Whale Optimization Algorithm Algorithm Research Articles

Hybrid Whale Optimization Algorithm for Energy Efficient Cognitive Radio Network

The general use of wireless sensor devices and their importance in terms of deployment cost, size, and user friendly have given an increase to many different applications of cognitive radio networks. In cognitive radio networks, energy efficiency is a very important problem. In literature, many different methods are developed by researchers which are not able to produce the best results. Hence in this paper, a hybrid technique is developed to attain the energy efficiency deliberation intended for properly maintaining objective signal to interference plus noise ratio (SINR) need for the received interferences and cognitive users at a receiver of primary under a reference value. In the proposed methodology, interference threshold protection margin and protection factor to the SINR target is developed. The hybrid WOFA algorithm can be a mixing of the Whale Optimization Algorithm (WOA) and Firefly Algorithm (FA). In the WOA algorithm, updating positions of the whales are achieved with the utilization of the FA algorithm. The proposed method is designed in the MATLAB platform and it is compared with the existing approaches of WOA by robustness in addition to energy efficiency under the disturbance of channel gain. The proposed method is analyzed with the two different cases such as Target SINR ratio condition is 3.52dB and Target SINR ratio condition is 5.11dB respectively.

Solving a traveling salesman problem using meta-heuristics

In this article, we have introduced an advanced new method of solving a traveling salesman problem (TSP) with the whale optimization algorithm (WOA), and K-means which is a partitioning-based algorithm used in clustering. The whale optimization algorithm first was introduced in 2016 and later used to solve a TSP problem. In the TSP problem, finding the best path, which is the path with the lowest value in the fitness function, has always been difficult and time-consuming. In our algorithm, we want to find the best tour by combining it with K-means which is a clustering method. In other words, we want to divide our problem into smaller parts called clusters, and then we join the clusters based on their distances. To do this, the WOA algorithm, TSP, and K-means must be combined. Separately, the WOA-TSP algorithm which is an unclustered algorithm is also implemented to be compared with the proposed algorithm. The results are shown through some figures and tables, which prove the effectiveness of this new method.

A Combined Prediction Model for Hog Futures Prices Based on WOA‐LightGBM‐CEEMDAN

An integrated hog futures price forecasting model based on whale optimization algorithm (WOA), LightGBM, and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is proposed to overcome the limitations of a single machine learning model with low prediction accuracy and insufficient model stability. The simulation process begins with a grey correlation analysis of the hog futures price index system in order to identify influencing factors; after that, the WOA‐LightGBM model is developed, and the WOA algorithm is used to optimize the LightGBM model parameters; and, finally, the residual sequence is decomposed and corrected by using the CEEMDAN method to build a combined WOA‐LightGBM‐CEEMDAN model. Furthermore, it is used for comparison experiments to check the validity of the model by using data from CSI 300 stock index futures. Based on all experimental results, the proposed combined model shows the highest prediction accuracy, surpassing the comparative model. The model proposed in this study is accurate enough to meet the forecasting accuracy requirements and provides an effective method for forecasting future prices.

Exploratory Analysis of Different Metaheuristic Optimization Methods for Medical Image Enhancement

Metaheuristic optimization algorithms (MOAs) are popularly deployed for medical image enhancement (MIE) purposes. However, with an ever-increasing rate of newer MOAs being proposed in the literature, the question arises as to whether there exist any significant advantage(s) among these different MOAs, particularly as it pertains to MIE. In this paper, we explore this question by analyzing nine well-known MOAs for MIE, namely the artificial bee colony, cuckoo search, differential evolution, firefly, genetic algorithm, particle swarm optimization (PSO), covariance matrix adaptive evolutionary strategy (CMAES), whale optimization algorithm (WOA), and the grey wolf optimization (GWO) algorithms. First, instead of measuring an MOA’s performance based on the number of generations, we adopted the fitness computation rate (FCR), which enables MOAs to be compared in a fairer sense. Secondly, we used a combination of a well-known transformation function and a robust evaluation function as our objective function in the MOAs considered in our study. Then, medical images were obtained from the Medpix database with representative samples selected from across the different parts of the body for MIE evaluation purposes. Within the constraints of the datasets used, the results indicate that, while the GWO and WOA algorithms performed slightly better empirically than the other methods over an average of 1000 Monte Carlo trials, there was little/no statistical significant difference between the other methods. The timing performance also demonstrates that there was no significant difference in the real-time processing speeds of the various MOAs, particularly when evaluated under the same FCR. As a consequence, preliminary findings from our study suggest that employing a range of past and current MOAs or proposing newer MOAs for MIE may not necessarily guarantee substantial comparative enhancement benefits. This might suggest that under high FCR levels, any MOA can be utilized for MIE.

A new optimal static synchronous series compensator‐governorcontrol action for small signal stability enhancement of random renewable penetrated hydro‐dominated power system

AbstractSubject to intermittent nature of renewable sources, small signal stability (SSS) is going to be a challenging task for power system operators. Also as per current deregulated market, stress is imposed on optimal usage of present resources like mechanical governors. In this work a new coordinated optimal damping control action of fractional static synchronous series compensator (SSSC) and governor is proposed to the critical condition of power system for SSS enhancement considering sudden and random variation in solar photovoltaic (SPV) and wind sources with different operating condition of hydro generations and change in reference voltage. Both SSSC and governor coordinate to damp system oscillations to improve stability. A new hybrid differential evolution (DE) with whale optimization algorithm (WOA) is proposed to tune the gains of SSSC and governor in proposed controller. A multi objective function incorporating speed and real power deviation has been taken for optimization problem. It has been observed that varying operating condition of hydro generator along with variations in SPV and wind sources instigate low frequency oscillation and proposed control action has better damping efficacy in comparison to only SSSC and governor. Also, the proposed multi‐objective DE‐WOA control law performs better than only DE and WOA algorithm.

Cloud-Assisted Privacy-Preserving Method for Healthcare Using Adaptive Fractional Brain Storm Integrated Whale Optimization Algorithm

The security of medical data in the cloud is the key consideration of cloud customers. While publishing the medical data, the cloud distributor may suffer from data leakages and attacks such that the data may leak. In order to resolve this, this article devises the developed Adaptive Fractional Brain Storm Integrated Whale Optimization Algorithm (AFBS_WOA), which is the hybridization of Adaptive Fractional Brain Storm Optimization (AFBSO) and Whale Optimization algorithm (WOA). The developed AFBS_WOA algorithm generates the key matrix coefficient for retrieving the perturbed database in order to preserve the privacy of healthcare data in the cloud. The developed AFBS-WOA scheme utilized the fitness function involving utility and privacy measures for calculating the secret key. Here, the privacy-preserved database is obtained by multiplying the input database with a key matrix based on developed AFBS-WOA using the Tracy–Singh product. For data retrieval, the secret key is shared with the service provider in order to retrieve the database, and then the data are accessed. Moreover, the experimental result demonstrates that the developed AFBS_WOA model attained the maximum utility and privacy measure of 0.1872 and 0.8755 using the Hungarian dataset.

Swarm intelligence optimization of the group method of data handling using the cuckoo search and whale optimization algorithms to model and predict landslides

The robustness of landslide prediction models has become a major focus of researchers worldwide. We developed two novel hybrid predictive models that combine the self-organizing, deep-learning group method of data handling (GMDH) with two swarm intelligence optimization algorithms, i.e., cuckoo search algorithm (CSA) and whale optimization algorithm (WOA) for spatially explicit prediction of landslide susceptibility. Eleven landslide-causing factors and 334 historic landslides in a 31,340 km2 landslide-prone area in Iran were used to produce geospatial training and validation datasets. The GMDH model was employed to develop a basic predictive model that was then restructured and its parameters were optimized using the CSA and WOA algorithms, yielding the novel hybrid GMDH-CSA and GMDH-WOA models. The hybrid models were validated and compared to the standalone GMDH model by calculating the area under the receiver operating characteristic (AUC) curve and root mean square error (RMSE). The results demonstrated that the hybrid models overcame the computational shortcomings of the basic GMDH model and significantly improved landslide susceptibility prediction (GMDH-CSA, AUC = 0.909 and RMSE = 0.089; GMDH-WOA, AUC = 0.902 and RMSE = 0.129; standalone GMDH, AUC = 0.791 and RMSE = 0.226). Further, the hybrid models were more robust than the standalone GMDH model, showing consistently excellent performance when the training and validation datasets were changed. Overall, the swarm intelligence-optimized models, but not the standalone model, identified the best trade-offs among objectives, accuracy, and robustness.

Non-linear static and dynamic buckling analysis of laminated composite cylindrical shell embedded in non-linear elastic foundation using the swarm-based metaheuristic algorithms

In this paper, by determining the optimal fiber's angles for maximum critical buckling load, the non-linear static and dynamic buckling analyses of laminated composite cylindrical shells resting on non-linear elastic foundation subjected to external loading are investigated. The laminated composite cylindrical with three, four, and five layers is considered. In the present study, first, the optimal fiber's angles are found using the swarm-based metaheuristic algorithms, then, the non-linear static and dynamic buckling analyses are carried out at optimum fiber directions. According to classical shell theory, von-Kármán equation, and Hooke's law, the stress-strain relations are derived for the laminated composite cylindrical shell. Then, based on the Galerkin's method, the discretized motion equation is obtained. For the optimization problem, the design variables are ply angles, and the objective function is maximizing the critical buckling load. Four recently developed swarm-based metaheuristic algorithms including, grey wolf optimizer (GWO), whale optimization algorithm (WOA), grasshopper optimization algorithm (GOA), and salp swarm algorithm (SSA), are utilized to solve these optimization problems. Based on the results, the optimization algorithms have improved the value of the critical buckling load significantly. Also, the WOA algorithm had better results than the others, while the GOA was the weakest.

Characterization of abnormalities in breast cancer images using nature‐inspired metaheuristic optimized convolutional neural networks model

SummaryConvolutional neural networks (CNN) are deep learning models widely reported as performing well in several image classification tasks. Training the networks for optimal performance is considered an NP‐hard problem. The combination of a metaheuristic algorithm with CNN has been proposed to address this problem because the metaheuristic algorithms have efficient performance, parameter tuning, and stagnation prevention methods. Moreover, there is now an increasing need to apply the best performing metaheuristic algorithm to optimize the parameters, training and learning rate of the CNN models. This study aims to investigate the best performing metaheuristic algorithm for fine‐tuning the weights, biases, and hyperparameters of CNN networks for solving the problem of characterization of abnormalities in breast images. Furthermore, hybrid models consisting of a CNN architecture and five representative metaheuristic algorithms to efficiently detect breast cancer abnormalities are presented. The adopted approach involves training a CNN network using genetic algorithm (GA), whale optimization algorithm (WOA), multiverse optimizer (MVO), satin bower optimization (SBO), and life choice‐based optimization (LCBO) algorithms to optimize only weights and bias of the model. Two categories of experiments were carried out: the first involved training of the CNN model, while the second involved optimizing the training of CNN model with metaheuristic algorithms. A comparative analysis of the impact of the proposed GA, WOA, MVO, SBO, and LCBO metaheuristic algorithms on the performance of the CNN architecture was carried out. Empirical and statistical analyses are presented to validate further the findings obtained in the study. Results obtained showed that MVO, SBO and LCBO outperformed GA, WOA. The classification accuracy obtained for CNN‐GA, CNN‐WOA, CNN‐MVO, CNN‐SBO, and CNN‐LCBO at the fifth epoch was 0.76, 0.75, 0.84, 0.80, and 0.86, respectively. At the same time, the traditional CNN achieved an accuracy of 0.66. The outcome of this study showed that contrary to widespread practice, physics‐based, biology‐based, and human‐based optimization algorithms promise better performance parameter tuning for CNN as compared with evolutionary‐based and swarm‐based metaheuristic algorithms.

SHADE–WOA: A metaheuristic algorithm for global optimization

Differential evolution and its variants have already proven their worth in the field of evolutionary optimization techniques. This study further enhances the success history-based adaptive differential evolution (SHADE) by hybridizing it with a modified Whale optimization algorithm (WOA). In the new algorithm, the two algorithms, SHADE and modified WOA, carry out the search process independently and share information like the global best solution and whole population and thus guides both the algorithms to explore and exploit new promising areas in the search space. It also reduces the chance of being trapped in local optima and stagnation. The proposed algorithm (SHADE–WOA) is tested, evaluating CEC 2017 functions using dimensions 30, 50, and 100. The results are compared with modified DE algorithms, namely SaDE, SHADE, LSHADE, LSHADE-SPACMA, and LSHADE-cnEpSin, also with modified WOA algorithms, namely ACWOA, AWOA, IWOA, HIWOA, and MCSWOA. The new algorithm’s efficiency in solving real-world problems is examined by solving two unconstrained and four constrained engineering design problems. The performance is verified statistically using non-parametric statistical tests like Friedman’s test and Wilcoxon’s test. Analysis of numerical results, convergence analysis, diversity analysis, and statistical analysis ensures the enhanced performance of the proposed SHADE–WOA.

Optimal parameter estimation of overhead transmission line considering different bundle conductors with the uncertainty of load modeling

AbstractThe overhead power line is used for the transmission and distribution of electrical power across long distances. It consists of multiple conductors mounted on poles or towers. The parameters of the overhead transmission lines (TLs) are dependent upon certain factors that are associated with bundle conductors. This research work uses a whale optimization algorithm (WOA) to calculate the overhead AC TL parameters. The proposed technique is applied to single‐phase and three‐phase AC TLs. It can be observed that within an AC TL, a change in one parameter will cause the corresponding variation in other parameters. This work has determined capacitance and inductance per unit length for three‐phase using proposed WOA algorithms at different bundle conductor arrangements. However, the study of load modeling for voltage stability is also presented.

Whale Optimization Algorithm with Applications to Power Allocation in Interference Networks

Power allocation plays a pivotal role in improving the communication performance of interference-limitedwireless network (IWN). However, the optimization of power allocation is usually formulated as a mixed-integernon-linear programming (MINLP) problem, which is hard to solve. Whale optimization algorithm (WOA)has recently gained the attention of the researcher as an efficient method to solve a variety of optimizationproblems. WOA algorithm also has the disadvantages of low convergence accuracy and easy to fall into local optimum.To solve the above problems, we propose Cosine Compound Whale Optimization Algorithm (CCWOA).First of all, its unique cosine nonlinear convergence factor can balance the rate of the whole optimization processand prevent the convergence speed from being too fast. Secondly, the inertia weight and sine vector canincrease the probability of jumping out of the local optimal solution. Finally, the Archimedean spiral can reducethe risk of losing the optimal solution. A representative benchmark function is selected to test the convergencerate of CCWOA algorithm and the optimization performance of jumping out of local optimum. Compared withthe representative algorithms PFP and GAP, the optimization effect of CCWOA is almost consistent with theabove two algorithms, and even exceeds 4% - 6% in numerical value. The advantage of CCWOA is that it haslower algorithm complexity, which has a good advantage when the network computing resources are fixed. Inaddition, the optimization effect of CCWOA is higher than that of WOA, which lays a good foundation for furtherapplication of swarm intelligence optimization algorithm in network resource allocation.

Improved grey wolf algorithm for optimization problems

The grey wolf optimization (GWO) is a nature inspired and meta-heuristic algorithm, it has successfully solved many optimization problems and give better solution as compare to other algorithms. However, due to its poor exploration capability, it has imbalance relation between exploration and exploitation. Therefore, in this research work, the poor exploration part of GWO was improved through hybrid with whale optimization algorithm (WOA) exploration. The proposed grey wolf whale optimization algorithm (GWWOA) was evaluated on five unimodal and five multimodal benchmark functions. The results shows that GWWOA offered better exploration ability and able to solve the optimization problem and give better solution in search space. Additionally, GWWOA results were well balanced and gave the most optimal in search space as compare to the standard GWO and WOA algorithms.

Performance Evaluation of Fiber Wireless (FiWi) Access Network Using Position Optimization of ONUs

Aims: Optimize position of ONUs using Whale Optimization Algorithm (WOA) to make cost-effective FiWi network. Background: Fiber-Wireless (FiWi) is a network which provides higher bandwidth and better stability at lower cost to the users. The placement of network components (such as ONU) in FiWi is of utmost importance since it comes under the network planning. ONU placement mainly focuses on this thing that how efficiently ONUs are placed so that with fewer number of ONUs all the routers get interconnected. Objective: Optimize position of ONUs using WOA algorithm such that, with minimum ONUs all routers can connects with satisfactory network performance. Methods: Extensive simulation is carried out to implement proposed work. A simulation model and code is developed in MATLAB to get the results for existing and proposed algorithms for varying number of variables such as number of ONUs, wireless routers, grid sizes etc. Conclusion: The present work optimizes the location of ONUs using encircling prey mechanism and spiral update mechanism of WOA. Results show that proposed work gives best result in terms of minimum number of ONUs in the network with almost comparable PDR and TTDPN with that of deterministic.

Skewed normal cloud modified whale optimization algorithm for degree reduction of S-λ curves

Whale optimization algorithm (WOA) is a new meta-heuristic algorithm for mathematical description of the foraging behavior of whales. Cloud model (CM) is an effective model to describe cognitive uncertainty, at the same time, it can comprehensively describe the randomness and fuzziness in uncertain phenomena. Skew normal distribution (SND) can better describe the biological behavior situation when the environment changes. In this paper, a new skew normal cloud model (SNCM) is established in the first place by combining the CM with the SND and the skew normal membership function to describe the fuzziness and randomness of environmental change. Secondly,because of the randomness and fuzziness of the whales’ foraging behavior, in order to improve the exploration and exploitation ability of WOA,an emendatory WOA based on the skew normal cloud (SNC) is proposed through the use of the SNCM to modify the shrinking encircling and spiral update strategies of WOA, and the adaptive position and skewness parameters in the SNC are designed to increase the exploration capability in prophase and the exploitation capability in anaphase. Lastly,the experimental results of the complex CEC2017 test set verify the effectiveness of the emendatory WOA under different strategies and different dimensions and different improved WOA algorithm and other representative heuristic algorithms. Three degree reduction of S − λ curves verify the practicability of the the modified WOA in the field of curve design.

Reliability-aware task scheduling for energy efficiency on heterogeneous multiprocessor systems

Recent studies mainly focus on high performance or low power consumption for task scheduling on heterogeneous multiprocessor systems (HMSs). Dynamic voltage and frequency scaling (DVFS) is an important energy reduction technique, which adjusts the voltage and frequency of the processor while the task is executing. However, some studies have shown that reducing the voltage of processor increases the transient failure rate, which reduces system reliability. In this paper, we aim at addressing the scheduling problem of optimizing energy under makespan and reliability constraints on HMSs with DVFS. We first propose an improved whale optimization algorithm (WOA) deploying opposition-based learning and individual selection strategy, which can balance the exploration and exploitation ability. To maintain population diversity, we then apply a constrained rank-based method which retains some infeasible individuals in the population. Finally, we reschedule the Critical Path Nodes (CPNs) to further improve the performance of improved WOA. The main difference between our work and most previous works is that we study a new scheduling problem, and utilize an improved WOA algorithm integrating with rescheduling CPNs and a constrained rank-based method. Extensive experiments are conducted to evaluate our proposed algorithm, and the evaluation results show that our proposed algorithm is compelling in comparison with the state-of-the-art algorithms.

Weighted Salp Swarm and Salp Swarm Algorithms in FiWi access network: A new paradigm for ONU placement

Fiber Wireless (FiWi) access network is a promising next generation broadband access network as it provides high bandwidth, better stability and anywhere-anytime connection at lower cost to the users. It integrates the wireless access network and optical access network at front-end and back-end respectively. Optimizing the ONUs position plays an important role in FiWi network as it affects the network performance and network cost. The present work focuses on ONU placement problem and proposes an efficient algorithms for optimizing the ONU’s position. A nature inspired Salp Swarm Algorithm (SSA) and Weighted Salp Swarm Algorithm (WSSA) are applied for optimal placement of ONUs based on different configurations of wireless routers and ONUs. To the best of our knowledge, these algorithms have never been used in the field of FiWi network. These novel algorithms optimize ONU’s position to minimize cost function of the network. Cost function is the average distance between an ONU and its primary wireless routers. An extensive simulation is performed to analyze the effectiveness of the proposed work. The results of proposed algorithms are compared with the well known existing Whale optimization algorithm (WOA). Results show that the proposed WSSA and SSA outperform the WOA. WSSA provides better result than SSA and WOA in terms of lower cost function value, more number of routers connected in 1-hop, increased average ONU connectivity (AONUC), faster convergence rate and lesser execution time. SSA provides better result than the WOA algorithm. It is shown in the result that the uniform placement of ONUs gives the best result than the random placement of ONUs for all the algorithms.

Task scheduling on cloud computing based on sea lion optimization algorithm

PurposeSea Lion Optimization (SLnO) algorithm involves the ability of exploration and exploitation phases, and it is able to solve combinatorial optimization problems. For these reasons, it is considered a global optimizer. The scheduling operation is completed by imitating the hunting behavior of sea lions.Design/methodology/approachCloud computing (CC) is a type of distributed computing, contributory in a massive number of available resources and demands, and its goal is sharing the resources as services over the internet. Because of the optimal using of these services is everlasting challenge, the issue of task scheduling in CC is significant. In this paper, a task scheduling technique for CC based on SLnO and multiple-objective model are proposed. It enables decreasing in overall completion time, cost and power consumption; and maximizes the resources utilization. The simulation results on the tested data illustrated that the SLnO scheduler performed better performance than other state-of-the-art schedulers in terms of makespan, cost, energy consumption, resources utilization and degree of imbalance.FindingsThe performance of the SLnO, Vocalization of Whale Optimization Algorithm (VWOA), Whale Optimization Algorithm (WOA), Grey Wolf Optimization (GWO) and Round Robin (RR) algorithms for 100, 200, 300, 400 and 500 independent cloud tasks on 8, 16 and 32 VMs was evaluated. The results show that SLnO algorithm has better performance than VWOA, WOA, GWO and RR in terms of makespan and imbalance degree. In addition, SLnO exhausts less power than VWOA, WOA, GWO and RR. More precisely, SLnO conserves 5.6, 21.96, 22.7 and 73.98% energy compared to VWOA, WOA, GWO and RR mechanisms, respectively. On the other hand, SLnO algorithm shows better performance than the VWOA and other algorithms. The SLnO algorithm's overall execution cost of scheduling the cloud tasks is minimized by 20.62, 39.9, 42.44 and 46.9% compared with VWOA, WOA, GWO and RR algorithms, respectively. Finally, the SLnO algorithm's average resource utilization is increased by 6, 10, 11.8 and 31.8% compared with those of VWOA, WOA, GWO and RR mechanisms, respectively.Originality/valueTo the best of the authors’ knowledge, this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.

Efficient visual tracking approach via whale optimizer and corrected background weighted histogram

There are mainly two components in almost every visual object tracking algorithm, which are the object presentation and the searching mechanism. In the literature, metaheuristic algorithms have been recently, widely used as searching method in visual tracking. In fact, the more discriminative is their combined object presentation the better is their precision. Salient background information is often inside the first detected region of the object, which may decrease considerably the tracking performance. In this work, we combine a powerful metaheuristic searching method, whale optimization algorithm (WOA), with the discriminative presentation named as corrected background weighted histogram (CBWH) to improve the tracking accuracy in difficult environments. WOA algorithm is used because of its strong searching ability, which enable it avoid being trapped in local optimum, and also its lowest computation cost compared to other metaheuristic algorithms. The WOA sensitivity parameters are studied experimentally to be adjusted in visual tracking. For a fair assessment of the proposed approach, its performance has been evaluated on 20 video sequences, from the famous object tracking benchmark OTB15, and compared with six (6) other state-of-art trackers. The evaluations were carried quantitatively and qualitatively on challenging situations and have provided satisfying results. The experimental results shows that WOA combined with CBWH can lead to further improvement, and better success rate in tracking.

Whale Optimization Algorithm Bat Chaotic Map Multi Frekuensi for Finding Optimum Value

Optimization is one of the most interesting things in life. Metaheuristic is a method of optimization that tries to balance randomization and local search. Whale Optimization Algorithm (WOA) is a metaheuristic method that is inspired by the hunting behavior of humpback whales. WOA is very competitive compared to other metaheuristic algorithms, but WOA is easily trapped in a local optimum due to the use of encircling mechanism in its search space resulting in low performance. In this research, the WOA algorithm is combined with the BAT chaotic map multi-frequency (BCM) algorithm. This method is done by inserting the BCM algorithm in the WOA search phase. The experiment was carried out with 23 benchmarks test functions which were run 30 times continuously with the help of Matlab R2012a. The experimental results show that the WOABCM algorithm is able to outperform the WOA and WOABAT algorithms in most of the benchmark test functions. The increase of performance in the average of optimum value of WOABCM when compared to WOA is 2.27x10 ^ 3.