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Despite the simplicity of the whale optimization algorithm (WOA) and its success in solving some optimization problems, it faces many issues. Thus, WOA has attracted scholars' attention, and researchers frequently prefer to employ and improve it to address real-world application optimization problems. As a result, many WOA variations have been developed, usually using two main approaches improvement and hybridization. However, no comprehensive study critically reviews and analyzes WOA and its variants to find effective techniques and algorithms and develop more successful variants. Therefore, in this paper, first, the WOA is critically analyzed, then the last 5 years' developments of WOA are systematically reviewed. To do this, a new adapted PRISMA methodology is introduced to select eligible papers, including three main stages: identification, evaluation, and reporting. The evaluation stage was improved using three screening steps and strict inclusion criteria to select a reasonable number of eligible papers. Ultimately, 59 improved WOA and 57 hybrid WOA variants published by reputable publishers, including Springer, Elsevier, and IEEE, were selected as eligible papers. Effective techniques for improving and successful algorithms for hybridizing eligible WOA variants are described. The eligible WOA are reviewed in continuous, binary, single-objective, and multi/many-objective categories. The distribution of eligible WOA variants regarding their publisher, journal, application, and authors' country was visualized. It is also concluded that most papers in this area lack a comprehensive comparison with previous WOA variants and are usually compared only with other algorithms. Finally, some future directions are suggested.

Kalman Filter (KF) that is also known as linear quadratic estimation filter estimates current states of a system through time as recursive using input measurements in mathematical process model. Thus algorithm is implemented in two steps: in the prediction step an estimation of current state of variables in uncertainty conditions is presented. In the next step, after obtaining the measurement, previous estimation is updated by weighted arithmetic mean. Accordingly, using KF in non-linear systems can be difficult. For nonlinear systems Extended KF (EKF) and Unscented KF (UKF) represent the first-order and higher order linear approximations. KF cannot predict appropriate values for modeling system behavior in more complicated systems. In the current study, in addition to referring to basic methods, a review on recent researches on Multiple Model (MM) filters has been done. More reliable estimations obtain by using two or more filters with different models in parallel, by allocating an estimation to each filter, outputs of each filter are calculated. MM Adaptive Estimation (MMAE) and Interacting MM (IMM) are the most used methods for estimating MMs.

Throughout the centuries, nature has been a source of inspiration, with much still to learn from and discover about. Among many others, Swarm Intelligence (SI), a substantial branch of Artificial Intelligence, is built on the intelligent collective behavior of social swarms in nature. One of the most popular SI paradigms, the Particle Swarm Optimization algorithm (PSO), is presented in this work. Many changes have been made to PSO since its inception in the mid 1990s. Since their learning about the technique, researchers and practitioners have developed new applications, derived new versions, and published theoretical studies on the potential influence of various parameters and aspects of the algorithm. Various perspectives are surveyed in this paper on existing and ongoing research, including algorithm methods, diverse application domains, open issues, and future perspectives, based on the Systematic Review (SR) process. More specifically, this paper analyzes the existing research on methods and applications published between 2017 and 2019 in a technical taxonomy of the picked content, including hybridization, improvement, and variants of PSO, as well as real-world applications of the algorithm categorized into: health-care, environmental, industrial, commercial, smart city, and general aspects applications. Some technical characteristics, including accuracy, evaluation environments, and proposed case study are involved to investigate the effectiveness of different PSO methods and applications. Each addressed study has some valuable advantages and unavoidable drawbacks which are discussed and has accordingly yielded some hints presented for addressing the weaknesses of those studies and highlighting the open issues and future research perspectives on the algorithm.

Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.

This article discusses several definitions of the fractional Laplace operator L = — (—Δ) α /2 in R d , also known as the Riesz fractional derivative operator; here α ∈ (0,2) and d ≥ 1. This is a core example of a nonlocal pseudo-differential operator, appearing in various areas of theoretical and applied mathematics. As an operator on Lebesgue spaces ℒ p (with p ∈ [1,∞)), on the space 𝒞 0 of continuous functions vanishing at infinity and on the space 𝒞 bu of bounded uniformly continuous functions, L can be defined, among others, as a singular integral operator, as the generator of an appropriate semigroup of operators, by Bochner’s subordination, or using harmonic extensions. It is relatively easy to see that all these definitions agree on the space of appropriately smooth functions. We collect and extend known results in order to prove that in fact all these definitions are completely equivalent: on each of the above function spaces, the corresponding operators have a common domain and they coincide on that common domain.

Recent advances in computer vision have allowed broad applications in every area of life, and agriculture is not left out. For the agri-food industry, the use of advanced technology is essential. Owing to deep learning’s capability to learn robust features from images, it has witnessed enormous application in several fields. Fruit detection and classification remains challenging due to the form, color, and texture of different fruit species. While studying the impact of computer vision on fruit detection and classification, we pointed out that till 2018 many conventional machine learning methods were utilized while a few methods exploited the application of deep learning methods for fruit detection and classification. This has prompted us to pursue an extensive study on surveying and implementing deep learning models for fruit detection and classification. In this article, we intensively discussed the datasets used by many scholars, the practical descriptors, the model’s implementation, and the challenges of using deep learning to detect and categorize fruits. Lastly, we summarized the results of different deep learning methods applied in previous studies for the purpose of fruit detection and classification. This review covers the study of recently published articles that utilized deep learning models for fruit identification and classification. Additionally, we also implemented from scratch a deep learning model for fruit classification using the popular dataset “Fruit 360” to make it easier for beginner researchers in the field of agriculture to understand the role of deep learning in the agriculture domain.

Nowadays, deep learning is a current and a stimulating field of machine learning. Deep learning is the most effective, supervised, time and cost efficient machine learning approach. Deep learning is not a restricted learning approach, but it abides various procedures and topographies which can be applied to an immense speculum of complicated problems. The technique learns the illustrative and differential features in a very stratified way. Deep learning methods have made a significant breakthrough with appreciable performance in a wide variety of applications with useful security tools. It is considered to be the best choice for discovering complex architecture in high-dimensional data by employing back propagation algorithm. As deep learning has made significant advancements and tremendous performance in numerous applications, the widely used domains of deep learning are business, science and government which further includes adaptive testing, biological image classification, computer vision, cancer detection, natural language processing, object detection, face recognition, handwriting recognition, speech recognition, stock market analysis, smart city and many more. This paper focuses on the concepts of deep learning, its basic and advanced architectures, techniques, motivational aspects, characteristics and the limitations. The paper also presents the major differences between the deep learning, classical machine learning and conventional learning approaches and the major challenges ahead. The main intention of this paper is to explore and present chronologically, a comprehensive survey of the major applications of deep learning covering variety of areas, study of the techniques and architectures used and further the contribution of that respective application in the real world. Finally, the paper ends with the conclusion and future aspects.

Entropy weight method (EWM) is a commonly used weighting method that measures value dispersion in decision-making. The greater the degree of dispersion, the greater the degree of differentiation, and more information can be derived. Meanwhile, higher weight should be given to the index, and vice versa. This study shows that the rationality of the EWM in decision-making is questionable. One example is water source site selection, which is generated by Monte Carlo Simulation. First, too many zero values result in the standardization result of the EWM being prone to distortion. Subsequently, this outcome will lead to immense index weight with low actual differentiation degree. Second, in multi-index decision-making involving classification, the classification degree can accurately reflect the information amount of the index. However, the EWM only considers the numerical discrimination degree of the index and ignores rank discrimination. These two shortcomings indicate that the EWM cannot correctly reflect the importance of the index weight, thus resulting in distorted decision-making results.

Despite its rapid development, Physics-Informed Neural Network (PINN)-based computational solid mechanics is still in its infancy. In PINN, the loss function plays a critical role that significantly influences the performance of the predictions. In this paper, by using the Least Squares Weighted Residual (LSWR) method, we proposed a modified loss function, namely the LSWR loss function, which is tailored to a dimensionless form with only one manually determined parameter. Based on the LSWR loss function, an advanced PINN technique is developed for computational 2D and 3D solid mechanics. The performance of the proposed PINN technique with the LSWR loss function is tested through 2D and 3D (geometrically nonlinear) problems. Thoroughly studies and comparisons are conducted between the two existing loss functions, the energy-based loss function and the collocation loss function, and the proposed LSWR loss function. Through numerical experiments, we show that the PINN based on the LSWR loss function is effective, robust, and accurate for predicting both the displacement and stress fields. The source codes for the numerical examples in this work are available at https://github.com/JinshuaiBai/LSWR_loss_function_PINN/ .

Mathematical programming and meta-heuristics are two types of optimization methods. Meta-heuristic algorithms can identify optimal/near-optimal solutions by mimicking natural behaviours or occurrences and provide benefits such as simplicity of execution, a few parameters, avoidance of local optimization, and flexibility. Many meta-heuristic algorithms have been introduced to solve optimization issues, each of which has advantages and disadvantages. Studies and research on presented meta-heuristic algorithms in prestigious journals showed they had good performance in solving hybrid, improved and mutated problems. This paper reviews the sparrow search algorithm (SSA), one of the new and robust algorithms for solving optimization problems. This paper covers all the SSA literature on variants, improvement, hybridization, and optimization. According to studies, the use of SSA in the mentioned areas has been equal to 32%, 36%, 4%, and 28%, respectively. The highest percentage belongs to Improved, which has been analyzed by three subsections: Meat-Heuristics, artificial neural networks, and Deep Learning.