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.
... 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
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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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Inspired by the process of migration and reproduction of flora, this paper proposes a novel artificial flora (AF) algorithm. This algorithm can be used to solve some complex, non-linear, discrete optimization problems. Although a plant cannot move, it can spread seeds within a certain range to let offspring to find the most suitable environment. The stochastic process is easy to copy, and the spreading space is vast; therefore, it is suitable for applying in intelligent optimization algorithm. First, the algorithm randomly generates the original plant, including its position and the propagation distance. Then, the position and the propagation distance of the original plant as parameters are substituted in the propagation function to generate offspring plants. Finally, the optimal offspring is selected as a new original plant through the selection function. The previous original plant becomes the former plant. The iteration continues until we find out optimal solution. In this paper, six classical evaluation functions are used as the benchmark functions. The simulation results show that proposed algorithm has high accuracy and stability compared with the classical particle swarm optimization and artificial bee colony algorithm.
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To overcome the curse of dimensionality problem, a binary variant of the whale optimization algorithm (bWOA) with V-shaped is proposed. A hyperbolic tangent function is employed as a fitness function for mapping the continuous values to binary ones. Feature selection (FS) has attracted much attention in recent years and played a critical role in dealing with high-dimensional problems and can be modeled as an optimization problem. Eleven datasets from UCI repository from various applications are used. During the experiments, the effectiveness of feature selection is tested via a different type of data and size of features in the generic dataset. Furthermore, Wilcoxon’s rank-sum nonparametric statistical test was carried out at 5\% significance level to judge whether the results of the proposed algorithms differ from those of the other compared algorithms in a statistically significant way. The quantitative and qualitative results revealed that the proposed binary algorithm in the FS domain is capable of minimizing the number of selected features as well as maximizing the classification accuracy within an appropriate time.
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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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Since the introduction of cellular automata in the late 1940s they have been used to address various types of problems in computer science and other multidisciplinary fields. Their generative capabilities have been used for simulating and modelling various natural, physical and chemical phenomena. Besides these applications, the lattice grid of cellular automata has been providing a by-product interface to generate graphical contents for digital art creation. One important aspect of cellular automata is symmetry, detecting of which is often a difficult task and computationally expensive. In this paper a swarm intelligence algorithm—Stochastic Diffusion Search—is proposed as a tool to identify points of symmetry in the cellular automata-generated patterns.
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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.
Article
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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Article
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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.
Article
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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.
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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.
Article
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.
Article
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.
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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.
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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.
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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.
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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.