Book

# Swarm Intelligence Algorithms: A Tutorial

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## Abstract

Swarm intelligence algorithms are a form of nature-based optimization algorithms. Their main inspiration is the cooperative behavior of animals within specific communities. This can be described as simple behaviors of individuals along with the mechanisms for sharing knowledge between them, resulting in the complex behavior of the entire community. Examples of such behavior can be found in ant colonies, bee swarms, schools of fish or bird flocks. Swarm intelligence algorithms are used to solve difficult optimization problems for which there are no exact solving methods or the use of such methods is impossible, e.g. due to unacceptable computational time. This book thoroughly presents the basics of 24 algorithms selected from the entire family of swarm intelligence algorithms. Each chapter deals with a different algorithm describing it in detail and showing how it works in the form of a pseudo-code. In addition, the source code is provided for each algorithm in Matlab and in the C ++ programming language. In order to better understand how each swarm intelligence algorithm works, a simple numerical example is included in each chapter, which guides the reader step by step through the individual stages of the algorithm, showing all necessary calculations. This book can provide the basics for understanding how swarm intelligence algorithms work, and aid readers in programming these algorithms on their own to solve various computational problems. This book should also be useful for undergraduate and postgraduate students studying nature-based optimization algorithms, and can be a helpful tool for learning the basics of these algorithms efficiently and quickly. In addition, it can be a useful source of knowledge for scientists working in the field of artificial intelligence, as well as for engineers interested in using this type of algorithms in their work. If the reader already has basic knowledge of swarm intelligence algorithms, we recommend the book: "Swarm Intelligence Algorithms: Modifications and Applications" (Edited by A. Slowik, CRC Press, 2020), which describes selected modifications of these algorithms and presents their practical applications.
... Adjust the salps that have been outside the search space according to the lower and upper bounds. Repeat the algorithm until the end condition is satisfied, then return the bet salp as the solution [36][37][38] . [36][37][38] . ...
... Repeat the algorithm until the end condition is satisfied, then return the bet salp as the solution [36][37][38] . [36][37][38] . ...
... Equation 1 computes the v 1 parameter, which is responsible for the balance between exploration and exploitation, where T is the maximum number of iterations and t is the current iteration of [36][37][38] . ...
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... In this study, the whale optimization (WO) algorithm is implemented to solve the problems of TA and PA detailed in the previous subsection. The WO algorithm is a recently developed nature inspired and swarm-based global stochastic optimizer [23,24,31]. It mimics hunting behaviour of humpback whales to find optimal solution. ...
... Due to its simple structure, less required operator, fast convergence capability and a good balance feature between exploration and exploitation stages, it has been tremendously gained attention by the researchers in a short time. To reach much more details on the WO algorithm, readers can refer to [23,31]. ...
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In this paper, firstly, optimal sizing and placement of photovoltaic-based distributed generation units (PVDGUs) and passive harmonic filters (PFs) are proposed to improve both the PVDGU hosting capacity and bus voltage profile of the distorted radial distribution systems. The objective of the proposed approach (PA) is defined as minimizing the rms deviation and total harmonic distortion of the bus voltages while maximizing the hosting capacity. Its constraints are considered as bus voltage total and individual harmonic distortion limits placed in IEEE standard 519, permissible bus voltage rms intervals, and the numbers and total powers of the PVDGUs and PFs. Secondly, it is aimed to investigate the performance of the PA on the improvement of the hosting capacity and voltage profile. Thus, for the modified IEEE 33 bus test system containing nonlinear loads, it is comparatively evaluated with a traditional PF planning approach (TA) based on minimization of the total voltage harmonic distortion. Finally, the effects of the harmonic analysis algorithm and PVDGU harmonic model preferences on the solutions of both approaches are also analysed. One of the major conclusions obtained from the analysis is that PA achieves significantly higher PVDGU hosting capacity while providing total voltage harmonic distortion mitigation performance very close to TA. In addition, PA achieves almost the same hosting capacity for all considered harmonic models and harmonic analysis algorithms. However, this is not the case for TA.
... As the most important type of optimization algorithm, swarm intelligence is inspired by the collective behavior of social insects or animals, which has the advantages of robustness, speed, autonomy, and parallelism. Various representative swarm intelligence optimization algorithms have been put forward so far, such as the particle swarm optimization (PSO) algorithm [39], artificial bee colony (ABC) algorithm [40], social spider optimization (SSO) algorithm [41], firefly algorithm [42], and so on. These algorithms are widely applied to improve objective task accuracy or efficiency in a variety of fields, and they can achieve superior results compared to other optimization methods. ...
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Sensor management is a crucial research subject for multi-sensor multi-target tracking in wireless sensor networks (WSNs) with limited resources. Bearings-only tracking produces further challenges related to high nonlinearity and poor observability. Moreover, energy efficiency and energy balancing should be considered for sensor management in WSNs, which involves networking and transmission. This paper formulates the sensor management problem in the partially observable Markov decision process (POMDP) framework and uses the cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter for tracking. A threshold control method is presented to reduce the impact on tracking accuracy when using bearings-only measurements for sequential update. Moreover, a Cauchy–Schwarz divergence center is defined to construct a new objective function for efficiently finding the optimal sensor subset via swarm intelligence optimization. This is also conducive to dynamic clustering for the energy efficiency and energy balancing of the network. The simulation results illustrate that the proposed solution can achieve good tracking performance with less energy, and especially that it can effectively balance network energy consumption and prolong network lifetime.
... Compared with the traditional mathematical approaches, SI algorithms have the advantages of simple structure, convenient implementation, and robust performance. In recent decades, various SI algorithms have been developed, such as ant colony optimization (ACO) (Colorni et al. 1991), particle swarm optimization (PSO) (Kennedy, and Eberhart 1995), artificial bee colony (ABC) (Karaboga 2005), artificial fish swarm optimization (AFSO) (Li et al. 2002), firefly algorithm (FA) (Yang 2009), grey wolf optimizer (GWO) (Mirjalili et al. 2014), chicken swarm optimization (CSO) (Meng et al. 2014), and so on (Slowik 2020). ...
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The chicken swarm optimization (CSO) is a novel swarm intelligence algorithm, which mimics the hierarchal order and foraging behavior in the chicken swarm. However, like other population-based algorithms, CSO also suffers from slow convergence and easily falls into local optima, which partly results from the unbalance between exploration and exploitation. To tackle this problem, this paper proposes a chicken swarm optimization with an enhanced exploration–exploitation tradeoff (CSO-EET). To be specific, the search process in CSO-EET is divided into two stages (i.e., exploration and exploitation) according to the swarm diversity. In the exploratory search process, a random solution is employed to find promising solutions. In the exploitative search process, the best solution is used to accelerate convergence. Guided by the swarm diversity, CSO-EET alternates between exploration and exploitation. To evaluate the optimization performance of CSO-EET in both theoretical and practical problems, it is compared with other improved CSO variants and several state-of-the-art algorithms on two groups of widely used benchmark functions (including 102 test functions) and two real-world problems (i.e., circle packing problem and survival risk prediction of esophageal cancer). The experimental results show that CSO-EET is better than or at least comparable to all competitors in most cases.
... One of the most well-known SI algorithms is Particle Swarm Optimization (PSO) [5] which mimics the motion of bird flocks and schooling fish. Other SI algorithms available in the literature can be listed as follows: Salp Swarm Algorithm (SSA) [6], Whale Optimization Algorithm (WOA) [1], Firefly Algorithm (FA) [7], Grey Wolf Optimizer (GWO) [8], Artificial Bee Colony algorithm (ABC) [9], etc. For physics-based methods, these algorithms simulate the physical laws in the universe. ...
Article
In this paper, an evolutionary symbiotic organisms search algorithm as a hybridization of differential evolution and symbiotic organisms search is developed for shape and size optimization of truss structures with free vibration and transient behavior under multiple constraints. For that aim, a mutation operator combined by two global differential evolution operators and a novel symbiotic organisms search operator is proposed to reinforce the exploration ability of the proposed algorithm. This newly suggested symbiotic organisms search operator is relied upon the symbiotic relationship in such a way that an arbitrary organism can receive benefits from both mutualisms and commensalisms. A threshold is automatically integrated into the mutation step to switch from the exploration capability to the exploitation one. In addition, an elitist scheme is applied to the selection phase to purify the most potential candidates for the next symbiotic ecosystem. Accordingly, the present algorithm can result in a high-quality optimal solution with a better convergence evolution. 26 mathematical functions and 7 well-known benchmark problems regarding size and shape truss optimization under multiple constraints are tested to verify the effectiveness of the proposed methodology. Obtained outcomes have indicated that the developed algorithm outperforms both original algorithms and many existing approaches in the literature. To further illustrate the ability of the proposed paradigm, two among the above five examples under transient excitations with strength, displacement, and buckling constraints are then optimized.
Chapter
The article presents the popularity of nature-based optimization methods in the context of issues related to digital filters. An analysis was made concerning the number of publications in popular scientific databases. Attention was paid to publications that are related to nature-inspired optimization methods and their application to digital filters design. The results obtained from scientific databases make it possible to identify the most popular optimization methods in the context of their applications to digital filters. In this paper, we also point out the thematic areas in which the articles related to nature-inspired optimization methods and digital filters are published more often.
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Multilevel inverters (MLIs) are one of the most popular topics of power electronics. Selective harmonic elimination (SHE) method is used to eliminate low-order harmonics in the MLI output voltage by determining the optimum switching angles. It includes the solution of nonlinear sets of transcendental equations. The optimization becomes more difficult as the number of levels in MLIs increases. Therefore, various metaheuristic algorithms have emerged toward obtaining optimal solutions to find the switching angles in the SHE problem in the last decade. In this study, a number of recent metaheuristics, such as ant lion optimization (ALO), hummingbird algorithm (AHA), dragonfly algorithm (DA), harris hawk optimization, moth flame optimizer (MFO), sine cosine algorithm (SCA), flow direction algorithm (FDA), equilibrium optimizer (EO), atom search optimization, artificial electric field algorithm and arithmetic optimization algorithm (AOA), are employed as an attempt to find the best optimization framework to identify switching moments in 11-level MLI. Marine predator algorithm (MPA), whale optimization algorithm (WOA), grey wolf optimizer (GWO), particle swarm optimization (PSO), multiverse optimizer (MVO), teaching–learning-based optimization (TLBO), and genetic algorithm (GA), which are widely used in solving this problem, are selected for performance analysis. AHA, ALO, AOA, DA, EO, FDA, GA, GWO, MFO, MPA, MVO, PSO, SCA, SSA, TLBO and WOA methods meet maximum 8% THD requirement specified in IEEE 519 standard in the range of 0.4–0.9 modulation index. Simulation results show that MFO is superior other algorithms in terms of THD minimization, convergence rate, a single iteration time and robustness.
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In many developing countries, non-technical losses and electricity stealing constitute serious problems for electric power companies. This paper demonstrates a practical scheme for determining and reducing non-technical losses in the power network by detecting the suspected area where incorrect meter readings and electricity theft occur. The method is cast as a mathematical optimization problem to be resolved using the dispersive flies algorithm to identify and minimize measurement errors while lowering electricity losses and costs. The findings demonstrate the approach’s effectiveness and its applicability in real-world scenarios.
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The paper presents an innovative OFNBee optimization method based on combining the swarm intelligence with the use of directed fuzzy numers OFN. In the introduction, the issues related to the subject of the study, including bee algorithms and OFN numbers, were reviewed. The innovative OFNBee algorithm was presented and verified against a set of known benchmarks functions such as Sphere, Rastrigin, Griewank, Rosenbrock, Schwefel and Ackley. These functions have been applied due to their reliability in the literature. In the further part of the study, the configuration of the algorithm parameters is carried out, including the launch of each mathematical function several dozen times for different data, such as different population sizes. The key part of the research and analysis was to compare OFNBee with six standard ABC, MBO, IMBO, TLBO, HBMO, BBMO bee algorithms. The article ends with a summary and an indication of the possible future works.
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The article presents issues related to hybrid nature-inspired population-based algorithms of global optimization and their industrial applications. To this end, the article presents a general concept of nature-inspired population-based optimization methods and the ways in which those methods can be hybridized with other techniques. Concrete literature-based examples have been used to illustrate each type of hybridization. The paper also demonstrates the publication popularity of selected hybrid nature-inspired population-based optimization algorithms and indicates their most common application areas. Moreover, the paper refers to the computational and implementation complexity of the algorithms in question. Next, the focus shifts to industrial applications of hybrid nature-inspired population-based optimization methods. References have been made to numerous works that present different versions of hybrid optimization algorithms, showing the areas of their practical application. Moreover, the paper discusses the problems inherent in hybrid optimization methods as well as indicates open research points in this field.
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Aiming at the problem of slow convergence speed and ease of falling into local optimum when solving high dimensional problems, this paper proposes an improved chicken swarm optimization algorithm. The improved chicken swarm optimization includes four aspects, namely, cock position update mode, hen position update mode, chick position update mode and population update strategy, so it is abbreviated as ICSO-RHC. On the basis of algorithm improvement, the influence of the number of retained elite individuals and control parameters on the convergence speed of the algorithm is discussed. The calculation results of the test function show that when the number of elite individuals in the population is 1, and the control parameters is a random number uniformly distributed between 0,1, the algorithm has a faster convergence speed. In addition, in order to verify the performance of ICSO-RHC, 30 test functions and CEC 2005 benchmark functions were selected. The calculation results of these test functions show that the success rate of ICSO-RHC is significantly higher than other algorithms, both for low-dimensional and high-dimensional optimization problems. The average iteration number and average running time are significantly lower than other algorithms. Finally, ICSO-RHC and other improved algorithms in the literature are used to optimize the parameters of four practical engineering problems. The optimization results show that the statistical results obtained by ICSO-RHC are significantly better than other algorithms. The calculation results of the test functions and the actual engineering problems show that the performance of ICSO-RHC proposed in this paper is significantly better than other algorithms.
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The sink nodes in large-scale wireless sensor networks (LSWSNs) are responsible for receiving and processing the collected data from sensor nodes. Identifying the locations of sink nodes in LSWSNs play a vital role in term of saving energy. Furthermore, sink nodes have extremely extra resources such as large memory, powerful batteries, long-range antenna, etc. This paper proposes a multi-objective whale optimization algorithm (MOWOA) to determine the lowest number of sink nodes that cover the whole network. The major aim of MOWOA is to reduce the energy consumption and prolongs the lifetime of LSWSNs. To achieve these objectives, a fitness function has been formulated to decrease energy consumption and maximize the network’s lifetime. The experimental results revealed that the proposed MOWOA achieved a better efficiency in reducing the total power consumption by 26% compared with four well-known optimization algorithms: multi-objective grasshopper optimization algorithm, multi-objective salp swarm algorithm, multi-objective gray wolf optimization, multi-objective particle swarm optimization over all networks sizes.
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The elephant herding optimization (EHO) algorithm is a relatively novel population-based optimization technique, which mimics herding behavior and can be modeled into two operators: clan updating operators and separating operators. Also, in the literature, EHO has received a great deal of attention from researchers since it was proposed applied to many application fields for its advantages of excellent global optimization ability and ease of implementation. However, there is still an insufficiency in the EHO algorithm regarding its lack of exploitation, which leads to slow convergence. In this paper, we propose three enhanced versions of EHO based on the $\gamma$ value termed EEHO15, EEHO20, and EEHO25 to overcome the problems of fast unjustified convergence toward the origin of the basic EHO. The exploration/exploitation abilities of the EEHO algorithms are achieved by the updating of the two operators (clan and separation operator). To tackle this drawback, a constant function is used as a benchmark for inspecting the biased convergence of evolutionary algorithms in general. Moreover, we utilize CEC’17 test suite benchmark functions to test the performance of the proposed three versions of EEHO against EHO, particle swarm optimization (PSO), bird swarm algorithm (BSA), and ant lion optimizer (ALO) algorithms. Eventually, the experimental results revealed that the proposed EEHO algorithms extremely obtained better results compared with other competitive algorithms.
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Nodes localization in a wireless sensor network (WSN) aims for calculating the coordinates of unknown nodes with the assist of known nodes. The performance of a WSN can be greatly affected by the localization accuracy. In this paper, a node localization scheme is proposed based on a recent bioinspired algorithm called Salp Swarm Algorithm (SSA). The proposed algorithm is compared to well-known optimization algorithms, namely, particle swarm optimization (PSO), Butterfly optimization algorithm (BOA), firefly algorithm (FA), and grey wolf optimizer (GWO) under different WSN deployments. The simulation results show that the proposed localization algorithm is better than the other algorithms in terms of mean localization error, computing time, and the number of localized nodes.
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Grey Wolf Optimizer (GWO) is a very efficient metaheuristic inspired by the hierarchy of the Canis-lupus wolves. It has been extensively employed to a variety of practical applications. Crow Search Algorithm (CSA) is a recently proposed metaheuristic algorithm which mimics the intellectual conduct of crows. In this paper, a hybrid GWO with CSA, namely GWOCSA is proposed which combines the strengths of both the algorithms effectively with the aim to generate promising candidate solutions in order to achieve global optima efficiently. In order to validate the competence of the proposed hybrid GWOCSA, a widely utilized set of 23 benchmark test functions having a wide range of dimensions and varied complexities, is used in this study. The results obtained by the proposed algorithm are compared with ten other algorithms in the literature for verification. The statistical results demonstrate that the GWOCSA outperforms other algorithms including the recent variants of GWO called Enhanced Grey Wolf Optimizer (EGWO) and Augmented Grey Wolf Optimizer (AGWO) in terms of high local optima avoidance ability and fast convergence speed. Furthermore, in order to demonstrate the applicability of the proposed algorithm at solving complex real-world problems, GWOCSA is also employed to solve the feature selection problem as well. The GWOCSA as feature selection approach is tested on 21 widely employed data sets acquired from the University of California at Irvine (UCI) repository. The experimental results are compared to the state-of-the-art feature selection techniques including the native GWO, EGWO and AGWO. The results reveal that the GWOCSA has comprehensive superiority in solving feature selection problem which proves the capability of the proposed algorithm in solving real-world complex problems.
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Effective feature selection determines the efficiency and accuracy of a learning process, which is essential in human activity recognition. In existing works, for simplification purposes, feature selection algorithms are mostly based on the assumption of feature independence. However, in some scenarios, the optimization method based on this independence hypothesis results in poor recognition performance. This article proposes a correlation-based binary particle swarm optimization method for feature selection in human activity recognition. In the proposed algorithm, the particle swarm optimization algorithm is no longer used as a black box. Meanwhile, correlation coefficients among the features are added to binary particle swarm optimization as a feature correlation factor to determine the position of particles, so that the feature with more information is more likely to be selected. The k-nearest neighbor classifier is then used as the fitness function in the particle swarm optimization to evaluate the performance of the feature subset, that is, feature combination with the highest k-nearest neighbor classifier recognition rate would be picked as the eigenvector. Experimental results show that the proposed method can work well with six classifiers, namely, J48, random forest, k-nearest neighbor, multilayer perceptron, naïve Bayesian, and support vector machine, and the new algorithm can improve the classification accuracy in the OPPORTUNITY Activity Recognition dataset.
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Grasshopper Optimization Algorithm (GOA) was modified in this paper, to optimize multi-objective problems, and the modified version is called Multi-Objective Grasshopper Optimization Algorithm (MOGOA). An external archive is integrated with the GOA for saving the Pareto optimal solutions. The archive is then employed for defining the social behavior of the GOA in the multi-objective search space. To evaluate and verify the effectiveness of the MOGOA, a set of standard unconstrained and constrained test functions are used. Moreover, the proposed algorithm was compared with three well-known optimization algorithms: Multi-Objective Particle Swarm Optimization (MOPSO), Multi-Objective Ant Lion Optimizer (MOALO), and Non-dominated Sorting Genetic Algorithm version 2 (NSGA-II); and the obtained results show that the MOGOA algorithm is able to provide competitive results and outperform other algorithms.
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This paper proposes a hybrid Electroencephalogram (EEG) classification approach based on grey wolf optimizer (GWO) enhanced support vector machines (SVMs) called GWO-SVM approach for automatic seizure detection. In order to decompose EEG into five sub-band components, the discrete wavelet transform (DWT) was utilized to extracted features set. Then, this features are used to train the SVM with radial basis function (RBF) kernel function. Further, GWO was used for selecting the significant feature subset and the optimal parameters of SVM in order to obtain a successful EEG classification. The experimental results proved that the proposed GWO-SVM approach, able to detect epileptic and could thus further enhance the diagnosis of epilepsy with accuracy 100%. Furthermore, the proposed approach has been compared with genetic algorithm (GA) with support vector machines (GA-SVMs) and SVM using RBF kernel function. The computational results reveal that GWO-SVM approach achieved better classification accuracy outperforms both GA-SVM and typical SVMs.
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This research work focus on the multiple sequence alignment, as developing an exact multiple sequence alignment for different protein sequences is a difficult computational task. In this research, a hybrid algorithm named Bacterial Foraging Optimization-Genetic Algorithm (BFO-GA) algorithm is aimed to improve the multi-objectives and carrying out measures of multiple sequence alignment. The proposed algorithm employs multi-objectives such as variable gap penalty minimization, maximization of similarity and non-gap percentage. The proposed BFO-GA algorithm is measured with various MSA methods such as T-Coffee, Clustal Omega, Muscle, K-Align, MAFFT, GA, ACO, ABC and PSO. The experiments were taken on four benchmark datasets such as BAliBASE 3.0, Prefab 4.0, SABmark 1.65 and Oxbench 1.3 databases and the outcomes prove that the proposed BFO-GA algorithm obtains better statistical significance results as compared with the other well-known methods. This research study also evaluates the practicability of the alignments of BFO-GA by applying the optimal sequence to predict the phylogenetic tree by using ClustalW2 Phylogeny tool and compare with the existing algorithms by using the Robinson-Foulds (RF) distance performance metric. Lastly, the statistical implication of the proposed algorithm is computed by using the Wilcoxon Matched-Pair Signed- Rank test and also it infers better results.
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This work proposes a new multi-objective algorithm inspired from the navigation of grass hopper swarms in nature. A mathematical model is first employed to model the interaction of individuals in the swam including attraction force, repulsion force, and comfort zone. A mechanism is then proposed to use the model in approximating the global optimum in a single-objective search space. Afterwards, an archive and target selection technique are integrated to the algorithm to estimate the Pareto optimal front for multi-objective problems. To benchmark the performance of the algorithm proposed, a set of diverse standard multi-objective test problems is utilized. The results are compared with the most well-regarded and recent algorithms in the literature of evolutionary multi-objective optimization using three performance indicators quantitatively and graphs qualitatively. The results show that the proposed algorithm is able to provide very competitive results in terms of accuracy of obtained Pareto optimal solutions and their distribution.
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A hybrid novel meta-heuristic optimization algorithm termed Whale Optimization Algorithm (WOA) and Support Vector Machines (SVMs) to obtain an Electroencephalogram (EEG) classification approach was proposed here in this paper for automatic seizure detection termed WOA-SVM. In the proposed approach, the Discrete Wavelet Transform (DWT) was applied to extract the main features and then decompose it into four level of decomposition tree. Furthermore, WOA was utilized to find the more significant feature subset of EEG from a larger feature pool as well as to enhance the parameters of SVM classifier. In order to detect epileptic, SVM with a Radial Basis kernel Function (RBF) was applied. Eventually, the proposed WOA-SVM approach is able to enhance the diagnosis of epilepsy as revealed from the statistical results with accuracy 100% for normal subject data versus epileptic data.
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Since there are some special constraints in a real foundry enterprise, including the limitation of starting time in some casting operations and the transportation time between two adjacent operations, processing interval constraint (PIC) and job transportation time (JTT) are introduced in this paper. With the consideration of PIC and JTT, a multi-objective casting production scheduling model is constructed to minimize makespan, the total production cost and the total delivery delay time. A hybrid discrete multi-objective grey wolf optimizer (HDMGWO) is developed to solve this model. An initialization strategy based on reducing job transportation time and processing time (RTP) are designed to improve the quality of initial population. A improved tabu search (ITS) algorithm is embedded into grey wolf optimizer (GWO) to overcome the premature convergence of the GWO. A modified search operator of GWO is designed to tackle discrete combinatorial optimization. A case example of the real foundry enterprise is illustrated to evaluate the effectiveness of proposed HDMGWO. Experimental results demonstrate that the proposed HDMGWO is superior in terms of the quality of solutions compared to five multi-objective algorithms. Real running in a casting ERP system verifies the applicability of the proposed scheduling model and the HDMGWO.
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In this paper, we propose a new hybrid population-based meta-heuristics algorithm inspired by grey wolves in order to solve integer programming and minimax problems. The proposed algorithm is called Multidirectional Grey Wolf Optimizer (MDGWO) algorithm. In the proposed algorithm, we try to accelerate the standard grey wolf optimizer algorithm (GWO) by invoking the multidirectional search method with it in order to accelerate the search instead of letting the standard GWO run for more iterations without significant improvement in the results. MDGWO starts the search by applying the standard GWO search for a number of iterations, and then the best-obtained solution is passed to the multidirectional search method as an intensification process in order to accelerate the search and overcome the slow convergence of the standard GWO algorithm. We test MDGWO algorithm on seven integer programming problems and 10 minimax problems. Moreover, we compare against 11 algorithms for solving integer programming problems and 10 algorithms for solving minimax problems. Furthermore, we show the efficiency of the proposed algorithm and its ability to solve integer and minimax optimization problems in reasonable time by giving several results of the experiments.
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To overcome the limitation of single search strategy of grey wolf optimizer (GWO) in solving various function optimization problems, we propose a multi-strategy ensemble GWO (MEGWO) in this paper. The proposed MEGWO incorporates three different search strategies to update the solutions. Firstly, the enhanced global-best lead strategy can improve the local search ability of GWO by fully exploiting the search space around the current best solution. Secondly, the adaptable cooperative strategy embeds one-dimensional update operation into the framework of GWO to provide a higher population diversity and promote the global search ability. Thirdly, the disperse foraging strategy forces a part of search agents to explore a promising area based on a self-adjusting parameter, which contributes to the balance between the exploitation and exploration. We conducted numerical experiments based on various functions form CEC2014. The obtained results are compared with other three modified GWO and seven state-of-the-art algorithms. Furthermore, feature selection is employed to investigate the effectiveness of MEGWO on real-world applications. The experimental results show that the proposed algorithm which integrate multiple improved search strategies, outperforms other variants of GWO and other algorithms in terms of accuracy and convergence speed. It is validated that MEGWO is an efficient and reliable algorithm not only for optimization of functions with different characteristics but also for real-world optimization problems.
Article
The bat algorithm (BA) has been shown to be effective to solve a wider range of optimization problems. However, there is not much theoretical analysis concerning its convergence and stability. In order to prove the convergence of the bat algorithm, we have built a Markov model for the algorithm and proved that the state sequence of the bat population forms a finite homogeneous Markov chain, satisfying the global convergence criteria. Then, we prove that the bat algorithm can have global convergence. In addition, in order to enhance the convergence performance of the algorithm and to identify the possible effect of parameter settings on convergence, we have designed an updated model in terms of a dynamic matrix. Subsequently, we have used the stability theory of discrete-time dynamical systems to obtain the stable parameter ranges for the algorithm. Furthermore, we use some benchmark functions to demonstrate that BA can indeed achieve global optimality efficiently for these functions.
Article
This paper proposes a novel optimization algorithm, called Emperor Penguin Optimizer (EPO), which mimics the huddling behavior of emperor penguins (Aptenodytes forsteri). The main steps of EPO are to generate the huddle boundary, compute temperature around the huddle, calculate the distance, and find the effective mover. These steps are mathematically modeled and implemented on 44 well-known benchmark test functions. It is compared with eight state-of-the-art optimization algorithms. The paper also considers for solving six real-life constrained and one unconstrained engineering design problems. The convergence and computational complexity are also analyzed to ensure the applicability of proposed algorithm. The experimental results show that the proposed algorithm is able to provide better results as compared to the other well-known metaheuristic algorithms.
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This paper proposes an improved version of the grasshopper optimization algorithm (GOA) based on the opposition-based learning (OBL) strategy called OBLGOA for solving benchmark optimization functions and engineering problems. The proposed OBLGOA algorithm consists of two stages: the first stage generates an initial population and its opposite using the OBL strategy; and the second stage uses the OBL as an additional phase to update the GOA population in each iteration. However, the OBL is applied to only half of the solutions to reduce the time complexity. To investigate the performance of the proposed OBLGOA, six sets of experiment series are performed, and they include twenty-three benchmark functions and four engineering problems. The experiments revealed that the results of the proposed algorithm were superior to those of ten well-known algorithms in this domain. Eventually, the obtained results proved that the OBLGOA algorithm can provide competitive results for optimization engineering problems compared with state-of-the-art algorithms.
Conference Paper
Vehicle Routing Problem with Time Windows (VRPTW) is known as scheduling problems of vehicles with a time interval which the extensions of VRP. The problem discuss the distribution of products between a depot and customers. This paper proposes a hybrid algorithm between Cat Swarm Optimization (CSO) and Crow Search (CS) to solve VRPTW. The CS algorithm helps the complexity of CSO algorithm to obtain the best solution. The memorized procedure of CS is applied in CSO. Simulation results show that CSO-CS algorithm is an alternative procedure for solving VRPTW. The better performance is obtained when number of population increased and the cdc decreased
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Photovoltaic (PV) installations are consistently increasing all over the world, leading to a high penetration to the electric grid. Tremendous efforts should be exerted to maintain the operation of the PV systems at optimal conditions. This paper introduces an optimal control strategy with the purpose of enhancing the performance of PV systems. This control strategy is based on the proportional-integral (PI) controller, which is designed by using the whale optimization algorithm (WOA). The response surface methodology (RSM) model is established to create the objective function and its constraints. The proposed WOAbased PI controllers are utilized to control the DC chopper and grid-side inverter in order to achieve a maximum power point tracking operation and improve the dynamic voltage response of the PV system, respectively. The effectiveness of the control strategy is tested under different operating conditions of the PV system such as (1) subject the system to symmetrical and unsymmetrical fault conditions, (2) study the system responses under different irradiation and temperature conditions using real data extracted from a field test, and (3) subject the system to a sudden load disturbance in an autonomous operation. This effectiveness is compared with that achieved using the generalized reduced gradient (GRG) algorithmbased PI controller. The validity of the proposed control strategy is extensively verified by the simulation results, which are performed using PSCAD/EMTDC environment.
Conference Paper
Distributed generation (DG) systems achieve an important role in electrical power networks due to their technical and economic benefits. This paper presents a novel application of the Crow Search Algorithm (CSA) with purpose of enhancing the performance of an inverter-based DG system. The control strategy of the inverter is based on a vector cascaded control scheme, which relies on the Proportional plus Integral (PI) controller. The proposed CSA is utilized to fine tune the PI controller parameters. The response surface methodology (RSM) is used to create the objective and constraint function of the optimization problem. The validity of the proposed control strategy is extensively verified using the simulation results, which are performed using PSCAD/EMTDC environment. These simulation results are investigated under different operating conditions such as 1) transition of the system from grid connected to islanded mode of operation, and 2) subject the system to a single line to ground fault in the autonomous mode. The effectiveness of the proposed controller is verified by comparing its results with that obtained using the genetic algorithm-based PI controller.
Conference Paper
The combined economic and emission dispatch (CEED) problem is a multi-objective non-linear optimization problem with several constraints. Its target is searching for optimum generation outputs of available generating units in a power system to supply the electrical loads and transmission losses at minimum generation costs combined with minimum pollutant emissions. To achieve an optimal solution for this problem, this paper proposes an application of a new meta-heuristic optimizer called crow search algorithm (CSA). CSA is inspired from the intelligent attitude of crows. It is very simple since it has only two adjustable parameters. The CSA is employed and developed in MATLAB for solving the CEED problem. It is applied to four test systems consisting of three thermal generators, the standard IEEE 30-bus model system, ten and forty thermal generators. A comparison between the developed CSA and other optimization algorithms such as particle swarm optimization (PSO), genetic algorithm (GA) and hybrid genetic algorithm (HGA) is executed in terms of solution equality and computation efficiency. Simulation results demonstrate clearly the effectiveness of the proposed CSA in solving the CEED problem since its obtained solution is faster and more efficient than that obtained by using other techniques.
Conference Paper
The increasing size of chemical search space of compound databases and importance of similarity measurements to drug discovery are main factors in chemical studies and research. In this paper, we propose a feature selection strategy using a Salp Swarm Algorithm (SSA) for predicting chemical activity. The K-nearest neighbor (KNN) was utilized for the fitness function of SSA. Also, we evaluated our proposed approach on a chemical dataset with a huge number of descriptors (attributes). The results were compared with other five well-known algorithms namely particle swarm optimization (PSO), Grasshopper Optimization Algorithm (GOA), Grey Wolf Optimizer(GWO), Sine Cosine Algorithm (SCA), Whale Optimization algorithm (WOA) using three initialization method and a superior accuracy was obtained with our proposed approach. In addition, in comparison with other algorithms that used the same data, our approach has a higher performance using less number of features.
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Classification accuracy highly dependents on the nature of features in a dataset which may contain irrelevant or redundant data. The main aim of feature selection is to eliminate these types of features to enhance the classification accuracy. The wrapper feature selection model works on the feature set to reduce the number of features and improve the classification accuracy simultaneously. In this work, a new wrapper feature selection approach is proposed based on Whale Optimization Algorithm (WOA). WOA is a newly proposed algorithm that has not been applied to feature selection problem yet. In this work, two binary variants of the WOA algorithm are proposed for the first time to search the optimal feature subsets for classification purposes. In the first one, we aim to study the influence of using the Tournament and Roulette Wheel selection mechanisms instead of using a random operator. In the second approach, crossover and mutation operators are used to enhance the exploitation of the WOA algorithm. The proposed methods are tested on standard benchmark datasets and then compared to three algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA), the Ant Lion Optimizer (ALO), and five standard filter feature selection methods. The paper also considers an extensive study of the parameter setting for the proposed technique. The results show the efficiency of the proposed approaches in searching for the optimal feature subsets.
Conference Paper
new Featuer selection method
Chapter
This chapter proposes a new method for determining the multilevel thresholding values for image segmentation. The proposed method considers the multilevel threshold as multi-objective function problem and used the whale optimization algorithm (WOA) to solve this problem. The fitness functions which used are the maximum between class variance criterion (Otsu) and the Kapur’s Entropy. The proposed method uses the whale algorithm to optimize threshold, and then uses this thresholding value to split the image. The experimental results showed the better performance of the proposed method to solving the multilevel thresholding problem for image segmentation and provided faster convergence with a relatively lower processing time.
Article
Optimal reactive power dispatch (ORPD) is a particular case of the optimal power flow. ORPD was usually considered as the minimization of an objective function representing the total active power losses in the electrical networks. The constraints involved are the generator voltages, tap regulating transformers ratios and the amount of reactive shunt compensators. The goal of this study is to find the best vector of control variables, so that the power loss decreasing can be realized. In this paper, a new metaheuristic technique inspired from the bubble-net hunting technique of humpback whales, namely whale optimization algorithm (WOA), has been applied to solve the ORPD problem. The WOA method has been examined and confirmed on the IEEE 14-bus, IEEE 30-bus, in addition to a practical and large scale Algerian electric 114-bus test system. The obtained outcomes have been compared with two own developed methods, namely, particle swarm optimization (PSO) and particle swarm optimization with time varying acceleration coefficients (PSO-TVAC). Afterwards, an analysis of variance (One-way ANOVA test) has been implemented in order to verify the performance of our proposed algorithm in solving the ORPD problem. In summary, the comparison study shows the potential of this recent optimization method, and proves its robustness and effectiveness in solving the ORPD problem.
Article
The work introduces a new methodology to solve multiobjective DER accommodation problem of distribution systems by combining a technique for order of preference by similarity to ideal solution (TOPSIS) and an improved elephant herding optimization (EHO) technique. A complex real-life multiobjective distributed energy resources (DERs) planning problem is formulated and solved using the proposed method. The aim is to determine the optimal sites and sizes of DERs to maximize the overall benefits of utility and consumers. The proposed technique is productively implemented on three small to large-scale benchmark test distribution systems of 33-bus, 118-bus and 880-bus. The optimal solutions obtained are compared with the methods available in the literature. The comparison shows that the proposed optimization method is promising.
Article
In this paper, we propose a new hybrid grey wolf optimizer (G-WO) algorithm with simplex Nelder-Mead method in order to solve integer programming and minimax problems. We call the proposed algorithm a Sim-plex Grey Wolf Optimizer (SGWO) algorithm. In the the proposed SGWO algorithm, we combine the GWO algorithm with the Nelder-Mead method in order to refine the best obtained solution from the standard GWO algorithm. We test it on 7 integer programming problems and 10 minimax problems in order to investigate the general performance of the proposed SGWO algorithm. Also, we compare SGWO with 10 algorithms for solving integer programming problems and 9 algorithms for solving minimax problems. The experiments results show the eﬃciency of the proposed algorithm and its ability to solve integer and minimax optimization problems in reasonable time. © 2017 Federacion Argentina de Cardiologia. All right reserved.