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The economic load dispatch (ELD) problem plays a crucial role in power system operation. In practice, the ELD problem becomes a non-convex, multi-constraint, non-linear optimization problem when considering the valve point effects, the prohibited operation zones, the ramp rate limit, and the multi-fuel options. To effectively solve this problem, this paper puts forward an improved differential evolution (DE) named OMLIDE based on opposition-mutual learning, hybrid mutation strategy, and parameters adaptive mechanism. OMLIDE differs from the traditional DE in that: (1) an opposition-mutual learning strategy is employed for population initialization to increase the probability of finding an optimal solution; (2) two novel mutation operators named DE/elite-to-ordinary/1 and DE/elite-to-ordinary/2 are hybridized and a selection probability is introduced to regulate them adaptively at different evolutionary stages; and (3) a parameters adaptive mechanism is presented to adjust the scaling factor and crossover rate. The proposed OMLIDE is first validated by the numerical benchmark functions of CEC 2014. Then it is applied to five non-convex ELD problems with valve-point effects and multi-fuel options. Simulation results demonstrate that OMLIDE provides better or highly competitive results in different terms compared with other peer algorithms. This work was supported by the Basic Research Program of Guizhou Province (Natural Science) (QiankeheBasic-ZK[2022]General121) and the National Natural Science Foundation of China (52167007).

Sorting solutions play a key role in using evolutionary algorithms (EAs) to solve many-objective optimization problems (MaOPs). Generally, different solution-sorting methods possess different advantages in dealing with distinct MaOPs. Focusing on this characteristic, this article proposes a general voting-mechanism-based ensemble framework (VMEF), where different solution-sorting methods can be integrated and work cooperatively to select promising solutions in a more robust manner. In addition, a strategy is designed to calculate the contribution of each solution-sorting method and then the total votes are adaptively allocated to different solution-sorting methods according to their contribution. Solution-sorting methods that make more contribution to the optimization process are rewarded with more votes and the solution-sorting methods with poor contribution will be punished in a period of time, which offers a good feedback to the optimization process. Finally, to test the performance of VMEF, extensive experiments are conducted in which VMEF is compared with five state-of-the-art peer many-objective EAs, including NSGA-III, SPEA/R, hpaEA, BiGE, and grid-based evolutionary algorithm. Experimental results demonstrate that the overall performance of VMEF is significantly better than that of these comparative algorithms.

In this paper, a new feature selection algorithm, called SFE (Simple, Fast, and Efficient), is proposed for high-dimensional datasets. The SFE algorithm performs its search process using a search agent and two operators: non-selection and selection. It comprises two phases: exploration and exploitation. In the exploration phase, the non-selection operator performs a global search in the entire problem search space for the irrelevant, redundant, trivial, and noisy features, and changes the status of the features from selected mode to non-selected mode. In the exploitation phase, the selection operator searches the problem search space for the features with a high impact on the classification results, and changes the status of the features from non-selected mode to selected mode. The proposed SFE is successful in feature selection from high-dimensional datasets. However, after reducing the dimensionality of a dataset, its performance cannot be increased significantly. In these situations, an evolutionary computational method could be used to find a more efficient subset of features in the new and reduced search space. To overcome this issue, this paper proposes a hybrid algorithm, SFE-PSO (particle swarm optimization) to find an optimal feature subset. The efficiency and effectiveness of the SFE and the SFE-PSO for feature selection are compared on 40 high-dimensional datasets. Their performances were compared with six recently proposed feature selection algorithms. The results obtained indicate that the two proposed algorithms significantly outperform the other algorithms, and can be used as efficient and effective algorithms in selecting features from high-dimensional datasets.

Hybridization in context to Evolutionary Computation (EC) strives to combine operators, components, and the best merits of different EC paradigms, to form a new evolutionary algorithm that enjoys a statistically superior performance, compared to its ancestors, over a wide range of application-specific optimization problems. In this paper, we propose a simple yet powerful amalgam composed of a modified Cultural Algorithm (CA) that is supported with an Enhanced Levy Flight Search (ELFS) to guide the search and further promote the harmony between the explorative and exploitative capacities of the conventional techniques. The novel amalgam, denoted by q-aCA + m IS, utilizes a balanced search scheme where it employs an adapted Influence Function (IF) with a novel quality function that establishes a harmony between the Knowledge Sources (KSs) in the Belief Space (BS), and between the BS and other components in the hybrid to produce the most suitable knowledge needed for a certain search mode. The CA framework is reinforced with an updated Selection Function (SF) that employs a successful selection strategy that uses the extended situational knowledge for the future selection of individuals. The proposed algorithm is tested using more than 50 benchmark functions that are taken from the IEEE CEC’06, and the IEEE CEC’19 competitions on constrained real-parameter optimization. Moreover, three well-known engineering design problems are used to test the validity of the algorithm for the solution of complex real-life problems. The comparative study indicates that the q-aCA + mIS algorithm was able to obtain a statistically superior performance and scalability behavior over most of the considered functions in comparison with other state-of-the-art algorithms.

K-nearest neighbor (KNN) based weighted multi-class twin support vector machines (KWMTSVM) is a novel multi-class classification method. In this paper, we propose a novel least squares version of KWMTSVM called LS-KWMTSVM by replacing the inequality constraints with equality constraints and minimized the slack variables using squares of 2-norm instead of conventional 1-norm. This simple modification leads to a very fast algorithm with much better results. The modified primal problems in the proposed LS-KWMTSVM solves only two systems of linear equations whereas two quadratic programming problems (QPPs) need to solve in KWMTSVM. The proposed LS-KWMTSVM, same as KWMTSVM, employed the weight matrix in the objective function to exploit the local information of the training samples. To exploit the inter class information, we use weight vectors in the constraints of the proposed LS-KWMTSVM. If any component of vectors is zero then the corresponding constraint is redundant and thus we can avoid it. Elimination of redundant constraints and solving a system of linear equations instead of QPPs makes the proposed LS-KWMTSVM more robust and faster than KWMTSVM. The proposed LS-KWMTSVM, commensurate as the KWMTSVM, all the training data points into a “1-versus-1-versus-rest” structure, and thus our LS-KWMTSVM generate ternary output {-1,0,+1} which helps to deal with imbalance datasets. Numerical experiments on several UCI and KEEL imbalance datasets(with high imbalance ratio) clearly indicate that the proposed LS-KWMTSVM has better classification accuracy compared with other baseline methods but with remarkably less computational time. This work was supported by Science and Engineering Research Board (SERB) under Early Career Research Award Grant No. ECR/2017/000053 and Ramanujan fellowship Grant No. SB/S2/ RJN-001/2016. This work was also supported by Council of Scientific & Industrial Research (CSIR), New Delhi, INDIA under Extra Mural Research (EMR) Scheme Grant No. 22(0751)/17/ EMR-II.

Neural networks have been successfully employed in various domains such as classification, regression and clustering, etc. Generally, the back propagation (BP) based iterative approaches are used to train the neural networks, however, it results in the issues of local minima, sensitivity to learning rate and slow convergence. To overcome these issues, randomization based neural networks such as random vector functional link (RVFL) network have been proposed. RVFL model has several characteristics such as fast training speed, direct links, simple architecture, and universal approximation capability, that make it a viable randomized neural network. This article presents the first comprehensive review of the evolution of RVFL model, which can serve as the extensive summary for the beginners as well as practitioners. We discuss the shallow RVFLs, ensemble RVFLs, deep RVFLs and ensemble deep RVFL models. The variations, improvements and applications of RVFL models are discussed in detail. Moreover, we discuss the different hyperparameter optimization techniques followed in the literature to improve the generalization performance of the RVFL model. Finally, we give potential future research directions/opportunities that can inspire the researchers to improve the RVFL's architecture and learning algorithm further.

Based on mating and environmental selections employed, multi-objective evolutionary algorithms (MOEAs) are classified as Pareto-based, decomposition-based and indicator-based approaches that are associated with their own advantages and disadvantages. To benefit from the advantages of different MOEAs, we propose an ensemble framework (ENMOEA) in which mating and environmental selections of diverse MOEAs are combined. ENMOEA is a single-population competitive ensemble, where resource allocation to individual mating operators is done adaptively. In addition, ENMOEA employs a two-level environmental selection where constituent environmental selection operators are first applied to label solutions as “selected” and “non-selected”. Solutions “selected” by most operators are preferred for future evolution. An external archive is employed to facilitate effective usage of function evaluations and achieve a better comprise between convergence and diversity. To demonstrate generality of ENMOEA, we developed two variants: 1) specific case (ENMOEAS - combines different Pareto-based MOEAs) and 2) general case (ENMOEAG - combines Pareto-based, indicator-based and decomposition-based MOEAs). From simulation results on various test suites (DTLZ, WFG and 16 real-world problems), it is evident that ENMOEA is robust to the parameters of the constituent algorithms. In addition, it is evident that the effectiveness of ensemble improves with the diversity of the constituent algorithms.

In this paper, we first integrate normalization to the Ensemble Deep Random Vector Functional Link network (edRVFL). This re-normalization step can help the network avoid divergence of the hidden features. Then, we propose novel variants of the edRVFL network. Weighted edRVFL (WedRVFL) uses weighting methods to give training samples different weights in different layers according to how the samples were classified confidently in the previous layer thereby increasing the ensemble's diversity and accuracy. Furthermore, a pruning-based edRVFL (PedRVFL) has also been proposed. We prune some inferior neurons based on their importance for classification before generating the next hidden layer. Through this method, we ensure that the randomly generated inferior features will not propagate to deeper layers. Subsequently, the combination of weighting and pruning, called Weighting and Pruning based Ensemble Deep Random Vector Functional Link Network (WPedRVFL), is proposed. We compare their performances with other state-of-the-art classification methods on 24 tabular UCI classification datasets. The experimental results illustrate the superior performance of our proposed methods.

Randomized neural networks have become more and more attractive recently since they use closed-form solutions for parameter training instead of gradient-based approaches. Among them, the random vector functional link network (RVFL) and its deeper version ensemble deep random vector functional link network (edRVFL) show great performance on both classification and regression tasks. However, the previous research on these two models mainly focuses on the supervised learning area. Although there have been efforts to extend the RVFL network to solve semi-supervised learning problems, the potential of the edRVFL network has not been fully investigated. Therefore, we propose a jointly optimized learning strategy for the edRVFL network (JOSedRVFL) for semi-supervised learning tasks in this paper. The JOSedRVFL network uses an iterative procedure to compute the output weights and consequently predicts the class labels of the unlabeled training data during the training process. In addition, we propose another semi-supervised edRVFL network (SS-edRVFL) using manifold regularization in this work. We then do a brief comparison between these two methods to illustrate their similarities and differences. In the experimental part, we conduct the first set of experiments using the UCI datasets to compare the performance of our proposed semi-supervised algorithms against 11 other classifiers to demonstrate the superior performance of the SS-edRVFL and JOSedRVFL networks. JOSedRVFL achieves the highest accuracy on all 4 datasets while SS-edRVFL takes the second place 3 times which is only worse than JOSedRVFL. Moreover, we apply the proposed methods to real-world applications using the electroencephalography-based emotion recognition dataset to compare the performance of RVFL-based methods (RVFL, SS-RVFL, and JOSRVFL) and their edRVFL counterparts (edRVFL, SS-edRVFL, and JOSedRVFL). Results from this test revealed that the edRVFL-based models (edRVFL, SS-edRVFL, and JOSedRVFL) can obtain higher accuracy than the RVFL-based versions (RVFL, SS-RVFL, and JOSRVFL) with the same learning framework on 45 real-world semi-supervised benchmarks. We then perform the Wilcoxon signed-rank test to show that JOSedRVFL is significantly better than 5 other competitors, which supports our claim that JOSedRVFL can be treated as a superior classifier for semi-supervised classification on both benchmark datasets and real-world applications. J. Del Ser would like to thank the Basque Government for its funding support through the EMAITEK and ELKARTEK programs (3KIA project, KK-2020/00049), as well as the consolidated research group MATHMODE (ref. IT1456-22).

Inspired by the ensemble strategy of machine learning, deep random vector functional link (dRVFL), and ensemble dRVFL (edRVFL) has shown state-of-the-art results on different datasets. Our present work first fills the gap of dRVFL and edRVFL work in the field of regression. We test and evaluate the performances of the dRVFLs on regression problems. Subsequently, we propose a novel regularization method boosted factor (BF), two dRVFLs variants edRVFL with skip connection (edRVFL-SC) and edRVFL with random skip connections (edRVFL-RSC) and one strategy ensemble skip connection edRVFL (esc-edRVFL) which show significant improvement over the original dRVFL. The BF is a newly introduced hyperparameter to scale the values of the activated hidden neurons to accommodate the diversity of the data, and it is also able to filter the neurons. edRVFL-SC and edRVFL-RSC are the edRVFL variants with skip connections. In edRVFL-SC, we apply dense skip connections to the edRVFL, which is inspired by the residual architecture in the deep learning area. However, due to the specificity of randomized networks, the simple skip connections are probably leading to the reuse of useless features. To address this problem, we propose a random skip connection-based edRVFL, which can keep the diversity in the latent space. esc-RVFL is an ensemble scheme that utilizes several edRVFL-RSC models trained on the different folds of the training dataset. The esc-edRVFL is identified as the best-performing algorithm through a comprehensive evaluation of 31 UCI datasets. Published version Open Access funding provided by the Qatar National Library.

Satellite observation scheduling plays a significant role in improving the efficiency of Earth observation systems. To solve the large-scale multi-satellite observation scheduling problem, this paper proposes an ensemble of meta-heuristic and exact algorithm based on a divide-and-conquer framework (EHE-DCF), including a task allocation phase and a task scheduling phase. In the task allocation phase, each task is allocated to a proper orbit based on a meta-heuristic incorporated with a probabilistic selection and a tabu mechanism derived from ant colony optimization and tabu search respectively. In the task scheduling phase, we construct a task scheduling model for every single orbit, and use an exact method (i.e., branch and bound, B&B) to solve this model. The task allocation and task scheduling phases are performed iteratively to obtain a promising solution. To validate the performance of EHE-DCF, we compare it with B&B, three divide-and-conquer based meta-heuristics, and a state-of-the-art meta-heuristic. Experimental results show that EHE-DCF can obtain higher scheduling profits and complete more tasks compared with existing algorithms. EHE-DCF is especially efficient for large-scale satellite observation scheduling problems., This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

In this paper, we propose ten synthetic datasets for point prediction and numeric uncertainty quantification (UQ). These datasets are split into train, validation, and test sets for model benchmarking. Equations and the description of each dataset are provided in detail. We also present representative shallow neural network (NN) training and Random Vector Functional Link (RVFL) training examples. Both training train models for the point prediction. We perform uncertainty quantification with the consideration of a gaussian and homoscedastic distribution. As the distribution consideration and models are rudimental, much room exists for further explorations and improvements. The dataset and scripts are available at the following link: https://github.com/dipuk0506/UQ-Data

The advent of Internet of Things (IoT) has bring a new era in communication technology by expanding the current inter-networking services and enabling the machine-to-machine communication. IoT massive deployments will create the problem of optimal power allocation. The objective of the optimization problem is to obtain a feasible solution that minimizes the total power consumption of the WSN, when the error probability at the fusion center meets certain criteria. This work studies the optimization of a wireless sensor network (WNS) at higher dimensions by focusing to the power allocation of decentralized detection. More specifically, we apply and compare four algorithms designed to tackle Large scale global optimization (LGSO) problems. These are the memetic linear population size reduction and semi-parameter adaptation (MLSHADE-SPA), the contribution-based cooperative coevolution recursive differential grouping (CBCC-RDG3), the differential grouping with spectral clustering-differential evolution cooperative coevolution (DGSC-DECC), and the enhanced adaptive differential evolution (EADE). To the best of the authors knowledge, this is the first time that LGSO algorithms are applied to the optimal power allocation problem in IoT networks. We evaluate the algorithms performance in several different cases by applying them in cases with 300, 600 and 800 dimensions.

The standard twin support vector machine (TSVM) uses the hinge loss function which leads to noise sensitivity and instability. In this paper, we propose a novel general twin support vector machine with pinball loss (Pin-GTSVM) for solving classification problems. We show that the proposed Pin-GTSVM is noise insensitive and more stable for re-sampling. Further, the computational complexity of the proposed Pin-GTSVM is similar to that of the TSVM. Thus, the pinball loss function does not increase the computation time of the proposed Pin-GTSVM. Numerical experiments with different noise are performed on 17 UCI and KEEL benchmark real-world datasets and the results are compared with other baseline methods. The comparisons clearly show that the proposed Pin-GTSVM has better generalization performance for noise corrupted datasets. This work is supported by Science and Engineering Research Board (SERB), Government of India under Early Career Research Award Scheme, Grant No. ECR/2017/000053 and Council of Scientific & Industrial Research (CSIR), New Delhi, INDIA under Extra Mural Research (EMR) Scheme Grant No. 22(0751)/17/EMR-II. We gratefully acknowledge the Indian Institute of Technology Indore for providing facilities and support.

Currently, evolutionary multiobjective optimization (EMO) algorithms have been successfully used to find a good approximation of many-objective optimization problems (MaOPs). To measure the performance of EMO algorithms, many benchmark multiobjective test problems have been constructed. Among them, DTLZ and WFG are two representative test suites with the scalability to the number of variables and objectives. It should be pointed out that MaOPs can be more challenging if they are involved with difficult problem features, such as objective scalability, complicated Pareto set, bias, disconnection, or degeneracy. In this paper, a set of ten new test problems with above-mentioned difficulties are constructed. Some experimental results on these test problems found by two popular EMO algorithms, i.e., MOEA/D and NSGA-III, are reported and analyzed. Moreover, the performance of these two EMO algorithms with different population sizes on these test problems are also studied. This work was supported by National Natural Science Foundation of China under Grant 61573279 , Grant 61175063 , Grant U1811461 , Grant 11690011 , and Grant 61721002 . This work was also supported by a grant from ANR/RGC Joint Research Scheme sponsored by the Research Grants Council of the Hong Kong Special Administrative Region , China and France National Research Agency (Project No. A-CityU101/16 ).

A solar cell or photovoltaic (PV) module is electrically represented by an appropriate circuit model with certain defined parameters. The parameters are required to be correctly computed from solar cell characteristic and/or a set of experimental data for simulation and control of the PV system. However, experimental data or accurate characteristic data (i.e. current-voltage or I-V curve) of a PV module may not be readily available. The manufacturer of a PV system usually provides relevant information on open circuit, short circuit and maximum power points. Therefore, an alternate approach is to estimate the PV system parameters by utilizing the I-V characteristic data at these three major points. The process involves formulation and solution of complex non-linear equations from an adopted solar cell model. This paper proposes an application of an advanced adaptive differential evolution algorithm on the problem of PV module parameter estimation using minimum available information from the manufacturer datasheet by implementing single-diode and double-diode models. Linear population size reduction technique of success history based adaptive differential evolution (L-SHADE) algorithm is implemented to minimize the error of current-voltage relationships at the above-mentioned three important points defining the I-V characteristic. The algorithm facilitates evolution of solutions that result in almost zero error (

Optimal active–reactive power dispatch problems (OARPD) are non-convex and highly nonlinear complex optimization problems. Typically, such problems are expensive in terms of computational time and cost due to the load variations over the scheduling period. The conventional constraint-based solvers that are generally used to tackle such problems require a considerable high budget and may not provide high quality solutions. In the last decade, complexity of OARPD has further increased due to the incorporation of renewable energy sources such as: wind, solar and small-hydro generators. More specifically, the incorporation of renewable sources introduces uncertainty in generation on top of the load variations in conventional OARPD, making the problem more complicated. Recently, Differential Evolution (DE) is viewed as an excellent algorithm to solve OARPD problems, due to its effectiveness to optimize the objective function which is subject to many operational constraints. A new efficient Differential Evolution algorithm, denoted as DEa-AR, is propounded to solve the contemporary stochastic optimal power flow OARPD problems considering the renewable generators. DEa-AR uses arithmetic recombination crossover and adapts the scaling factor based on Laplace distribution. In addition, an efficient archive strategy that acts as a corresponding image of the population and stores the inferior individuals for later use, is also incorporated. The target behind using this strategy is to consider the information of inferior individuals as a direction toward finding new good solutions. The IEEE 57-bus system is used to evaluate the OARPD problems with different stochastic scenarios based on different probability distributions employed to model parameters of renewable energy sources. The performance of the proposed work is compared with other state-of-the-art algorithms. Simulation results indicate that the proposed technique can solve the OARPD problems with renewable sources effectively and can provide high quality solutions. The proposed algorithm is ranked the first with a Friedman rank equals to 1.8333 with a clear statistical significant difference compared with the most recent studies on the used problems.

Photovoltaic modeling has attracted researchers’ attention worldwide because of its importance in the photovoltaic system design. Therefore, several photovoltaic models have been introduced as static and dynamic photovoltaic models. Moreover, a novel fractional order dynamic photovoltaic model has been recently developed to enhance the accuracy and flexibility of the conventional integral order one. The unknown parameters of these models should be extracted accurately to achieve a proper photovoltaic system design and operation. In this work, novel Chaotic Heterogeneous Comprehensive Learning Particle Swarm Optimizer variants are introduced, where the Heterogeneous Comprehensive Learning Particle Swarm Optimizer is combined with ten different chaos maps to adapt its parameters. Six Chaotic Heterogeneous Comprehensive Learning Particle Swarm Optimizer variants are proposed in addition to the standard Heterogeneous Comprehensive Learning Particle Swarm Optimizer version to identify the parameters of both the static and the dynamic models based on different experimental datasets. To demonstrate the superiority of the developed variants, their results are compared to the most recent state-of-the-art algorithms with the aid of statistical analysis methods. The main outcome is that, in both of the static and the dynamic photovoltaic models, the Chaotic Heterogeneous Comprehensive Learning Particle Swarm Optimizer variants show their efficiency, accuracy and robustness not only over Heterogeneous Comprehensive Learning Particle Swarm Optimizer but also over recently published algorithms. They provide better fitting relative to the experimental datasets with the least deviation error and the fastest convergence speed as well. In the case of static models, the fourth variant of Chaotic Heterogeneous Comprehensive Learning Particle Swarm Optimizer with an iterative map for the single diode model, the third variant of Chaotic Heterogeneous Comprehensive Learning Particle Swarm Optimizer with singer map for the double diode model of solar cell. On the other hand, for the dynamic models, the second Chaotic Heterogeneous Comprehensive Learning Particle Swarm Optimizer variant with sinusoidal map for the integral order dynamic photovoltaic model and the sixth variant of Chaotic Heterogeneous Comprehensive Learning Particle Swarm Optimizer with Gauss/mouse map for the fractional order dynamic photovoltaic model offer the best performance.

Optimizing reactive power flow in electrical network is an important aspect of system study as the reactive power supports network voltage which needs to be maintained within desirable limits for system reliability. A network consisting of only conventional thermal generators has been extensively studied for optimal active and reactive power dispatch. However, increasing penetration of renewable sources into the grid necessitates power flow studies incorporating these sources. This paper presents a formulation and solution procedure for stochastic optimal reactive power dispatch (ORPD) problem with uncertainties in load demand, wind and solar power. Appropriate probability density functions (PDFs) are considered to model the stochastic load demand and the power generated from the renewable energy sources. Numerous scenarios are created running Monte-Carlo simulation and scenario reduction technique is implemented to deal with reduced number of scenarios. Real power loss and steady state voltage deviation of load buses in the network are set as the objectives of optimization. Success history based adaptive differential evolution (SHADE) is adopted as the basic search algorithm. SHADE has been successfully integrated with a constraint handling technique, called epsilon constraint (EC) handling, to handle constraints in ORPD problem. The effectiveness of a proper constraint handling technique is substantiated with case studies for deterministic ORPD on base configurations of IEEE 30-bus and 57-bus systems using SHADE-EC algorithm. The single-objective and multi-objective stochastic ORPD cases are also solved using the SHADE-EC algorithm. The results are discussed, compared and critically analyzed in this study. National Research Foundation (NRF) Accepted version This project is funded by the National Research Foundation Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) program.

In evolutionary computation, balancing the diversity and convergence of the population for multiobjective evolutionary algorithms (MOEAs) is one of the most challenging topics. Decomposition-based MOEAs are efficient for population diversity, especially when the branch partitions the objective space of multiobjective optimization problem (MOP) into a series of subspaces, and each subspace retains a set of solutions. However, a persisting challenge is how to strengthen the population convergence while maintaining diversity for decomposition-based MOEAs. To address this issue, we first define a novel metric to measure the contributions of subspaces to the population convergence. Then, we develop an adaptive strategy that allocates computational resources to each subspace according to their contributions to the population. Based on the above two strategies, we design an objective space partition-based adaptive MOEA, called OPE-MOEA, to improve population convergence, while maintaining population diversity. Finally, 41 widely used MOP benchmarks are used to compare the performance of the proposed OPE-MOEA with other five representative algorithms. For the 41 MOP benchmarks, the OPE-MOEA significantly outperforms the five algorithms on 28 MOP benchmarks in terms of the metric hypervolume.

In multiobjective optimization, the relationship between decision space and objective space is generally assumed to be a one-to-one mapping, but it is not always the case. In some problems, different variables have the same or similar objective value, which means a many-to-one mapping. In this situation, there is more than one Pareto Set (PS) mapping to the same Pareto Front (PF) and these problems are called multimodal multiobjective problems. This paper proposes a multimodal multiobjective differential evolution algorithm to solve these problems. In the proposed method, the difference vector is generated taking the diversity in both decision and objective space into account. The way to calculate crowding distance is quite different from the others. In the crowding distance calculation process, all the selected individuals are taken into account instead of considering each Pareto rank separately. The crowding distance in decision space is replaced with the weighted sum of Euclidean distances to its neighbors. In the environmental selection process, not all the individuals in top ranks are selected, because some of them may be very crowded. Instead, the potential solutions in the bottom rank are given a chance to evolve. With these operations, the proposed algorithm can maintain multiple PSs of multimodal multiobjective optimization problems and improve the diversity in both decision and objective space. Experimental results show that the proposed method can achieve high comprehensive performance. We acknowledge financial support by the National Natural Science Foundation of China (61922072, 61876169, 61976237, 61806179 and 61873292), Key R&D and Promotion Projects in Henan Province (212102210510), the Key Scientific Research Projects in Colleges and Universities of Henan Province (Grant No.19A120014) and Scholarship under the State Scholarship Fund by the China Scholarship Council.

In this paper, we propose deep learning frameworks based on the randomized neural network. Inspired by the principles of Random Vector Functional Link (RVFL) network, we present a deep RVFL network (dRVFL) with stacked layers. The parameters of the hidden layers of the dRVFL are randomly generated within a suitable range and kept fixed while the output weights are computed using the closed-form solution as in a standard RVFL network. We also propose an ensemble deep network (edRVFL) that can be regarded as a marriage of ensemble learning with deep learning. Unlike traditional ensembling approaches that require training several models independently from scratch, edRVFL is obtained by training a single dRVFL network once. Both dRVFL and edRVFL frameworks are generic and can be used with any RVFL variant. To illustrate this, we integrate the deep learning RVFL networks with a recently proposed sparse pre-trained RVFL (SP-RVFL). Experiments on 46 tabular UCI classification datasets and 12 sparse datasets demonstrate that the proposed deep RVFL networks outperform state-of-the-art deep feed-forward neural networks (FNNs).

This letter identifies original independent works in the domain of randomization-based feedforward neural networks. In the most common approach, only the output layer weights require training while the hidden layer weights and biases are randomly assigned and kept fixed. The output layer weights are obtained using either iterative techniques or non-iterative closed-form solutions. The first such work (abbreviated as RWNN) was published in 1992 by Schmidt et al. for a single hidden layer neural network with sigmoidal activation. In 1994, a closed form solution was offered for the random vector functional link (RVFL) neural networks with direct links from the input to the output. On the other hand, for radial basis function neural networks, randomized selection of basis functions’ centers was used in 1988. Several works were published thereafter, employing similar techniques but with different names while failing to cite the original or relevant sources. In this letter, we make an attempt to identify and trace the origins of such randomization-based feedforward neural networks and give credits to the original works where due and hope that the future research publications in this field will provide fair literature review and appropriate experimental comparisons. We also briefly review the limited performance comparisons in the literature, two recently proposed new names, randomization-based multi-layer or deep neural networks and provide promising future directions.

Unmanned aerial vehicle (UAV) path planning enables UAVs to avoid obstacles and reach the target efficiently. To generate high-quality paths without obstacle collision for UAVs, this article proposes a novel autonomous path planning algorithm based on a tangent intersection and target guidance strategy (APPATT). Guided by a target, the elliptic tangent graph method is used to generate two sub-paths, one of which is selected based on heuristic rules when confronting an obstacle. The UAV flies along the selected sub-path and repeatedly adjusts its flight path to avoid obstacles through this way until the collision-free path extends to the target. Considering the UAV kinematic constraints, the cubic B-spline curve is employed to smooth the waypoints for obtaining a feasible path. Compared with A∗, PRM, RRT and VFH, the experimental results show that APPATT can generate the shortest collision-free path within 0.05 seconds for each instance under static environments. Moreover, compared with VFH and RRTRW, APPATT can generate satisfactory collision-free paths under uncertain environments in a nearly real-time manner. It is worth noting that APPATT has the capability of escaping from simple traps within a reasonable time. This work was supported in part by the National Natural Science Foundation of China under Grant 62073341, in part by the Natural Science Fund for Distinguished Young Scholars of Hunan Province under Grant 2019JJ20026, and in part by the National Natural Science Foundation of Hunan Province under Grant 2020JJ4748.

Ensemble methods with “perturb and combine” strategy have shown improved performance in the classification problems. Recently, random forest algorithm was ranked one among 179 classifiers evaluated on 121 UCI datasets. Motivated by this, we propose a new approach for the generation of oblique decision trees. At each non-leaf node, the training data samples are grouped in two categories based on the Bhattachrayya distance with randomly selected feature subset. Then, twin bounded support vector machine (TBSVM) is used to get two clustering hyperplanes such that each hyperplane is closer to data points of one group and as far as possible from the data points of other group. Based on these hyperplanes, each non-leaf node is splitted to generate the decision tree. In this paper, we used different base models like random forest (RaF), rotation forest (RoF), random sub rotation forest (RRoF) to generate the different oblique decision tree forests named as TBRaF, TBRoF and TBRRoF, respectively. In earlier oblique decision trees, like multisurface proximal support vector machine (MPSVM) based oblique decision trees, matrices are semi-positive definite and hence different regularization methods are required. However, no explicit regularization techniques need to be applied to the primal problems as the matrices in the proposed TBRaF, TBRoF and TBRRoF are positive definite. We evaluated the performance of the proposed models (TBRaF, TBRoF and TBRRoF) on 49 datasets taken from the UCI repository and on some real-world biological datasets (not in UCI). The experimental results and statistical tests conducted show that TBRaF and TBRRoF outperform other baseline methods. This work was supported by Science and Engineering Research Board (SERB) as Early Career Research Award grant no. ECR/2017/000053 and Department of Science and Technology as Ramanujan fellowship grant no. SB/S2/RJN-001/2016.

Differential evolution (DE) has been a simple yet effective algorithm for global optimization problems. The performance of DE highly depends on its operators and parameter settings. In the last couple of decades, many advanced variants of DE have been proposed by modifying the operators and introducing new parameter tuning methods. However, the majority of the works on advanced DE have been concentrated upon the mutation and crossover operators. The initialization and selection operators are less explored in the literature. In this work, we implement the orthogonal array-based initialization of the population and propose a neighborhood search strategy to construct the initial population for the DE-based algorithms. We also introduce a conservative selection scheme to improve the performance of the algorithm. We analyze the influence of the proposed initialization and selection schemes on several variants of DE. Results suggest that the proposed methods highly improve the performance of DE algorithm and its variants. Furthermore, we introduce an ensemble strategy for parameter adaptation techniques in DE. Incorporating all the proposed initialization, selection, and parameter adaptation strategies, we develop a new variant of DE, named OLSHADE-CS. The performance of OLSHADE-CS is found to be highly competitive and significantly better in many cases when compared with the performance of the state-of-the-art algorithms on CEC benchmark problems.

This paper deals with the problem of scheduling identical parallel batch processing machines. In this scheduling system, each machine processes a set of jobs in a batch simultaneously and each job in the batch is characterized by its processing time, ready time and job size. We propose a hybrid discrete cuckoo search (HDCS) algorithm to minimize makespan for this scheduling problem. The HDCS is constructed, based on a modified variable neighborhood search and cuckoo search algorithm. In the proposed algorithm, we present a modified Levy flight in the cuckoo search to transform a continuous position in the HDCS into a discrete schedule for generating a new solution. The process parameters of the proposed HDCS are tuned by implementing the desirability-based Taguchi method to optimize both solution quality and run time. The results of exhaustive computational experimentation on a large number of randomly generated sparse as well as non-sparse problem instances show that the proposed algorithm is more effective and efficient than the state-of-the-art algorithms.

This letter discusses non-iterative learning methods with closed-form solution such as the kernel ridge regression and randomization based single hidden layer feedforward neural networks like random vector functional link (RVFL). Similarities and differences between these methods are also discussed. Irrelevance of kernel-trick for randomized neural networks is explained. The need for dual formulation or constrained optimization formulation for kernel methods and RVFL is distinguished. Finally, the articles in this special issue focusing on non-iterative learning methods with closed-form solution are summarized. A common conclusion in these articles is that the RVFL developed in the early 1990s outperforms the extreme learning machines (ELM). This conclusion is consistent with the earlier findings [1] , [2] , [3] that the direct links enhance the performance of the RVFL.

Over the last few decades, a plethora of improved evolutionary algorithms was developed with exquisite performance on numerical and real-world problems . Among such algorithms, the Cultural Algorithm is a hyper-heuristic evolutionary algorithm, which explicitly utilizes the knowledge represented in the belief space as an essential component to guide the evolutionary search. In this paper, a new enhanced Cultural Algorithm incorporates a fuzzy system with a modified Levy flight search that is introduced as a new component. The new algorithm namely, b-fCA+m LF, utilizes a balanced search mode using a customized belief space with a quality function to harmonize how the knowledge sources work in parallel. The communication protocols between the population space and the belief space are established through the modified fuzzy acceptance and influence functions. Using these new functions, the best individuals are selected to create new knowledge in an effective manner. Similarly, the best knowledge is selected to evolve the individuals in the population space and guide the evolutionary search towards the promising regions. A modified Levy flight search is proposed and utilizes the information from the belief space as an input to support the evolution process to generate better solutions. The algorithm is tested on the benchmark suite taken from the IEEE-CEC’15 competition on learning-based real-parameter single objective optimization , and is compared with other algorithms including the best performer algorithms in this competition. The results suggest that the proposed algorithm is statistically better and is able to produce higher quality solutions than the other state-of-the-art algorithms. A case study on the well-known 120-bar dome truss design problem is also presented to test the validity of the proposed algorithm for the solution of complex design problems. The results of this problem show the ability of the proposed algorithm to generate good solutions with fewer function evaluations, compared to reported results in the literature and other well-known algorithms.

Economic-environmental power dispatch is one of the most popular bi-objective non-linear optimization problems in power system. Classical economic power dispatch problem is formulated with only thermal generators often ignoring security constraints of the network. But importance of reduction in emission is paramount from environmental sustainability perspective and hence penetration of more and more renewable sources into the electrical grid is encouraged. However, most common forms of renewable sources are intermittent and uncertain. This paper proposes multiobjective economic emission power dispatch problem formulation and solution incorporating stochastic wind, solar and small-hydro (run-of-river) power. Weibull, lognormal and Gumbel probability density functions are used to calculate available wind, solar and small-hydro power respectively. Some conventional generators of the standard IEEE 30-bus system are replaced with renewable power sources for study purpose. Network security constraints such as transmission line capacities and bus voltage limits are also taken into consideration alongwith constraints on generator capabilities and prohibited operating zones for the thermal units. Decomposition based multiobjective evolutionary algorithm and summation based multiobjective differential evolution algorithm are applied to the problem under study. An advanced constraint handling technique, superiority of feasible solutions, is integrated with both the multiobjective algorithms to comply with system constraints. The simulation results of both the algorithms are summarized, analyzed and compared in this study. NRF (Natl Research Foundation, S’pore) Accepted version

Short-term electric load forecasting plays an important role in the management of modern power systems. Improving the accuracy and efficiency of electric load forecasting can help power utilities design reasonable operational planning which will lead to the improvement of economic and social benefits of the systems. A hybrid incremental learning approach composed of Discrete Wavelet Transform (DWT), Empirical Mode Decomposition (EMD) and Random Vector Functional Link network (RVFL) is presented in this work. RVFL network is a universal approximator with good efficiency because of the randomly generated weights between input and hidden layers and the close form solution for parameter computation. By introducing incremental learning, along with ensemble approach via DWT and EMD into RVFL network, the forecasting performance can be significantly improved with respect to both efficiency and accuracy. The electric load datasets from Australian Energy Market Operator (AEMO) were used to evaluate the effectiveness of the proposed incremental DWT-EMD based RVFL network. Moreover, the attractiveness of the proposed method can be demonstrated by the comparison with eight benchmark forecasting methods. NRF (Natl Research Foundation, S’pore)

Many parameter adaptation methods were proposed for Differential Evolution (DE) algorithm. Although these methods succeed in enhancing the performance of DE when solving a diverse set of optimization problems, locating the optimal solution is still a challenging task in most of these methods for complex optimization problems. To improve the performance of DE, this study presents a new enhanced algorithm based on our published work namely LSHADE with ensemble parameter sinusoidal adaptation, LSHADE-EpSin, which ranked the joint winner in IEEE CEC2016 competition on real-parameter single objective optimization. The method proposes a mixture of two sinusoidal formulas and a Cauchy distribution to balance the exploration and the exploitation of already found best solutions. A restart method is used at later generations to enhance the quality of the found solutions. The proposed algorithm also introduces a novel approach to adapt the population size by using a niching-based reduction scheme. In this mechanism, two separate niches are used before performing the population reduction, to reduce the population size in an effective manner. The proposed algorithm namely ensemble sinusoidal differential evolution with niching reduction, EsDEr-NR, is tested on the IEEE CEC2014 problems used in the special session and competitions on real-parameter single objective optimization of the IEEE CEC2016. The results statistically affirm the efficiency of the proposed approach to obtain better results compared to the other state-of-the-art algorithms from the literature including CMA-ES variants.

An efficient windfarm layout to harness maximum power out of the wind is highly desirable from technical and commercial perspectives. A bit of flexibility on layout gives leeway to the designer of windfarm in planning facilities for erection, installation and future maintenance. This paper proposes an approach where several options of optimized usable windfarm layouts can be obtained in a single run of decomposition based multi-objective evolutionary algorithm (MOEA/D). A set of Pareto optimal vectors is obtained with objective as maximum output power at minimum wake loss i.e. at maximum efficiency. Maximization of both output power and windfarm efficiency are set as two objectives for optimization. The objectives thus formulated ensure that in any single Pareto optimal solution the number of turbines used are placed at most optimum locations in the windfarm to extract maximum power available in the wind. Case studies with actual manufacturer data for wind turbines of same as well as different hub heights and with realistic wind data are performed under the scope of this research study. NRF (Natl Research Foundation, S’pore)

Differential evolution (DE) is one of the most popular and efficient evolutionary algorithms for numerical optimization and it has gained much success in a series of academic benchmark competitions as well as real applications. Recently, ensemble methods receive an increasing attention in designing high-quality DE algorithms. However, previous efforts are mainly devoted to the low-level ensemble of mutation strategies of DE. This study investigates the high-level ensemble of multiple existing efficient DE variants. A multi-population based framework (MPF) is proposed to realize the ensemble of multiple DE v ariants to derive a new algorithm named EDEV for short. EDEV consists of three highly popular and efficient DE variants, namely JADE (adaptive differential evolution with optional external archive), CoDE (differential evolution with composite trial vector generation strategies and control parameters) and EPSDE (differential evolution algorithm with ensemble of parameters and mutation strategies). The whole population of EDEV is partitioned into four subpopulations, including three indicator subpopulations with smaller size and one reward subpopulation with much larger size. Each constituent DE variant in EDEV owns an indicator subpopulation. After every predefined generations, the most efficient constituent DE variant is determined and the reward subpopulation is assigned to that best performed DE variant as an extra reward. Through this manner, the most efficient DE variant is expected to obtain the most computational resources during the optimization process . In addition, the population partition operator is triggered at every generation, which results in timely information sharing and tight cooperation among the component DE variants. Extensive experiments and comparisons have been done based on the CEC2005 and CEC2014 benchmark suit, which shows that the overall performance of EDEV is superior to several state-of-the-art peer DE variants. The success of EDEV reveals that, through an appropriate ensemble framework, different DE variants of different merits can support one another to cooperatively solve optimization problems .

In this study, we introduce a novel approach of variable reduction and integrate it into evolutionary algorithms in order to reduce the complexity of optimization problems. We develop reduction processes of variable reduction for derivative unconstrained optimization problems (DUOPs) and constrained optimization problems (COPs) with equality constraints and active inequality constraints. Variable reduction uses the problem domain knowledge implied when investigating optimal conditions existing in optimization problems. For DUOPs, equations involving derivatives are considered while for COPs, we discuss equations expressing the equality constraints. From the relationships formed in this way, we obtain relationships among the variables that have to be satisfied by optimal solutions. According to such relationships, we can utilize some variables (referred to as core variables) to express some other variables (referred to as reduced variables). We show that the essence of variable reduction is to produce a minimum collection of core variables and a maximum number of reduced variables based on a system of equations. We summarize some application-oriented situations of variable reduction and stress several important issues related to the further application and development of variable reduction. Essentially, variable reduction can reduce the number of variables and eliminate equality constraints, thus reducing the dimensionality of the solution space and improving the efficiency of evolutionary algorithms. The approach can be applied to unconstrained, constrained, continuous and discrete optimization problems only if there are explicit variable relationships to be satisfied in the optimal conditions. We test variable reduction on real-world and synthesized DUOPs and COPs. Experimental results and comparative studies point at the effectiveness of variable reduction.

Recent studies in Machine Learning indicates that the classifiers most likely to be the bests are the random forests. As an ensemble classifier, random forest combines multiple decision trees to significant decrease the overall variances. Conventional random forest employs orthogonal decision tree which selects one “optimal” feature to split the data instances within a non-leaf node according to impurity criteria such as Gini impurity, information gain and so on. However, orthogonal decision tree may fail to capture the geometrical structure of the data samples. Motivated by this, we make the first attempt to study the oblique random forest in the context of time series forecasting. In each node of the decision tree, instead of the single “optimal” feature based orthogonal classification algorithms used by standard random forest, a least square classifier is employed to perform partition. The proposed method is advantageous with respect to both efficiency and accuracy. We empirically evaluate the proposed method on eight generic time series datasets and five electricity load demand time series datasets from the Australian Energy Market Operator and compare with several other benchmark methods.

Hybrid active power filter (HAPF) is an advanced form of harmonic filter combining advantages of both active and passive filters. In HAPF, selection of active filter gain, passive inductive and capacitive reactances, while satisfying system constraints on individual and overall voltage and current harmonic distortion levels, is the main challenge. To optimize HAPF parameters, this paper proposes an approach based on differential evolution (DE) algorithm called L-SHADE. SHADE is the success history based parameter adaptation technique of DE optimization process for a constrained, multimodal non-linear objective function. L-SHADE improves the performance of SHADE with linearly reducing the population size in successive generations. The study herein considers two frequently used topologies of HAPF for parameter estimation. A single objective function consisting of both total voltage harmonic distortion (VTHD) and total current harmonic distortion (ITHD) is formulated and finally harmonic pollution (HP) is minimized in a system comprising of both non-linear source and non-linear loads. Several case studies of a selected industrial plant are performed. The output results of L-SHADE algorithm are compared with a similar past study and also with other well-known evolutionary algorithms.

Random Vector Functional Link (RVFL) is popular among researchers in many areas of machine learning. RVFL is preferred by many researchers as RVFL can produce good performance with relatively little training time. Recent works extend RVFL into deep and ensemble versions. However, RVFL does not have effective feature extraction methods commonly used in time series classification. This results in poor performance of RVFL in time series classification tasks. Also, deep RVFL is a relatively new and evolving area of research. In this paper, we present a framework that extracts features from Residual Networks (Resnet) and trains Ensemble Deep Random Vector Functional Link (edRVFL). We use features extracted from every residual block to train an ensemble of edRVFLs. We propose the following enhancements to edRVFL. Firstly, we diversity the structure of edRVFL and the direct link features to encourage diversity. Secondly, we built an ensemble of edRVFLs with the top two activation functions. Thirdly, we use two-stage tuning to save computational costs. Lastly, we perform a weighted average of all decisions made by every edRVFL. Experiments on the 55 largest UCR datasets show that using features extracted from all Residual blocks improves performance. All our proposed enhancements help improve classification accuracy or computational effort. Consequently, our proposed framework outperforms all traditional and deep learning-based time series classification methods.

The use of optimization algorithms for designing Infinite Impulse Response (IIR) filters has been considered in many studies. The concern in this area is the multimodal error surface of such filters and their fitting with filter coefficients. The order of the modeled system has a direct effect on the number of coefficients, complexities of the error surface, and the filter’s stability. This paper proposes an efficient approach based on a variable length particle swarm optimization algorithm with a weighted sum fitness function (WS-VLPSO). The proposed WS-VLPSO is utilized as an effective adaptive algorithm for designing optimal IIR filters. The approach is based on the inclusion of the order as a discrete variable in the particle vector, which is done with the goal of intelligent minimizing of order and thereby reducing the design complexity of IIR filters. To ensure the optimality of the systems, the objective function is considered as a weighted sum. Also, a new criterion called Optimum Modeling Indicator (OMI) is introduced, a measure to determine the percentage reduction of order and the success rate of the proposed approach. The proposed algorithm is also applied for solving the sensor coverage problem as another real-world variable length engineering optimization application. Evaluation of simulation results, with Monte-Carlo simulation, indicates the acceptable improvement of identified structures and the significant performance of the proposed approaches. Note that the source codes of the paper will be publicly available at https://github.com/ali-ece .

The challenge of accurately forecasting a time series covers numerous disciplines, from economics to engineering. Among the thousands of machine learning models, random vector functional link (RVFL) is a robust and efficient model which has demonstrated its success in various challenging forecasting problems. RVFL is an efficient universal function appropriator that randomly generates the weights between the input and hidden layers. However, RVFL still lacks the strong ability to extract meaningful multi-scale features from input data because of the single-layer random mapping of enhancement nodes. Therefore, we propose to combine the empirical wavelet transformation (EWT) with RVFL to strengthen the multi-scale feature extraction ability. The EWT can decompose the original time series into several sub-series which carry the information of different frequencies. Besides, we propose a walk-forward decomposition mechanism to implement the EWT. By introducing such a walk-forward mechanism and the combination of EWT and RVFL, the hybrid model achieves high accuracy and averts the data leakage problem during forecasting. A detailed and comprehensive empirical study on twenty-six public time series validates the proposed model’s superiority compared with ten popular baseline models from the literature.

Ensemble classifiers with random vector functional link network have shown improved performance in classification problems. In this paper, we propose two approaches to solve the classification problems. In the first approach, the original input space’s data points are mapped explicitly into a randomized feature space via neural network wherein the weights of the hidden layer are generated randomly. After feature projection, classification models twin bounded support vector machines (SVM), least squares twin SVM, twin k -class SVM, least squares twin k -class SVM and robust energy based least squares twin SVM are trained on the extended features (original features and randomized features). In the second approach, twin bounded support vector machines (SVM), least squares twin SVM, twin k -class SVM, least squares twin k -class SVM and robust energy based least squares twin SVM models are used to generate the weights of the hidden layer architecture and the weights of output layer are optimized via closed form solution. The performance of both the proposed architectures is evaluated on 33 datasets — including datasets from the UCI repository and fisheries data (not in UCI). Both the experimental results and statistical tests conducted demonstrate that the proposed approaches perform significantly better than the other baseline models. We also analyze the effect of the number of enhanced features on the performance of the given models.