong exploration capability. However, it cannot balance the exploitation with exploration ability in the search process. To enhance the performance of the DE algorithm, this paper proposes a new algorithm named hybrid harmony differential evolution algorithm (HHSDE). The key features of HHSDE algorithm are as follows. First, a new mutation operation is developed for improving the efficiency of mutation, in which the New Harmony generation mechanics of the harmony algorithm (HS) is employed. Second, the harmony memory size is updated with the iteration. Third, a self-adaptive parameter adjustment strategy is presented to control scaling factor. Fourth, a new evaluation method is proposed to effectively assess the algorithm convergence performance. Two classical DE algorithms, HS algorithm, improvement Differential evolution algorithm(ISDE) and Hybrid Artificial Bee Colony algorithm with Differential Evolution(HABCDE) have been tested against HHSDE based on 25 benchmark functions of CEC2005 and the results reveal that the proposed algorithm is better than the other algorithms under consideration.

In this article, the concurrent optimal design of a planar five-bar parallel robot for a high-speed pick and place task is considered. A trade-off between trajectory tracking, energy consumption and deformation of the flexible links is sought. Due to the high-speed operation, the minimization of the vibratory effect is considered since the design stage. Thus, the design is stated as a non-linear multi-objective dynamic optimization problem that is solved through the Differential Evolution (DE) algorithm, as well as, feasibility rules for constraints handling. Mechanical structural variables that modify the inertial parameters of the rigid and flexible links, as well as, control variables related to gains of a PID controller are considered as independent variables. This problem is subject to maximum torque that each motor could provide; inherent constraints for link manufacture; dimensional synthesis; Grashof’s criterion and initial and boundary conditions. Results show that it is possible, despite the vibrational phenomenon, to reduce the energy consumption without loss of precision through an appropriate mass balance of the actuated links.

Due to the computational complexity of multilevel image thresholding, Swarm Intelligence Optimization Algorithm (SIOA) has been widely applied to improve the calculation efficiency. Therefore, more and more attention has been paid to exploring the application of the latest SIOA in multilevel segmentation. This article takes Otsu and fuzzy entropy as the objective functions, using Coyote Optimization Algorithm (COA) for multilevel thresholds optimization selection, through fuzzy median aggregation of local neighborhood information and then forms the Fuzzy Coyote Optimization Algorithm (FCOA), so that the thresholding image segmentation can be achieved in the end. To prevent the COA algorithm from falling into the local optimum, this article follows the differential evolution strategy adopted by the standard COA, using the number of iterations to construct the differential scaling factor to form the Improved Coyote Optimization Algorithm (ICOA). The experimental results show that fuzzy Kapur entropy and fuzzy median value aggregation-based ICOA(FICOA) achieves better image segmentation quality. Compared with Grey Wolf Optimizer (GWO), Fuzzy Modified Quick Artificial Bee Colony and Aggregation Algorithm (FMQABCA) and Fuzzy Modified Discrete Grey Wolf Optimizer and Aggregation Algorithm (FMDGWOA), FCOA and FICOA have certain advantages in visual effects of image segmentation and PSNR, FSIM evaluation indices. Particularly compared with GWO (also a wolf evolutionary algorithm), FICOA shows significant advantages.

In the decomposition-based multiobjective evolutionary algorithms (MOEA/Ds), a set of subproblems are optimized by using the evolutionary search to exploit the feasible regions. In recent studies of MOEA/Ds, it was found that the design of recombination operators would significantly affect their performances. Therefore, this paper proposes a novel genetically hybrid differential evolution strategy (GHDE) for recombination in MOEA/Ds, which works effectively to strengthen the search capability. Inspired by the existing studies of recombination operators in MOEA/Ds, two composite operator pools are introduced, each of which includes two distinct differential evolution (DE) mutation strategies, one emphasizing convergence and the other focusing on diversity. Regarding each selected operator pool, two DEs are applied on parents’ genes to hybridize offspring by adaptive parameters tuning. Moreover, a fitness-rate-rank-based multiarmed bandit (FRRMAB) is embedded into our algorithm to select the best operator pool by collecting their recently achieved fitness improvement rates. After embedding GHDE into an MOEA/D variant with dynamical resource allocation, a variant named MOEA/D-GHDE is presented. Various test multiobjective optimization problems (MOPs), i.e., UF, F test suites, and MOPs with difficult-to-approximate (DtA) PF boundaries, are used to assess performances. Compared to several competitive MOEA/D variants, the comprehensive experiments validate the superiority of our algorithm.

Differential evolution (DE) has been applied to solve complex optimization problems. An effective DE algorithm should be convergent and able to jump out of the local optimal solution. Motivated by these considerations, an improved differential evolution is proposed, which is based on the oppositional solution, elite sharing schemes, the heuristic crossover operator and combined with a self-adaptive parameter setting strategy. The algorithm is denoted as SOSESDE. First, in the early stage of evolution, the disturbance oppositional strategy is applied to the worse individuals to increase the search space since the oppositional search strategy will generate redundant offspring by the same genetic operation, which can be avoided by random perturbation. Then, an elite sharing scheme is used for information exchange. In this scheme, the K-means is first used to divide the present population into several subpopulations, and then, the elitist in each subpopulation is taken for mutation operation. In addition, the related parameters $F$ and $CR$ are self-adaptively adjusted based on the results of the Wilcoxon signed-rank test and the probability that a parent is selected for the next generation. Besides, the heuristic crossover operator is constructed by using uniform design method. Finally, 53 benchmark functions are optimized using SOSESDE, and the results are compared with those of various state-of-the-art algorithms. The experiments show that compared to these algorithms, SOSESDE exhibits better performance.

Data clustering is the process of identifying natural groupings or clusters based on a certain similarity measure in muti-dimensional data. Aiming at the dynamic clustering problem where the number of clusters cannot be determined in advance, a hybrid dynamic clustering method based on the marine predators algorithm (MPA) and particle swarm optimization (PSO) algorithm was proposed. The position update strategy of the PSO algorithm was used to make up for the lack of MPA in global searching. The fixed-length coding strategy with the real number coding method was used to deal with the variable length clustering optimization problem, and the unfeasible solution processing strategy and the penalty function strategy are adopted to improve the performance of the algorithm and achieve simultaneous optimization of the number of clusters and cluster centers. The proposed MPA-PSO algorithm with PSO algorithm, MPA, Differential Evolution (DE) algorithm, Spotted Hyena Optimizer (SHO), Lightning Searching Algorithm (LSA) and Equilibrium Optimizer (EO) are adopted to carry out the clustering simulation experiments on four artificial data sets and six real data sets (Iris, Wine, Wisconsin breast cancer, Vowel, Seeds, and Wdbc) in UCI databases. Three performance indicators (the number of clusters, ARI and Accuracy) are used to evaluate the clustering results. The experimental results show that the proposed method can not only successfully find the correct number of clusters, but also obtain stable results for most test problems.

Seepage monitoring is a vital task in the risk management of concrete dams. Considering the lag effect of input factors, this paper presents a novel seepage monitoring model for concrete dams and proposes an effective identification method of lag process. Firstly, extreme gradient boosting (XGBoost) were adopted to predict the dam seepage. Hybridizing grey wolf optimization (HGWO) which integrates differential evolution (DE) into grey wolf optimization (GWO) and five–fold cross validation were utilized to optimize the hyper–parameters of XGBoost. Secondly, under the same search range and four evaluation indicators, the models optimized respectively by HGWO and three other algorithms were compared to confirm the global optimization capability of HGWO. Six state–of–art methods were also introduced to verify the effectiveness and feasibility of the proposed model. Then, based on the computation method of factor importance in decision tree models, we evaluated the relative importance of each component in the proposed model. Finally, according to the factor importance, the lag process of upstream water level and rainfall was identified, meanwhile a new equivalent water level calculation method is proposed. Monitoring data from three piezometric tubes on a concrete dam were taken as the experimental object. The results show that the improved HGWO has stronger global optimization ability, and the HGWO–XGBoost model achieves satisfactory prediction for seepage in concrete dams. Compared with the traditional trial–and–error method, the lag process computation method proposed in this paper provides a better recognition effect, which is of great value to the seepage monitoring and control of concrete dams.

A fully automated design is proposed in this work employing optimal deep learning features for classifying gastrointestinal infections. Here, three prominent infections– ulcer, bleeding, polyp and a healthy class are considered as class labels. In the initial stage, the contrast is improved by fusing bi-directional histogram equalization with top-hat filtering output. The resultant fusion images are then passed to ResNet101 pre-trained model and trained once again using deep transfer learning. However, there are challenges involved in extracting deep learning features including impertinent information and redundancy. To mitigate this problem, we took advantage of two metaheuristic algorithms– Enhanced Crow Search and Differential Evolution. These algorithms are implemented in parallel to obtain optimal feature vectors. Following this, a maximum correlation-based fusion approach is applied to fuse optimal vectors from the previous step to obtain an enhanced vector. This final vector is given as input to Extreme Learning Machine (ELM) classifier for final classification. The proposed method is evaluated on a combined database. It accomplished an accuracy of 99.46%, which shows significant improvement over preceding techniques and other neural network architectures.

Constrained optimization problems (COPs) are common in many fields, and the search algorithm and constraint handling technique play important roles in the constrained evolution algorithms. In this article, we propose a new optimization algorithm named CETDE based on ensemble differential evolution (DE) and a two-level epsilon-constrained method. In the ensemble DE variant, some promising parameters and mutation strategies constitute the candidate pool, and each element in the pool coexists throughout the search process and competes to generate new solutions. The two-level epsilon method is proposed by incorporating a generation and a population comparison level to retain more promising solutions without degrading the solution quality. Moreover, a diversity promotion scheme is developed to improve the population distribution when the search becomes trapped in a small region. The superior performance of CETDE is validated by comparison with some state-of-the-art COEAs over two sets of artificial benchmarks and five real-world problems. The competitive results show that CETDE is an effective method for solving COPs.

For the split delivery vehicle routing problem in the distribution link of logistics where the optimization objective is to minimize the total distance of the transportation path, a hybrid discrete differential evolution (HDDE) algorithm is adopted in this study. The algorithm applies the encoding and decoding method based on the remaining vehicle capacity to split the demand of customer point and adjust the splitting node to the optimal position of its path. In order to avoid the prematurity of the algorithm, the perturbation mechanism is added, i.e. , the three-point insertion method is used in the crossover stage. To ensure the higher quality of the solution, the idea of tabu search is introduced in three cases: initial population generation, selection operation and local optimal situation. Finally, through the numerical experiments based on benchmark data, the HDDE algorithm is compared with other competitive algorithms to demonstrate its domination.

In today's age of industrialization, sensor devices installed on equipment generate a vast amount of data. One of the engineers' main jobs is utilizing these data to provide better solutions to industrial problems. This availability of extensive data partly led to the creation of predictive maintenance (PdM). In PdM, existing and previous conditions of devices are used to predict their future behavior for optimal maintenance. Most of these PdM approaches are typical time-series predictions. Machine learning tools like Recurrent Neural Networks (RNNs) are excellent tools for time-series predictions. However, most RNNs suffer from training issues due to the unstable gradient problem. Thus, networks such as the Echo State Network (ESN), were designed to solve them. The ESN solves the gradient problem by training only the output weights using simple linear regression. Despite this ease, the selection of ESN parameters and topology is a considerable design challenge. This problem is often formulated as a typical optimization problem. Metaheuristic algorithms are known to be excellent tools for solving optimization problems. Hence, in this work, we design an improved Grasshopper Optimization Algorithm (GOA) based ESN. The proposed technique uses a new solution representation with a simplified attraction and repulsion mechanisms to enhance performance. Our target application is to predict the Remaining Useful Life (RUL) of turbofan engines. The method outperforms the Cuckoo Search (CS), Differential Evolution (DE), Particle Swarm Optimization (PSO), Binary PSO (BPSO), the original GOA, the classical ESN, deep ESN, and LSTM. We have provided all implemented codes and data at the GitHub repository. https://github.com/bala-221/Airplane-fault-prediction.

The state of charge (SOC) estimation of Li-ion batteries has attracted substantial interests in recent years. Kalman Filter has been widely used in real-time battery SOC estimation, however, to build a suitable dynamic battery state-space model is a key challenge, and most existing methods still use the off-line modelling approach. This paper tackles the challenge by proposing a novel sparse learning machine for real-time SOC estimation. This is achieved first by developing a new learning machine based on the traditional least squares support vector machine (LS-SVM) to capture the process dynamics of Li-ion batteries in real-time. The least squares support vector machine is the least squares version of the conventional support vector machines (SVMs) which suffers from low model sparseness. The proposed learning machine reduces the dimension of the projected high dimensional feature space with no loss of input information, leading to improved model sparsity and accuracy. To accelerate computation, mapping functions in the high feature space are selected using a fast recursive method. To further improve the model accuracy, a weighted regularization scheme and the differential evolution (DE) method are used to optimize the parameters. Then, an unscented Kalman filter (UKF) is used for real-time SOC estimation based on the proposed sparse learning machine model. Experimental results on the Federal Urban Drive Schedule (FUDS) test data reveal that the performance of the proposed algorithm is significantly enhanced, where the maximum absolute error is only one sixth of that obtained by the conventional LS-SVMs and the mean square error of the SOC estimations reaches to 10-7, while the proposed method is executed nearly 10 times faster than the conventional LS-SVMs.

Parameters identification of photovoltaic (PV) models based on measured current-voltage characteristics curves is significant for the simulation, evaluation and control of PV systems. To accurately and reliably identify the parameters of different PV models, a novel optimization algorithm, multi-strategy success-history based adaptive differential evolution with linear population size reduction (MLSHADE), is proposed. MLSHADE mainly divides evolutionary process into two phases during every generation. According to the definition of class probability variable, the population individuals of first phase are assigned to different two populations for exploration and exploitation, respectively. The novelty of MLSHADE algorithm lies primarily in three improvements: (i) a new weighted mutation strategy is used to enrich the population diversity of later iterations for differential evolution population in the first phase; (ii) inferior solutions search (ISS) technique is presented to avoid falling into local optimum for covariance matrix adaptation evolution strategy population in the first phase; and (iii) Eigen Gaussian random walk strategy is proposed to help maintain effectively the balance between the global exploration and local exploitation abilities in the second phase. The experiments on CEC 2018 test suite illustrate that the proposed MLSHADE exerts the better performances against the stat-of-the-art algorithms in terms of accuracy, reliability and time consumption. The proposed MLSHADE is used to solve the parameters identification problems of different PV models including single diode, double diode, and PV module. Comprehensive experiment results and analyses indicate that MLSHADE can obtain a highly competitive performance compared with other state-of-the-art algorithms, especially in terms of accuracy and reliability.

Recently, fuel cells (FCs) have found vast employment in several applications. However, unique maximum power point tracking (MPPT) exists for each set of operating condition for the efficient operation of FCs. Therefore, this paper presents a differential evolution optimization algorithm (DEOA)-based optimized fuzzy-logic (OFLC) MPPT method for enhancing the maximum power extraction of FCs. The various settings for the membership functions (MFs) of the input and output variables are optimized in the proposed method. Thence, more degree-of-freedom can be employed for accurate and fast tracking of the optimal power point of the proton exchange membrane FCs (PEMFCs). Whereas, existing MPPT methods in the literature for FC applications suffer from decreased degree-of-freedom for optimizing their performance, and lack of adaptivity, which obstructs their suitability for the wide operating range of FCs. The superiority and performance effectiveness of the proposed OFLC MPPT method have been validated and compared with the most prevalent techniques in the literature. Moreover, the robustness and sensitivity of the proposed OFLC MPPT method have been tested at various step changes in the water content of membrane and various temperature changes. Moreover, the proposed design of the suggested OFLC MPPT is general and it can be implemented on low-cost microcontrollers. The results verify the superior performance of the proposed OFLC MPPT method from the accurate and fast MPPT extraction, smooth output power with low ripple, and simplicity of the design point of views.

Obtaining suitable parameters of photovoltaic models based on measured current-voltage data of the PV system is vital for assessing, controlling, and optimizing photovoltaic systems. To acquire specific parameters of photovoltaic models, we proposed a meta-heuristic algorithm named hybrid symbiotic differential evolution moth-flame optimization (HSDE-MFO) algorithm. The proposed algorithm implements our new proposed symbiotic algorithm structure (SAS). This structure is inspired by soybean-rhizobium nodule symbiosis in nature. The proposed SAS divides the population into two parallel working sub-groups, i.e., soybean group and rhizobium group. Soybean group that focuses on exploration is updated by the strategies in the DE algorithm; the rhizobium group that emphasizes on exploitation is renewed by the strategies in the MFO algorithm. Artificial particle selection strategy and artificial flames generation strategy are developed to generate high-quality mutant materials and high-quality flames, respectively. The above-proposed methods balance the exploration ability and exploitation ability and ensure a bionic structure of the proposed algorithm. Moreover, a new elite strategy is developed to offer a chaotic particle to further refine the quality of the current population. The proposed HSDE-MFO is employed to solve the parameters identification problem of photovoltaic models, i.e., single diode, double diode, and photovoltaic module and compared with recently well-established algorithms. Experimental results indicate that HSDE-MFO can acquire precise parameters of the three photovoltaic models and stable performance in 30 independent runs.

Scheduling of community microgrids (CMGs) is an important and challenging optimization problem. Generally, the optimization is performed to schedule resources of CMGs at minimum cost. In recent years, a number of algorithms have been proposed to solve such problems. However, the performance of these algorithms is far from ideal due to the presence of different complex equality and inequality constraints in CMGs. Furthermore, most of the current works ignore energy storage (ES) degradation costs in the optimization model, which has a significant impact on the life of ES. This paper develops both single and bi-objective optimization models by considering the life of ES along with the operating cost for scheduling a CMG. An efficient heuristic-enhanced Differential Evolution (DE) approach is proposed to solve these models; by exploiting the structure of equality constraints, the proposed heuristic is able to generate feasible solutions quickly. The significance of the proposed heuristic is that it can generate a high-quality solution with a considerably lower computational effort. Numerical simulations were performed to evaluate the performance of the proposed method, and obtained results were compared with the state-of-the-art algorithm. The simulation results corroborate the efficacy of the proposed method.

For the purpose of addressing the multi-objective optimal reactive power dispatch (MORPD) problem, a two-step approach is proposed in this paper. First of all, to ensure the economy and security of the power system, the MORPD model aiming to minimize active power loss and voltage deviation is formulated. And then the two-step approach integrating decision-making into optimization is proposed to solve the model. Specifically speaking, the first step aims to seek the Pareto optimal solutions (POSs) with good distribution by using a multi-objective optimization (MOO) algorithm named classification and Pareto domination based multi-objective evolutionary algorithm (CPSMOEA). Furthermore, the reference Pareto-optimal front is generated to validate the Pareto front obtained using CPSMOEA; in the second step, integrated decision-making by combining fuzzy c-means algorithm (FCM) with grey relation projection method (GRP) aims to extract the best compromise solutions which reflect the preferences of decision-makers from the POSs. Based on the test results on the IEEE 30-bus and IEEE 118-bus test systems, it is demonstrated that the proposed approach not only manages to address the MORPD issue but also outperforms other commonly-used MOO algorithms including multi-objective particle swarm optimization (MOPSO), preference-inspired coevolutionary algorithm (PICEAg) and the third evolution step of generalized differential evolution (GDE3)., Comment: Accepted by IEEE Access

High-performance microelectromechanical systems (MEMS) are playing a critical role in modern engineering systems. Due to computationally expensive numerical analysis and stringent design specifications nowadays, both the optimization efficiency and quality of design solutions become challenges for available MEMS shape optimization methods. In this paper, a new method, called self-adaptive surrogate model-assisted differential evolution for MEMS optimization (ASDEMO), is presented to address these challenges. The main innovation of ASDEMO is a hybrid differential evolution mutation strategy combination and its self-adaptive adoption mechanism, which are proposed for online surrogate model-assisted MEMS optimization. The performance of ASDEMO is demonstrated by a high-performance electro-thermo-elastic micro-actuator, a high-performance corrugated membrane micro-actuator, and a highly multimodal mathematical benchmark problem. Comparisons with state-of-the-art methods verify the advantages of ASDEMO in terms of efficiency and optimization ability.

As fossil fuel is being depleted, the percentage of wind power capacity in total electricity generation is increasing. In order to improve the absorption capacity of wind power, wind power prediction has been introduced. Aiming at the disadvantage of low prediction accuracy and unstable model of traditional extreme learning machine (ELM), a kernel extreme learning machine based on differential evolution (DE) and cross validation optimization method is proposed to predict short-term wind power generation. Firstly, the average mean square error (MSE) verified by k folding and cross validation is adopted as the error function of the model to improve the stability and generalization performance of the model. Secondly, differential evolution algorithm is used to optimize the regularization coefficient and kernel width of the kernel extreme learning machine with cross validation and improve the precision of model is 8.34%. Finally, compared with the application of extreme learning machine with genetic algorithm and cross validation to a wind farm prediction case in northwest China, the experimental results show that the convergence rate of this method is twice that of genetic algorithm (GA) optimization algorithm, and the accuracy is higher.

This paper discusses the performance of a multi-method ensemble meta-heuristic for optimization in a problem of submerged arches design. Specifically, the Coral Reefs Optimization algorithm with Substrate Layers (CRO-SL) is proposed. It is a multi-method evolutionary ensemble which combines different searching structures in a single population. In this case, some novel searching strategies such as the Firefly algorithm and the Water Wave Optimization have been proposed to be included in the CRO-SL algorithm. In addition, some other traditional searching structures such as classical crossovers, Gaussian mutation operators, Harmony search and Differential Evolution search strategies have also been implemented in the algorithm. The proposed CRO-SL has been applied to the optimal design of submerged arches in deep waters, considering several design aspects such as the bending moment of the beam and the airspace of the arch. The evaluation of the submerged arches quality is obtained after the simulation of the arches by means of a finite elements computational software, which has been hybridized with the CRO-SL algorithm in the process of fitness calculation. It will be shown that the CRO-SL is able to obtain excellent solutions to submerged arches design problems. For this, the computational performance of each substrate (different searching strategies) in this optimization problem will be discussed and the results obtained will be compared with those in alternative works for similar experiments.

Multimodal optimization problem (MMOP) is one of the most common problems in engineering practices that requires multiple optimal solutions to be located simultaneously. An efficient algorithm for solving MMOPs should balance the diversity and convergence of the population, so that the global optimal solutions can be located as many as possible. However, most of existing algorithms are easy to be trapped into local peaks and cannot provide high-quality solutions. To better deal with MMOPs, considerations on the solution quality angle and the evolution stage angle are both taken into account in this paper and a multi-angle hierarchical differential evolution (MaHDE) algorithm is proposed. Firstly, a fitness hierarchical mutation (FHM) strategy is designed to balance the exploration and exploitation ability of different individuals. In the FHM strategy, the individuals are divided into two levels (i.e., low/high-level) according to their solution quality in the current niche. Then, the low/high-level individuals are applied to different guiding strategies. Secondly, a directed global search (DGS) strategy is introduced for the low-level individuals in the late evolution stage, which can improve the population diversity and provide these low-level individuals with the opportunity to re-search the global peaks. Thirdly, an elite local search (ELS) strategy is designed for the high-level individuals in the late evolution stage to refine their solution accuracy. Extensive experiments are developed to verify the performance of MaHDE on the widely used MMOPs test functions i.e., CEC’2013. Experimental results show that MaHDE generally outperforms the compared state-of-the-art multimodal algorithms.

In model-based testing, the test suites are derived from design models of system specification documents instead of actual program codes to reduce cost and time of testing. In search-based software testing approach, the nature inspired meta-heuristic search algorithms are used for automating and optimizing the test suite generation process of software testing. This paper proposes a concrete model-based testing framework; using UML behavioral state chart model along with the hybrid version of the two most popular nature inspired algorithms, Firefly algorithm (FA) and Differential Algorithm (DE). The hybrid algorithm is adopted to generate optimized test suits for the benchmark triangle classification problem. Experimental results evidently show that the hybrid FA-DE search algorithm outperforms the individual model-based Firefly and Differential Evolution algorithm’s performances in terms of time complexity, better exploration and exploitation as well as variations in test case generation process. The framework generates optimized test data for complete transition path coverage of the available feasible paths of the example problem.

Differential Evolution (DE) is a simple and effective stochastic algorithm for optimization problems, and it became much more popular in recent year because of its easy-implementation and excellent performance. Nevertheless, the performance of DE algorithm is greatly affected by the trial vector generation strategy including mutation strategy and parameter control, both of which still exist some weaknesses, e.g. the premature convergence to some local optima of a mutation strategy and the misleading interaction among control parameters. Therefore in this paper, a novel Di-DE algorithm is proposed to tackle these weaknesses. A depth information based external archive was advanced in our novel mutation strategy, which can get a better perception of the landscape of objective in an optimization. Moreover, a novel grouping strategy was also employed in Di-DE and parameters were updated separately so as to avoid the misleading among parameters. Moreover, a cooperative strategy for information interchange was also advanced aiming at improving the efficiency of the exploration behavior. By absorbing these advancements, the novel Di-DE algorithm can secure better performance in comparison with other famous optimization algorithms. The algorithm validation was conducted on CEC2013 and CEC2017 test suites, and the results revealed the competitiveness of our Di-DE algorithm in comparison with those famous optimization algorithms including Particle Swarm Optimization (PSO) variants, QUasi-Affine TRansformation Evolution (QUATRE) variants and Differential Evolution (DE) variants.

Although several multi-operator and multi-method approaches for solving optimization problems have been proposed, their performances are not consistent for a wide range of optimization problems. Also, the task of ensuring the appropriate selection of algorithms and operators may be inefficient since their designs are undertaken mainly through trial and error. This research proposes an improved optimization framework that uses the benefits of multiple algorithms, namely, a multi-operator differential evolution algorithm and a co-variance matrix adaptation evolution strategy. In the former, reinforcement learning is used to automatically choose the best differential evolution operator. To judge the performance of the proposed framework, three benchmark sets of bound-constrained optimization problems (73 problems) with 10, 30 and 50 dimensions are solved. Further, the proposed algorithm has been tested by solving optimization problems with 100 dimensions taken from CEC2014 and CEC2017 benchmark problems. A real-world application data set has also been solved. Several experiments are designed to analyze the effects of different components of the proposed framework, with the best variant compared with a number of state-of-the-art algorithms. The experimental results show that the proposed algorithm is able to outperform all the others considered.

Among many evolutionary algorithms, differential evolution (DE) has received much attention over the last two decades. DE is a simple yet powerful evolutionary algorithm that has been used successfully to optimize various real-world problems. Since it was introduced, many researchers have developed new methods for DE, and one of them makes use of a mutation based on the Cauchy distribution to increase the convergence speed of DE. The method monitors the results of each individual in the selection operator and performs the Cauchy mutation on consecutively failed individuals, which generates mutant vectors by perturbing the best individual with the Cauchy distribution. Therefore, the method can locate the consecutively failed individuals to new positions close to the best individual. Although this approach is interesting, it fails to take into account establishing a balance between exploration and exploitation. In this paper, we propose a sigmoid based parameter control that alters the failure threshold for performing the Cauchy mutation in a time-varying schedule, which can establish a good ratio between exploration and exploitation. Experiments and comparisons have been done with six conventional and six advanced DE variants on a set of 30 benchmark problems, which indicate that the DE variants assisted by the proposed algorithm are highly competitive, especially for multimodal functions.

We propose a two-stage niching algorithm that separates local optima areas in the first stage and finds the optimum point of each area using any optimization technique in the second stage. The proposed first stage has complementary characteristics to the shortcoming of Nearest-better Clustering (NBC). We introduce a weighted gradient and distance-based clustering method (WGraD) and two methods for determining its weights to find out niches and overcome NBC. The WGraD creates spanning trees by connecting each search point to other suitable one decided by weighted gradient information and weighted distance information among search points. Since weights influence its clustering result, we propose two weight determination methods 1 and 2. The weight determination method 1 firstly forms one spanning tree and then uses a dynamic pruning method and the Hill-Valley test to cut long edges and repair them. The weight determination method 2 assigns different weights to different search points based on distance information. We combine these methods into WGrad, i.e. WGraD 1 and WGraD 2 , and compare the characteristics of NBC, WGraD 1 , and WGraD 2 using differential evolution (DE) as a baseline search algorithm for obtaining the optimum of each niche after clustering local areas. We design a controlled experiment and run (NBC + DE), (WGraD 1 + DE) and (WGraD 2 + DE) on 8 benchmark functions from CEC 2015 test suite for single objective multiniche optimization. The experimental results confirmed that the proposed strategy can overcome the shortcoming of NBC and be a complementary niche method of NBC.

Prolonging sensor and network life is a significant concern for wireless sensor networks and in this paper we present a novel optimization technique for determining the superframe slot allocation for a beacon-enabled 802.15.4 superframe operating with sensors with different data acquisition periods. The optimization approach is based on a differential evolution algorithm that leverages a flat cluster network topology to constrain the contention free period (CFP) and the contention access period (CAP) of the superframe. In this work we also define a multi-superframe structure to help conserve energy in the network. A sensitivity analysis of the optimization shows that the optimized results are not too sensitive to the clustering algorithm but are very sensitive to the original network configuration, such as number of nodes and their locations and transmission range, and therefore is better suited for static sensor networks. We also demonstrate that the optimized superframe results in a 5% gain in energy conservation over other approaches that optimize the superframe based on the ratio of the beacon order (BO) to superframe order (SO).

This paper discusses the performance comparison of three successful evolutionary algorithms for temperature control of ceramic infrared heater. In numerous commercial as well as industrial applications, efficient temperature control becomes a fundamental task. Despite the fact ON-OFF control is the most straightforward control strategy, it is not effective for all the applications. To optimize the performance of this system, tuning parameters of PID controller are computed using evolutionary algorithms. System identification is performed first and then controllers are designed. Step test is used here to build the empirical model of infrared heater. The performances of classical PID designed using Z-N method and optimal PID controllers designed using particle swarm optimization (PSO), Differential Evolution (DE) and Artificial Bee Colony (ABC) evolutionary algorithms are compared through simulation results. To verify the simulation results, energy consumption is calculated by implementing the controllers using Arduino. DE tuned PID controller with ITAE is discovered to be an energy effective technique for temperature control of infrared heater with better settling time and peak overshoot.

As the complexity of the real-world engineering problems increases, numerous efficient constraint-handling methods and optimization algorithms have emerged recently. However, the majority of the research consider the constraint-handling method and the optimization algorithm independently. In this paper, we propose a constraint-based mutation operator, in which the constraint violation and objective function are considered simultaneously. We define the pbest individuals as the best in top 5% constraint violators if all the individuals are infeasible. In this way, we could guide the population move towards the feasible region. Two real-world engineering applications are used to test the performance of the I $\varepsilon$ JADE. Compared with the state-of-the-art algorithms, the experimental results illustrate the effectiveness of the I $\varepsilon$ JADE algorithm, which also exhibits a fast convergence rate in terms of computation efficiency.

Network slicing is a key component of the envisioned 5G network. The slicing process is mathematically known as a virtual network embedding problem (VNE). Embedding a large number of virtual networks to a real physical network over time is an NP-Hard problem, and it becomes more complex when regarding different requirements of distinct types of network slices. Thus, we propose a new VNE algorithm based on Differential Evolution called VNE-DE to map virtual networks to a physical substrate. VNE-DE seeks better allocation of resources taking into account the most common QoS parameters of slice requirements: bandwidth, delay and reliability. Furthermore, we compare it with two Genetic Algorithm approaches, and its outcomes demonstrate improvement in the accuracy of the allocation of resources regarding.

The cryptocurrency price movement behaves randomly and fluctuates like other stock markets. Prediction of cryptocurrency is a recent area of research interest and budding fast. The underlying nonlinearities in its price series make its prediction challenging. Sophisticated methodologies for accurate prediction of cryptocurrency are highly desired. Artificial neural networks (ANNs) are good approximators, however their accuracy is greatly subjective to optimal network structure and learning method. This article designs optimal ANNs for efficient cryptocurrency prediction using quasi opposition based Rao algorithms, i.e. QORA-ANN. The model explores a set of potential ANNs in the search space and lands at an optimal network through the evolving process. Historical data from four emerging cryptocurrencies such as Bitcoin, Litecoin, Ethereum, and Ripple are used to evaluate the QORA-ANN. The prediction ability of the proposed approach is compared with few similar methods such as ANN trained with genetic algorithm, differential evolution and particle swarm optimization (i.e. ANN-GA, ANN-DE, ANN-PSO), support vector machine (SVM), and multilayer perceptron (MLP). From exhaustive simulation studies and comparative result analysis it is found that the QORA-ANN method performed better than others and hence can be suggested as an efficient tool for cryptocurrencies prediction.

Birogul, Serdar/0000-0003-4966-5970 WOS: 000510021700004 Harri's Hawk Optimization (HHO) algorithm manifests as a new meta-heuristic algorithm in literature. When we look at studies that have used with this algorithm, we can see that its results in test functions and in the solutions of some test functions in IEEE Congress on Evolutionary Computation (CEC) are much better compared to other heuristic and meta heuristic algorithm results. In this study, an algorithm has been developed which has been hybridized with the mutation operators of Differential Evolution (DE) to further improve the HHO algorithm. This algorithm is named as Hybrid Harris Hawk Optimization based on Differential Evolution (HHODE). Performance of the proposed HHODE algorithm has been first compared with HHO and then compared with the results of other algorithms which have been most commonly used in the literature. In this comparison process, the most commonly used test functions in the literature and some of the other test functions in CEC2005 and CEC2017 as a new application field, have been solved. When the results of the comparison of HHODE with other algorithms are analyzed, it is observed that the balance between the exploratory tendency and exploitative tendency of the algorithm is well consistent. Formula 1 ranking method is used in the order of HHODE according to HHO and other algorithms. When a general evaluation of HHODE was performed, it was found to be an even more powerful algorithm as a result of the combination of strong features of both HHO and DE. The optimal power flow (OPF) problem is one of the most important problems of the modern power system. The HHODE algorithm is proposed to solve the OPF problem, which is considered without valve-point effect and prohibited zones (1) and with prohibited zones (2) in this paper. The effectiveness of the HHODE hybrid algorithm is tested on modified IEEE 30-bus test system. The result of HHODE algorithms are compared with other optimization algorithms in the literature.

The differential evolution (DE) optimization algorithm predominantly relies on elite individuals and random difference to direct evolution. Although the strategy is clear and easy to implement, identifying a suitable direction for the DE mutation strongly depends on the direction information provided beforehand. To address this, we present a neighbor-induced mutation operator that simulates the neighbor-induced movement of Antarctic krill to guide the evolution direction in a natural manner. Additionally, center dispersion is proposed to disperse the population and redistribute individual positions to escape search stagnation, inspired by the spreading out of krill around newly discovered food. Comprising the new operator and the center dispersion pattern, this paper proposes a neighbor-induced DE algorithm with dispersion pattern (NDEd). The results of the comparative experiments verify the effectiveness of the neighbor-induced mutation operator and the dispersion pattern. Further, experimental results from 28 test functions of CEC2013 demonstrate that NDEd performs better compared to the other classic DE algorithms.

A finite-time controller based on optimal path planning was developed for the agile CubeSat attitude maneuver. This achieved a stable attitude large-angle maneuver just by using momentum wheels and a magnetorquer, which is unlike other larger satellites that need a control moment gyroscope or thruster. The proposed optimal path planning algorithm was based on a quintic polynomial with three path segments in order to decrease angular velocity in the attitude maneuver process as far as possible to improve system stability under the condition of satisfying CubeSat's limited control capability, and there is also an improved differential evolution (DE) algorithm for the optimization of path planning, in which the variation and crossover coefficients all obey the beta distribution. The finite-time controller was based on the nonsingular terminal sliding mode, and an improved PD-type sigmoid function was proposed to replace the sign function. Finally, the physical simulation platform is built by using the NJUST-2 as an object, and the results revealed that the finite-time controller based on the Beta DE path planning can decrease angular velocity in the attitude maneuver process as far as possible to improve system stability under the condition of satisfying the CubeSat's limited control capability and then achieves a stable attitude large-angle maneuver just by using momentum wheels and a magnetorquer.

Differential evolution is a competent algorithm for solving single objective real-parameter optimization problems. In order to enhance the performance of adaptive DE algorithms based on successful parameters, in this paper, a new DE algorithm, called adaptive differential evolution restart and direction, abbreviated ADERD, is proposed for solving global numerical optimization problems over continuous space. In the proposed algorithm, a novel mutation strategy based on the feasible descent direction is introduced. Only individuals of the population top ranked with smaller errors adopt this novel strategy to mutate. Additionally, the variable coefficient is used in the restart mechanism first to avoid stagnation and/or jump out of the local optima. Modified mechanism of crossover probability sorting is also introduced. In order to better understand the effectiveness of our proposed strategies, those are integrated into two representative adaptive DE variants, i.e. JADE_ rcr and JADE_ sort. Experimental results demonstrate that the our proposed strategies are capable of enhancing the performance of JADE_ rcr and JADE_ sort. Improved JADE_ sort is denoted as ADERD_ sort. Experiments have been conducted on 30 functions presented in CEC 2017 competition. Moreover, compared with recent adaptive DE algorithms, ADERD_ sort obtains better, or at least comparable, results in terms of the quality of final solutions.

In this paper, a multiobjective differential evolution (MODE) algorithm is developed by incorporating the memory mechanism of particle swarm optimization. That is, the personal best concept is used in the MODE to memorize the evolution of each solution through maintaining a set of non-dominated solutions found by each solution. Besides the adaptive selection of multiple mutation operators that are often adopted in the MODE, an adaptive refining method is used to improve the global external archive. The MODE is referred to as the adaptive MODE with evolution memory (AMODEEM). A set of 30 benchmark problems selected from the literature are used to evaluate its performance. The computational results illustrate that the proposed AMODEEM is competitive or even superior to several powerful MODEs in the literature for most problems.

Differential evolution (DE) is a popular paradigm of evolutionary algorithms, which has been widely applied to solve diverse optimization problems and has gained much success in a series of academic benchmark competitions. Recently, ensemble methods received an increasing attention in designing high-quality DE algorithm. Motivated by this consideration, a novel two-stage ensemble of DE variants, called TSEDE, has been proposed in this paper. In TSEDE, based on the number of fitness evaluations, the whole evolutionary process is divided into two stages. In the former stage, TSEDE using a multi-population-based framework focuses on improving the searchability, which employs three popular and efficient DE variants, namely SHADE, JADE, and “DE/current-to-rand/1.” In the latter stage, LSHADE is used to emphasize the convergence. Moreover, an elite strategy is used to ensure that the current best solution is assigned to each constituent variant at each generation. TSEDE is tested on the CEC2005 benchmark suit and compared with nine typical algorithms. The results confirm that the proposed method is very competitive.

This paper presents a quadruple-band indoor base station antenna for 2G/3G/4G/5G mobile communications, which covers multiple frequency bands of 0.8 - 0.96 GHz, 1.7 - 2.7 GHz, 3.3 - 3.8 GHz and 4.8 - 5.8 GHz and has a compact size with its overall dimensions of 204 × 175 × 39 mm3. The lower frequency bands over 0.8 - 0.96 GHz and 1.7 - 2.7 GHz are achieved through the combination of an asymmetrical dipole antenna and parasitic patches. A stepped-impedance feeding structure is used to improve the impedance matching of the dipole antenna over these two frequency bands. Meanwhile, the feeding structure also introduces an extra resonant frequency band of 3.3 - 3.8 GHz. By adding an additional small T-shaped patch, the higher resonant frequency band at 5 GHz is obtained. The parallel surrogate model-assisted hybrid differential evolution for antenna optimization (PSADEA) is employed to optimize the overall quadruple-band performance. We have fabricated and tested the final optimized antenna whose average gain is about 5.4 dBi at 0.8 - 0.96 GHz, 8.1 dBi at 1.7 - 2.7 GHz, 8.5 dBi at 3.3 - 3.8 GHz and 8.1 dBi at 4.8 - 5.0 GHz respectively. The proposed antenna has high efficiency and is of low cost and low profile, which makes it an excellent candidate for 2G/3G/4G/5G base station antenna systems.

Depression has become a serious disease that affects people’s mental health. How to detect it promptly and accurately is a difficult task. Electroencephalogram can reflect the spontaneous biological potential signals in the cerebral cortex and is widely used in the prediction and diagnosis of depression. With electroencephalogram, the key and most difficult challenge is to find the brain regions and frequencies associated with depression, especially mild depression. At present, the most commonly used method is the combination of feature selection and classification algorithm for detection. However, the classification accuracy needs to be further improved. The differential evolution is a population-based adaptive global optimization algorithm. Due to its fast convergence and strong robustness, this paper uses it to optimize the extracted features to achieve better result. Then the k-nearest neighbor classification algorithm is used to classify patients with mild depression and normal people. The experiment is performed on a data set of 10 subjects with mild depression and 10 normal subjects. The results show that the method can find the relatively optimal features and distinguish the two groups of subjects better. It effectively improves the classification accuracy and efficiency, and is superior to other feature optimization methods.

Aiming to dynamic optimization problems (DOPs), this paper develops a novel general distributed multiple populations (DMP) framework for evolutionary algorithms (EAs). DMP employs six strategies designed in three levels (i.e., population-level, subpopulation-level, and individual-level) to deal with different kinds of DOPs. First, the population-level subpopulation division estimation strategy in initialization phase rationally divides the whole population into several subpopulations to explore distinct subareas of search space sufficiently. Then, during the steady evolutionary process, diversity preservation in individual-level and population-level accelerates the responsiveness of the whole population to a new landscape, while subpopulation-level self-learning of elitist individuals promotes the exploitation of promising areas. Moreover, in subpopulation-level, the archive quality assurance technique avoids repeat exploring the same peaks by storing the locations of different peaks with low redundancy. When landscape variation occurs, in population-level, historical information containing excellent evolutionary pattern is recorded to guide the population evolution better in the new environment. DMP framework is easy to implement in various EAs due to its well generality and independence about operators and parameters of the embedded algorithm. Four DMP-EAs are accomplished in this paper whose basic algorithms are particle swarm optimization (PSO) and differential evolution (DE) with different settings. The performance of the four proposed DMP-EAs is evaluated on all the widely used complex DOP benchmarks from CEC 2009. The testing results indicate that the DMP-EAs generally significantly outperform many state-of-the-art dynamic EAs (DEAs) on most of DOP benchmarks.

In the face of these diverse forms of opposition existed widely in real-world contexts, as a novel concept in computational intelligence, opposition-based learning (OBL) was originally introduced to accelerate the population-based algorithm. In addition, its superiority has been proved mathematically and experimentally. Two key elements (function prototype and algorithm design) that influence the algorithm performance, however, has not yet fully discussed in the past decade. In this paper, two OBL strategies are reexamined in respect of function prototype and algorithm design. In the first part of this paper, considering the position relationship between the optimal solution and the center point, some well-known benchmark functions are divided into three categories. Then, quasi-opposition-based differential evolution (QODE) is investigated by two approaches: solving several benchmark functions of various function types and solving the same functions with a different optimal solution. The numerical experiments reveal that “smart” matching between the benchmark functions and the QOBL is an important factor to the good performance of QODE. In the second part of this paper, a novel individual-based embedding method is proposed to coincide with the classical definition of opposition-based optimization. Then, two opposition-based differential evolution algorithms are compared to discuss the differences between the two embedding methods. The experimental results confirm that the convergence differences stem from the embedding method chosen in the OBL scheme rather than the utilization rate of opposite points. Furthermore, the impacts caused by various function types and jumping rate are also discussed. Published version

Considering the wide application of lithium-ion battery in life, the prediction of the remaining life of lithium-ion battery has become a research hotspot. Studies show, due to the improvement of the technology level of lithium-ion battery, its life is getting longer and longer. Even under the condition of accelerated life test, it is difficult to obtain enough available data for research in a short term. In order to solve the problem of how to accurately predict the residual life with the data-driven method under the condition of small sample size, an overall trend virtual sample generation method based on differential evolution (OT-DEVSG) is proposed. This method uses a differential evolution algorithm with better optimization performance, and improves the original mega-trend-diffusion (MTD) method, the range of virtual samples is effectively constrained and the trend of samples can be estimated more accurately. The method can effectively generate a virtual sample data sequence with time parameters, and adapt the virtual sample to the real-life sample trend, which solves the problem of insufficient degradation data of the lithium-ion batteries. Finally, we validate the effectiveness of the OT-DEVSG method with three existing data sets. The experimental results show that the proposed OT-DEVSG method is effective for solving the problem of long-term life prediction of lithium-ion batteries.

With regard to the characteristics of long process, multi-units, cross-logistics and batch production mode, the order planning problem at the steelmaking shop is studied with consideration of the plant-wide process logistics balance. The problem is to allocate the orders to the continuous casters over plan periods such that the semi-finished materials produced by the steelmaking process can be delivered to the downstream hot-rolling and cold-rolling processes on time at required volume. Based on the detailed analysis of unit layout characteristics of the plant-wide process and the order composition information, a hierarchical planning method is proposed to decompose the large-scale planning problem into a set of sub-problems that are sequential solved. For the order batching subproblem, we develop an integer programming model to consolidate orders with small demand into cast-lots by considering the key batching rules. The model is efficiently solved by the optimization solver of CPLEX. For the cast-lot scheduling subproblem, a novel mixed integer programming model is developed by considering the technological constraints, the facility capacity constraints, the logistics balance constraints, the inventory constraints, and the due date constraints. An improved differential evolution algorithm is proposed to solve the cast-lot scheduling subproblem. The main improvement strategy is that the superior individuals within an external archive are further enhanced through a variable neighborhood search mechanism. Computational results on random and practical instances of different scale problems verify the effectiveness of the proposed method.

In WSN, clustering is the prevailing technique that involves identifying the object network based on attribute values. It is the sink nodes' responsibility in WSNs toward receive and process the collected data from cluster members. On the subject of saving energy, knowing the positions of sink nodes in WSNs plays a vital role. Genetic algorithm, optimization of particle swarm, differential evolution, whale optimization algorithm, and optimization of the grey wolf is now becoming efficient clustering methods as per the meta-heuristic approach. Evaluation of the life span of the entire network, this paper proposes a whale optimization algorithm. The core objective of WOA-P proposed method is tends to decrease energy consumption and extend the life of the WSNs. The purpose of the objectives has been formulating to reduce power consumption and increase the lifespan of network to achieve these goals. Compared to three recognized optimization methods, the investigational results showed that the planned WOA completed better proficiency towards dropping the total energy consumption: differential evolution, GA, particle swarm algorithm, grey wolf optimization over the network.

Combinatorial double auctions improve the inefficiency of single-side auctions. However, the winner determination problem (WDP) is computationally challenging in combinatorial double auctions. Differential Evolution provides an approach to cope with the complexity for solving optimization problems. In this paper, the effectiveness of applying two DE based algorithms to solve the WDP in combinatorial double auctions will be studied. The first approach searches solutions in the continuous solution space using the standard DE and transforms the solution to discrete solutions to evaluate the fitness function values. The second approach searches solutions directly in the discrete solution space using binary operations in DE. The effectiveness of these two algorithms is compared by conduct several experiments.

The advantage of flexible structure makes it possible for reconfigurable manufacturing systems (RMS) to respond to business opportunities. One important issue is to form production process in RMS to meet the demand based on available resources. To form a process, it is required to assign manufacturing resources to carry out the operations in it efficiently. The decision problem is to find a configuration using the available resources. Recently, Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms have been developed to optimize processes. In this paper, another two mutation strategies are developed for binary DE. Performance of these algorithms to form production processes will be compared.

Differential Evolution (DE), the evolution algorithm (EA) in the repository of evolutionary computing (EC), is known for its simplicity and adaptability to high performance computing paradigms. The distributed algorithmic frameworks of DE are the natural extension of DE, as DE is highly suitable for parallel and distributed computing. This paper proposes a study on implementing an enhanced distributed differential algorithm framework (named as mtdDE - multithreaded distributed DE) with multi-threaded islands in a distributed framework, to attain maximum level of data parallelism. The main objective of mtdDE is to reduce the computation time and to improve the solution quality for the targeted optimization problems. This paper presents this study in two phases. The Phase I implements the traditional distributed DE (dDE) framework and compares its performance with a state-of-the-art distributed DE, on a set of 8 benchmarking functions. In Phase II, the proposed mtdDE was implemented and its performance was compared with the dDE on a set of 4 benchmarking problems. The performance metrics considered were - the objective function values (ofv), the mean objective function values (mov), the execution time (et) and the average execution time (aet). The results acquired for the performance metrics of the dDE and mtdDE were studied, and the study revealed that the mtdDE outperforms the dDE in terms of both the solution accuracy and the computation time. The detailed discussion about the algorithmic structure, the experimental setup, the results obtained and the comparative study were presented in this paper.

This paper is devoted to the problem of the phasor measurement units (PMUs) placement for power system state estimation using optimality criteria proposed by the theory of optimal experimental design, such as A-, D-, M-, I-, G-optimality criteria. The high complexity of the task posed limits on the possibilities of solving it by exact mathematical methods only to small scale power systems. The paper studies the possibility to use population-based optimization algorithms (Genetic Algorithm, Differential Evolution, Particle Swarm Optimization, and Ant Colony Optimization). To meet the state observability requirements, the repair procedure is incorporated in the population-based algorithms. This allows to overcome the drawbacks in the existing methods based on the assumption of a priory observability of the power system and to take into account the system contingencies such as the phasor failures, the PMU losses, and the branch outages. We demonstrate the effectiveness of the proposed method in terms of the PMU placement design's efficiency and computation efforts through the numerical simulations on a standard IEEE 118-bus system.

Recently, the single dendritic neuron with non-linear locality has been focused by many neuroscience researches. The dendrites are composed of several branches, and these branches correspond to three distributions in coordinate, which are used to classify the training data as required. To develop a new dendritic neuron model (DNM) for solving more practical problems, we use a recently proposed state-of-the-art optimization algorithm called spherical search algorithm as the training algorithm. The results based on several real-world classification tasks suggest that the proposed learning algorithm is more effective and promising for training DNM in comparison with another recently proposed differential evolution learning algorithm. It thereafter indicates that DNM, as a single neuron model, is a suitable and powerful classifier.