Opposition-based Learning Method Research Articles

Mantis Search Algorithm Integrated with Opposition-Based Learning and Simulated Annealing for Feature Selection

Feature selection (FS) plays a vital role in minimizing the high-dimensional data as much as possible to aid in enhancing the classification accuracy and reducing computational costs. The purpose of the FS techniques is to extract the most effective subset features, which might enable the machine learning (ML) algorithms to better grasp the input data’s patterns and improve their classification performance. Although several metaheuristic algorithms have been recently presented to solve this problem, they still suffer from several disadvantages, such as getting stuck in local optima, slow convergence speed, and a lack of population diversity, which prevent them from achieving the desired solutions in an acceptable time. Therefore, this study is presented to propose a new feature selection approach, namely OBMSASA, based on integrating the recently published mantis search algorithm with the opposition-based learning (OBL) method and simulated annealing (SA) to strengthen its exploration and exploitation operators. The OBL method aims to improve the exploration operator, making the algorithm able to avoid stagnation into local minima; meanwhile, the SA is used as a local search to further strengthen the exploration operator, thereby improving the convergence speed. The K-nearest neighbor algorithm is used to compute the accuracy of the selected feature. The proposed algorithm is assessed using 21 common datasets and compared to several rival optimizers in terms of several performance metrics, including convergence curve, average fitness, computational cost, length of selected features, and standard deviation, to observe its effectiveness and efficiency. The source code is publicly accessible at https://drive.mathworks.com/OBMSASA.

An improved golden jackal optimization algorithm for combined economic emission dispatch problems

In this research paper, a new improved golden jackal optimization (IGJO) algorithm is applied to address the combined economic emission dispatch (CEED) problem, along with various thermal generator constraints such as valve point loading (VPL) effect, generator limits (GL) in power system. The hunting behavior of the golden jackals is mimicked in the golden jackal optimization (GJO) algorithm. The main aim of the CEED problem is to find the best optimal generation scheduling while minimizing both fuel cost and emission besides meeting the different power system constraints. The original GJO algorithm faces challenges when dealing with high-dimensional optimization problems, as it tends to get trapped in local optima. To address this issue the opposition-based learning (OBL) method was adopted in this GJO algorithm to obtain the global optimal solution and ensure enhanced performance in finding the solution for the CEED problems. To assess the competitiveness of the IGJO algorithm, it is used for various CEED test problems available in the literature, and results are contrasted with other recent heuristic optimization algorithms. Simulation results show that the proposed IGJO performs more effectively than the other compared algorithms in terms of solution quality, and robustness.

A hybrid particle swarm optimization algorithm for solving engineering problem

To overcome the disadvantages of premature convergence and easy trapping into local optimum solutions, this paper proposes an improved particle swarm optimization algorithm (named NDWPSO algorithm) based on multiple hybrid strategies. Firstly, the elite opposition-based learning method is utilized to initialize the particle position matrix. Secondly, the dynamic inertial weight parameters are given to improve the global search speed in the early iterative phase. Thirdly, a new local optimal jump-out strategy is proposed to overcome the "premature" problem. Finally, the algorithm applies the spiral shrinkage search strategy from the whale optimization algorithm (WOA) and the Differential Evolution (DE) mutation strategy in the later iteration to accelerate the convergence speed. The NDWPSO is further compared with other 8 well-known nature-inspired algorithms (3 PSO variants and 5 other intelligent algorithms) on 23 benchmark test functions and three practical engineering problems. Simulation results prove that the NDWPSO algorithm obtains better results for all 49 sets of data than the other 3 PSO variants. Compared with 5 other intelligent algorithms, the NDWPSO obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function (f1-f13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${f}_{1}-{f}_{13}$$\\end{document}) with 3 kinds of dimensional spaces (Dim = 30,50,100) and 80% of the best optimal solutions for 10 fixed-multimodal benchmark functions. Also, the best design solutions are obtained by NDWPSO for all 3 classical practical engineering problems.

Fault diagnosis of rolling bearing based on SEMD and ISSA-KELMC

Enhancing the operational reliability of rotary machinery relies significantly on the effective diagnosis of faults in rolling bearings. This study introduces an innovative method to improve the accuracy of fault diagnosis of rolling bearings during operation. First, we propose a sine empirical mode decomposition (SEMD) designed to effectively mitigate mode mixing and decompose the vibration signals of rolling bearings into a series of intrinsic mode functions. Subsequently, we constructed and optimized a kernel extreme learning machine classifier (KELMC) using the improved sparrow search algorithm (ISSA). Within ISSA, the opposition-based Learning method is refined and applied to enhance the optimization performance of the sparrow search algorithm. Finally, the paper presents a novel method for the fault diagnosis of rolling bearings based on SEMD and ISSA-KELMC, which can effectively extract the fault features and accurately recognize the fault types of rolling bearings by taking advantage of the SEMD and ISSA-KELMC. The effectiveness of the proposed method was verified through two simulation and fault diagnosis experiments. The results demonstrated the efficiency of the method in diagnosing faults in rolling bearings under both consistent and variable working conditions. This approach is valuable for fault diagnosis and condition monitoring of rotating machinery.

GAN with opposition-based blocks and channel self-attention mechanism for image synthesis

Recently, image synthesis has always been a research hotspot in the field of deep learning. Generally, the methods based on generative adversarial networks (GANs) directly feed the semantic layout as input to obtain the photorealistic images for image synthesis. However, these methods based on GANs have not achieved satisfactory reconstructed results in quality. One of the main reasons is that the normalization layers in these methods will cause the loss of the semantic information. Another of the main reason is that the information contained in the semantic layout is sparse. In order to solve the above problems, GAN with opposition-based blocks and channel self-attention mechanism (OCGAN) is proposed. In OCGAN, the opposition-based learning method and the proposed adaptive normalization method are used to design the opposition-based blocks (OB Blks). The proposed channel self-attention mechanism (CSAM) is employed to give different focus to each channel of the semantic layout. The generator of OCGAN uses the opposition-based blocks and the channel self-attention mechanism to maintain and capture the important details from the semantic layouts. Experiments on several challenging datasets demonstrate the advantages of our method over existing approaches, regarding both visual quality and the representative evaluating criteria.

Hybrid Harmony Search Optimization Algorithm for Continuous Functions

This paper proposes a hybrid harmony search algorithm that incorporates a method of reinitializing harmonies memory using a particle swarm optimization algorithm with an improved opposition-based learning method (IOBL) to solve continuous optimization problems. This method allows the algorithm to obtain better results by increasing the search space of the solutions. This approach has been validated by comparing the performance of the proposed algorithm with that of a state-of-the-art harmony search algorithm, solving fifteen standard mathematical functions, and applying the Wilcoxon parametric test at a 5% significance level. The state-of-the-art algorithm uses an opposition-based improvement method (IOBL). Computational experiments show that the proposed algorithm outperforms the state-of-the-art algorithm. In quality, it is better in fourteen of the fifteen instances, and in efficiency is better in seven of fifteen instances.

Path Planning for Unmanned Delivery Robots Based on EWB-GWO Algorithm.

With the rise of robotics within various fields, there has been a significant development in the use of mobile robots. For mobile robots performing unmanned delivery tasks, autonomous robot navigation based on complex environments is particularly important. In this paper, an improved Gray Wolf Optimization (GWO)-based algorithm is proposed to realize the autonomous path planning of mobile robots in complex scenarios. First, the strategy for generating the initial wolf pack of the GWO algorithm is modified by introducing a two-dimensional Tent-Sine coupled chaotic mapping in this paper. This guarantees that the GWO algorithm generates the initial population diversity while improving the randomness between the two-dimensional state variables of the path nodes. Second, by introducing the opposition-based learning method based on the elite strategy, the adaptive nonlinear inertia weight strategy and random wandering law of the Butterfly Optimization Algorithm (BOA), this paper improves the defects of slow convergence speed, low accuracy, and imbalance between global exploration and local mining functions of the GWO algorithm in dealing with high-dimensional complex problems. In this paper, the improved algorithm is named as an EWB-GWO algorithm, where EWB is the abbreviation of three strategies. Finally, this paper enhances the rationalization of the initial population generation of the EWB-GWO algorithm based on the visual-field line detection technique of Bresenham's line algorithm, reduces the number of iterations of the EWB-GWO algorithm, and decreases the time complexity of the algorithm in dealing with the path planning problem. The simulation results show that the EWB-GWO algorithm is very competitive among metaheuristics of the same type. It also achieves optimal path length measures and smoothness metrics in the path planning experiments.

Locality sensitive hashing-driven multifactorial evolutionary algorithms for multitask optimization

In recent years, evolutionary multitasking optimization (EMTO) has attracted considerable attention. Different from the traditional algorithms that solve one optimization problem at a time, EMTO aims at solving multiple problems simultaneously, through transferring useful information among individuals. The most well-known algorithm in this area is the multifactorial evolutionary algorithm (MFEA). However, when designing the information sharing mechanism, MFEA and its variants focus solely on the properties of individuals in the objective space, while neglecting the valuable information in the decision space. To make full use of the inherent knowledge of the evolving population, this paper presents a novel EMTO framework by using the locality sensitive hashing (LSH) method to analyze the population distribution in the decision space and then guide the information sharing. Specifically, LSH uses hash functions to map the individuals in the decision space into hash codes, ensuring that similar individuals have a higher probability to be mapped into the same code. Then, based on the matching relationships of the hash codes and skill factors between individuals, different reproduction and evaluation strategies are exerted to satisfy the specific requirements under different conditions. This way, the knowledge from both the decision space and the objective space are utilized for the purpose of better manipulating the individuals. Additionally, an opposition-based learning method is integrated in this algorithm to enhance exploration. The comprehensive experimental studies confirm the efficacy and efficiency of the proposed method on both single-objective multitask benchmarks and multi-objective multitask benchmarks. According to the statistic tests, the proposed single-objective and multi-objective algorithms significantly outperform their best competitors on 14/18 and 12/18 tasks, respectively.

An opposition-based differential evolution clustering algorithm for emotional preference and migratory behavior optimization

Clustering has grown to be a research focus in recent years owing to the challenges of labeling massive collected data. Recent advances such as the emotional preference and migratory behavior clustering model jointly utilized the biogeography-based idea and inertia theorem for handling data clustering tasks. However, as with most clustering methods, the initialization for the solution is often purely random. Moreover, the search results vulnerably converge to local optima due to favorable exploration but short exploitation, which requires an additional process to balance them effectively. Inspired by the differential evolution (DE) strategy and the opposition-based learning (OBL) method, the paper proposed a novelty opposition-based differential evolution clustering algorithm for emotional preference and migratory behavior optimization named OBDE-EPMC. Specifically, we first utilize the OBL method to initialize the population to obtain a closer initial individual to the optimal solution. Thereafter, to ensure population diversity during the optimization, we applied the differential evolution (DE) strategy to expand the scope of the solution and the opposition-based learning method to generate an opposite one. Lastly, the historical solution scheme is added to retain the excellent solution within the population. In addition, the theoretical analysis and convergence property proof of OBDE-EPMC are presented. Numerous experiments were performed to compare the proposed OBDE-EPMC with the other seven clustering algorithms on a host of standard datasets. And several standards demonstrate the rationality and effectiveness of our proposed OBDE-EPMC algorithm.

Multi-workflow scheduling and resource provisioning in Mobile Edge Computing using opposition-based Marine-Predator Algorithm

Workflow Scheduling in Mobile Edge Computing (MEC) tries to allocate the best possible set of resources for the workflows, considering objectives such as deadline, cost, energy, Quality of Service (QoS), and so on. However, MEC may be under different workloads from the IoT and this may not have the required amount of resources to efficiently handle the workflows. To mitigate this problem, in this paper, we use proactive resource provisioning and workload prediction methods. For this purpose, we present a workload prediction method using a multilayer feed-forward Artificial Neural Network (ANN) model and apply its results for resource provisioning. Afterward, we present an opposition-based version of the Marine-Predator Algorithm (MPA) algorithm, denoted as OMPA. In this algorithm, we present a probabilistic opposition-based learning (OBL) method, which benefits from the OBL, Quasi OBL, and dynamic OBL methods. Afterward, the OMPA algorithm is used for training the multi-layer feed-forward ANN model and multi-workflow scheduling by taking into account factors such as the makespan and number of Virtual Machines (VMs). Extensive experiments conducted in the iFogSim simulator and on the NASA and Saskatchewan datasets indicate that the proposed scheme can achieve better results compared to other metaheuristic algorithms and scheduling schemes.

A Modified Whale Optimization Algorithm and Its Application in Seismic Inversion Problem

The whale optimization algorithm (WOA) is a popular swarm intelligence algorithm which simulates the hunting behavior of humpback whales. WOA has the deficiency of easily falling into the local optimal solutions. In order to overcome the weakness of the WOA, a modified variant of WOA called OCDWOA is proposed. There are four main operators introduced into the OCDWOA to enhance the search performance of WOA. The operators include opposition-based learning method, nonlinear parameter design, density peak clustering strategy, and differential evolution. The proposed algorithm is tested on 19 optimization benchmark functions and a seismic inversion problem. OCDWOA is compared with the classical WOA and three typical variants of WOA. The results demonstrate that OCDWOA outperforms the compared algorithms in terms of obtaining the global optimal solution.

Accurate Photovoltaic Models Based on an Adaptive Opposition Artificial Hummingbird Algorithm

The greater the demand for energy, the more important it is to improve and develop permanent energy sources, because of their advantages over non-renewable energy sources. With the development of artificial intelligence algorithms and the presence of so many data, the evolution of simulation models has increased. In this research, an improvement to one recent optimization algorithm called the artificial hummingbird algorithm (AHA) is proposed. An adaptive opposition approach is suggested to select whether or not to use an opposition-based learning (OBL) method. This improvement is developed based on adding an adaptive updating mechanism to enable the original algorithm to obtain more accurate results with more complex problems, and is called the adaptive opposition artificial hummingbird algorithm (AOAHA). The proposed AOAHA was tested on 23 benchmark functions and compared with the original algorithm and other recent optimization algorithms such as supply–demand-based optimization (SDO), wild horse optimizer (WHO), and tunicate swarm algorithm (TSA). The proposed algorithm was applied to obtain accurate models for solar cell systems, which are the basis of solar power plants, in order to increase their efficiency, thus increasing the efficiency of the whole system. The experiments were carried out on two important models—the static and dynamic models—so that the proposed model would be more representative of real systems. Two applications for static models have been proposed: In the first application, the AOAHA satisfies the best root-mean-square values (0.0009825181). In the second application, the performance of the AOAHA is satisfied in all variable irradiance for the system. The results were evaluated in more than one way, taking into account the comparison with other modern and powerful optimization techniques. Improvement showed its potential through its satisfactory results in the tests that were applied to it.

Short-Term Photovoltaic Power Prediction Based on Similar Days and Improved SOA-DBN Model

Existing methods in predicting short-term photovoltaic (PV) power have low accuracy and cannot satisfy actual demand. Thus, a prediction model based on similar days and seagull optimization algorithm (SOA) is proposed to optimize a deep belief network (DBN). Fast correlation-based filter (FCBF) method is used to select a meteorological feature set with the best correlation with PV output and avoid redundancy among meteorological factors affecting PV output. In addition, a comprehensive similarity index combining European distance and gray correlation degree is proposed to select the similar day. Then, SOA is used to optimize the number of neurons and the learning rate parameters in DBN. Based on the nonuniform mutation and opposition-based learning method, an improved seagull optimization algorithm (ISOA) with higher optimization accuracy is proposed. Finally, the ISOA-DBN prediction model is established, and the experimental analysis is conducted using the actual data of PV power stations in Australia. Results show that compared with DBN, support vector machine (SVM), extreme learning machine (ELM), radial basis function (RBF), Elman, and back propagation (BP), the mean absolute percentage error indicator of ISOA-DBN is only 1.512% on a sunny day, 5.975 on a rainy day, 3.359 on a cloudy to sunny day, and 1.911% on a sunny to cloudy day. Therefore, the good accuracy of the proposed model is verified.

An Improved Water Strider Algorithm for Optimal Design of Skeletal Structures

Water Strider Algorithm (WSA) is a new metaheuristic method that is inspired by the life cycle of water striders. This study attempts to enhance the performance of the WSA in order to improve solution accuracy, reliability, and convergence speed. The new method, called improved water strider algorithm (IWSA), is tested in benchmark mathematical functions and some structural optimization problems. In the proposed algorithm, the standard WSA is augmented by utilizing an opposition-based learning method for the initial population as well as a mutation technique borrowed from the genetic algorithm. By employing Generalized Space Transformation Search (GSTS) as an opposition-based learning method, more promising regions of the search space are explored; therefore, the precision of the results is enhanced. By adding a mutation to the WSA, the method is helped to escape from local optimums which is essential for engineering design problems as well as complex mathematical optimization problems. First, the viability of IWSA is demonstrated by optimizing benchmark mathematical functions, and then it is applied to three skeletal structures to investigate its efficiency in structural design problems. IWSA is compared to the standard WSA and some other state-of-the-art metaheuristic algorithms. The results show the competence and robustness of the IWSA as an optimization algorithm in mathematical functions as well as in the field of structural optimization.

Multi-criteria HPC task scheduling on IaaS cloud infrastructures using meta-heuristics

With the rapid increase in the use of cloud computing systems, an efficient task scheduling policy, which deals with the assignment of tasks to resources, is required to obtain maximum performance. Cloud task scheduling (CTS) is an established NP-Hard optimization problem that can be effectively tackled with meta-heuristic algorithms. The cuckoo search (CS) algorithm is a powerful swarm-intelligence meta-heuristic that has been successfully applied over a wide-range of real-life optimization problems, including task scheduling problems. Besides its strong exploration ability, the CS algorithm suffers from insufficient local search, lack of solution diversity towards the end, and slow convergence problem. These drawbacks produce inefficient cloud task schedules resulting in sub-optimal performance. In this manuscript, an improved CS-based scheduling algorithm called CSDEO is introduced, which combines the features of the Opposition-based learning (OBL) method, Cuckoo search, and Differential evolution (DE) algorithms to optimize workload makespan and energy consumption of the cloud resources. Our CSDEO algorithm firstly uses the OBL method to produce an optimal initial population by providing solutions across the entire solution space. Then, the CSDEO uses an effective way of switching between the CS exploration phase and the DE exploitation phase, depending on each solution's fitness. Experiments are conducted on the CloudSim simulator by using the CEA-Curie and HPC2N supercomputing workloads. The observations show that in the case of CEA-Curie workloads, the proposed CSDEO algorithm achieves makespan improvement in the range of 6.29–29.76% and energy consumption improvement in the range of 3.76–201.98% over well-known scheduling algorithms. In the case of HPC2N workloads, the improvement ranges of the CSDEO approach for the makespan and energy consumption metrics are 9.86–281.69% and 6.12–233.3%, respectively compared to the tested scheduling algorithms.

A whale optimization algorithm with chaos mechanism based on quasi-opposition for global optimization problems

Whale Optimization Algorithm (WOA), as a newly developed meta-heuristic algorithm, performs well in solving optimization problems. A WOA with chaos mechanism based on quasi-opposition (OBCWOA) is proposed in this paper to overcome the slow convergence speed of the original WOA and to avoid being trapped in local optimal solutions when dealing with high-dimensional problems. We applied two strategies to the original WOA: using chaos mechanism to generate initial value to improve convergence speed of the algorithm and using the opposition-based learning method to balance exploration and development ability of the algorithm to help the algorithm jump out of local optimal solutions. The proposed algorithm is compared with other algorithms on unimodal functions, multimodal functions and fixed dimensional multimodal functions, and is applied to a famous engineering design problem. Results show that combination of the two strategies can improve convergence speed and enhance global search ability of the original WOA. OBCWOA proposed in this paper performs better than the other existing algorithms.

The estimation of low and high-pass active filter parameters with opposite charged system search algorithm

Algorithms are frequently used to solve problems that have a large search space and take a long time to be mathematically solved. They can later be improved with different improvement methods based on the structure and the type of the problem. In this study, the charged system search algorithm (CSS), which has been successfully implemented in the solutions of numerous engineering problems studied within the literature, was improved by introducing opposition-based learning method (OBL) to it in two different methods. With these improved algorithms, solutions were developed for 30-dimensional multimodal test functions in the first place and the results were discussed. In the second place, the parameters of active filters given below were determined from E24 standard series with developed approaches.Filters are electronic circuits that enhance the wanted frequency components of electric signals applied on their inputs and remove harmonics and interferences from these signals. They are divided into two types; active and passive filters. Active filters are produced with transistors or op-amps. They are financially more advantageous compared to passive filters. These filters are preferred especially in low frequencies due to their low costs. Adjustable for a large frequency domain, active filters are very convenient in terms of size and weight and their designs are highly simple. They can easily be connected successively without affecting one another. In this study, the parameter values of Sallen-Key topology Butterworth low and high-pass active filters, which have an extensive area of use, were determined through improved algorithms.My suggestions for the future studies are these: the effects of the opposite position learning approach on other heuristic algorithms can be analysed solving test functions and different engineering problems; different approaches other than the two approaches proposed in this study, can be developed for the opposite position learning concept; LPF and HPF designs solved in the study can be solved for different degrees and stages and finally new designs can be done for different filter types and different resistor and capacitor series that haven’t been handled in this study.

A Multistrategy Artificial Bee Colony Algorithm Enlightened by Variable Neighborhood Search.

Artificial bee colony (ABC) has a good exploration ability against its exploitation ability. For enhancing its comprehensive performance, we proposed a multistrategy artificial bee colony (ABCVNS for short) based on the variable neighborhood search method. First, a search strategy candidate pool composed of two search strategies, i.e., ABC/best/1 and ABC/rand/1, is proposed and employed in the employed bee phase and onlooker bee phase. Second, we present another search strategy candidate pool which consists of the original random search strategy and the opposition-based learning method. Then, it is used to further balance the exploration and exploitation abilities in the scout bee phase. Last but not least, motivated by the scheme of neighborhood change of variable neighborhood search, a simple yet efficient choice mechanism of search strategies is presented. Subsequently, the effectiveness of ABCVNS is carried out on two test suites composed of fifty-eight problems. Furthermore, comparisons among ABCVNS and several famous methods are also carried out. The related experimental results clearly demonstrate the effectiveness and the superiority of ABCVNS.

A discrete oppositional multi-verse optimization algorithm for multi-skill resource constrained project scheduling problem

In this paper, a discrete oppositional multi-verse optimization (DOMVO) algorithm is proposed to address multi-skill resource constrained project scheduling problem (MS-RCPSP). Firstly, the black/white holes phase in DOMVO algorithm is designed by integrating path relinking technique. Secondly, two improved path relinking methods are presented and embedded into the proposed scheme to enhance search abilities. Thirdly, the opposition-based learning (OBL) method is employed as a hybrid strategy to improve the quality of solutions. Moreover, a repair-based decoding scheme is developed to generate schedules more efficiently. Additionally, the design-of-experiment (DOE) method is carried out to investigate the influence of parameters setting. Finally, the effectiveness of DOMVO is evaluated on the intelligent multi-objective project scheduling environment (iMOPSE) benchmark dataset and the computational comparisons indicate the superiority of the proposed DOMVO over the state-of-the-art algorithms in solving MS-RCPSP.

On the improvement in grey wolf optimization

Grey wolf optimization (GWO) is a recently developed nature-inspired global optimization method which mimics the social behaviour and hunting mechanism of grey wolves. Though the algorithm is very competitive and has been applied to various fields of research, it has poor exploration capability and suffers from local optima stagnation. So, in order to improve the explorative abilities of GWO, an extended version of grey wolf optimization (GWO-E) algorithm is presented. This newly proposed algorithm consists of two modifications: Firstly, it is able to explore new areas in the search space because of diverse positions assigned to the leaders. This helps in increasing the exploration and avoids local optima stagnation problem. Secondly, an opposition-based learning method has been used in the initial half of iterations to provide diversity among the search agents. The proposed approach has been tested on standard benchmarking functions for different population and dimension sizes to prove its effectiveness over other state-of-the-art algorithms. Experimental results show that the GWO-E algorithm performs better than GWO, bat algorithm, bat flower pollinator, chicken swarm optimization, differential evolution, firefly algorithm, flower pollination algorithm (FPA) and grasshopper optimization algorithm. Statistical testing of GWO-E has been done to prove its significance over other popular algorithms. Further, as a real-world application, the GWO-E is used to design non-uniform linear antenna array (LAA) for minimum possible sidelobe level and null control. Performance of GWO-E for the synthesis of LAA is evaluated by considering the several different case studies of LAA that exists in the literature, and the results are compared with the results of other popular meta-heuristic algorithms like genetic algorithm, ant lion algorithm, FPA, cat swarm optimization, GWO and many more. Numerical results further show the superior performance of GWO-E over original GWO and other popular algorithms.