Optimization Techniques in Engineering E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Sustainable Computing and Optimization
• Sprache: Englisch

Seitenzahl: 685

Veröffentlichungsjahr: 2023

Beschreibung

OPTIMIZATION TECHNIQUES IN ENGINEERING The book describes the basic components of an optimization problem along with the formulation of design problems as mathematical programming problems using an objective function that expresses the main aim of the model, and how it is to be either minimized or maximized; subsequently, the concept of optimization and its relevance towards an optimal solution in engineering applications, is explained. This book aims to present some of the recent developments in the area of optimization theory, methods, and applications in engineering. It focuses on the metaphor of the inspired system and how to configure and apply the various algorithms. The book comprises 30 chapters and is organized into two parts: Part I -- Soft Computing and Evolutionary-Based Optimization; and Part II -- Decision Science and Simulation-Based Optimization, which contains application-based chapters. Readers and users will find in the book: * An overview and brief background of optimization methods which are used very popularly in almost all applications of science, engineering, technology, and mathematics; * An in-depth treatment of contributions to optimal learning and optimizing engineering systems; * Maps out the relations between optimization and other mathematical topics and disciplines; * A problem-solving approach and a large number of illustrative examples, leading to a step-by-step formulation and solving of optimization problems. Audience Researchers, industry professionals, academicians, and doctoral scholars in major domains of engineering, production, thermal, electrical, industrial, materials, design, computer engineering, and natural sciences. The book is also suitable for researchers and postgraduate students in mathematics, applied mathematics, and industrial mathematics.

Leseprobe

Contents

Cover

Series Page

Title Page

Copyright Page

Dedication Page

Preface

Acknowledgments

Part 1: Soft Computing and Evolutionary-Based Optimization

1 Improved Grey Wolf Optimizer with Levy Flight to Solve Dynamic Economic Dispatch Problem with Electric Vehicle Profiles

1.1 Introduction

1.2 Problem Formulation

1.3 Proposed Algorithm

1.4 Simulation and Results

1.5 Conclusion

References

2 Comparison of YOLO and Faster R-CNN on Garbage Detection

2.1 Introduction

2.2 Garbage Detection

2.3 Experimental Results

2.4 Future Scope

2.5 Conclusion

References

3 Smart Power Factor Correction and Energy Monitoring System

3.1 Introduction

3.2 Block Diagram

3.3 Simulation

3.4 Conclusion

References

4 ANN-Based Maximum Power Point Tracking Control Configured Boost Converter for Electric Vehicle Applications

4.1 Introduction

4.2 Block Diagram

4.3 ANN-Based MPPT for Boost Converter

4.4 Closed Loop Control

4.5 Simulation Results

4.6 Conclusion

References

5 Single/Multijunction Solar Cell Model Incorporating Maximum Power Point Tracking Scheme Based on Fuzzy Logic Algorithm

5.1 Introduction

5.2 Modeling Structure

5.3 MPPT Design Techniques

5.4 Results and Discussions

5.5 Conclusion

References

6 Particle Swarm Optimization: An Overview, Advancements and Hybridization

6.1 Introduction

6.2 The Particle Swarm Optimization: An Overview

6.3 PSO Algorithms and Pseudo-Code

6.4 Advancements in PSO and Its Perspectives

6.5 Hybridization of PSO

6.6 Area of Applications of PSO

6.7 Conclusions

References

7 Application of Genetic Algorithm in Sensor Networks and Smart Grid

7.1 Introduction

7.2 Communication Sector

7.3 Electrical Sector

7.4 A Brief Outline of GAs

7.5 Sensor Network’s Energy Optimization

7.6 Sensor Network’s Coverage and Uniformity Optimization Using GA

7.7 Use GA for Optimization of Reliability and Availability for Smart Microgrid

7.8 GA Versus Traditional Methods

7.9 Summaries and Conclusions

References

8 AI-Based Predictive Modeling of Delamination Factor for Carbon Fiber–Reinforced Polymer (CFRP) Drilling Process

8.1 Introduction

8.2 Methodology

8.3 AI-Based Predictive Modeling

8.4 Performance Indices

8.5 Results and Discussion

8.6 Conclusions

References

9 Performance Comparison of Differential Evolutionary Algorithm-Based Contour Detection to Monocular Depth Estimation for Elevation Classification in 2D Drone-Based Imagery

9.1 Introduction

9.2 Literature Survey

9.3 Research Methodology

9.4 Result and Discussion

9.5 Conclusion

References

10 Bioinspired MOPSO-Based Power Allocation for Energy Efficiency and Spectral Efficiency Trade-Off in Downlink NOMA

10.1 Introduction

10.2 System Model

10.3 User Clustering

10.4 Optimal Power Allocation for EE-SE Tradeoff

10.5 Numerical Results

10.6 Conclusion

References

11 Performances of Machine Learning Models and Featurization Techniques on Amazon Fine Food Reviews

11.1 Introduction

11.2 Materials and Methods

11.3 Results and Experiments

11.4 Conclusion

References

12 Optimization of Cutting Parameters for Turning by Using Genetic Algorithm

12.1 Introduction

12.2 Genetic Algorithm GA: An Evolutionary Computational Technique

12.3 Design of Multiobjective Optimization Problem

12.4 Results and Discussions

12.5 Conclusion

References

13 Genetic Algorithm-Based Optimization for Speech Processing Applications

13.1 Introduction to GA

13.2 GA in Automatic Speech Recognition

13.3 Genetic Algorithm in Speech Emotion Recognition

13.4 Genetic Programming in Hate Speech Using Deep Learning

13.5 Conclusion

References

14 Performance of P, PI, PID, and NARMA Controllers in the Load Frequency Control of a Single-Area Thermal Power Plant

14.1 Introduction

14.2 Single-Area Power System

14.3 Automatic Load Frequency Control (ALFC)

14.4 Controllers Used in the Simulink Model

14.5 Circuit Description

14.6 ANN and NARMA L2 Controller

14.7 Simulation Results and Comparative Analysis

14.8 Conclusion

References

Part 2: Decision Science and Simulation-Based Optimization

15 Selection of Nonpowered Industrial Truck for Small Scale Manufacturing Industry Using Fuzzy VIKOR Method Under FMCDM Environment

15.1 Introduction

15.2 Fuzzy Set Theory

15.3 FVIKOR

15.4 Problem Definition

15.5 Results and Discussions

15.6 Conclusions

References

16 Slightly and Almost Neutrosophic gsα*—Continuous Function in Neutrosophic Topological Spaces

16.1 Introduction

16.2 Preliminaries

16.3 Slightly Neutrosophic

gsα

* – Continuous Function

16.4 Almost Neutrosophic

gsα

* – Continuous Function

16.5 Conclusion

References

17 Identification and Prioritization of Risk Factors Affecting the Mental Health of Farmers

17.1 Introduction

17.2 Materials and Methods

17.3 Result and Discussion

17.4 Conclusion

References

18 Multiple Objective and Subjective Criteria Evaluation Technique (MOSCET): An Application to Material Handling System Selection

18.1 Introduction

18.2 Multiple Objective and Subjective Criteria Evaluation Technique (MOSCET): The Proposed Algorithm

18.3 Illustrative Example

18.4 Conclusions

References

19 Evaluation of Optimal Parameters to Enhance Worker’s Performance in an Automotive Industry

19.1 Introduction

19.2 Methodology

19.3 Results and Discussion

19.4 Conclusions

References

20 Determining Key Influential Factors of Rural Tourism— An AHP Model

20.1 Introduction

20.2 Rural Tourism

20.3 Literature Review

20.4 Objectives

20.5 Methodology

20.6 Analysis

20.7 Results and Discussion

20.8 Conclusions

20.9 Managerial Implications

References

21 Solution of a Pollution-Based Economic Order Quantity Model Under Triangular Dense Fuzzy Environment

21.1 Introduction

21.2 Preliminaries

21.3 Notations and Assumptions

21.4 Formulation of the Mathematical Model

21.5 Numerical Illustration

21.6 Sensitivity Analysis

21.7 Graphical Illustration

21.8 Merits and Demerits

21.9 Conclusion

Acknowledgement

Appendix

References

22 Common Yet Overlooked Aspects Accountable for Antiaging: An MCDM Approach

22.1 Introduction

22.2 Literature Review

22.3 Analytic Hierarchy Process (AHP)

22.4 Result and Discussion

22.5 Conclusion

References

23 E-Waste Management Challenges in India: An AHP Approach

23.1 Introduction

23.2 Literature Review

23.3 Methodology

23.4 Results and Discussion

23.5 Conclusion

References

24 Application of k-Means Method for Finding Varying Groups of Primary Energy Household Emissions in the Indian States

24.1 Introduction

24.2 Literature Review

24.3 Materials and Methods

24.4 Exploratory Data Analysis

24.5 Results and Discussion

24.6 Conclusion

References

25 Airwaves Detection and Elimination Using Fast Fourier Transform to Enhance Detection of Hydrocarbon

25.1 Introduction

25.2 Related Works

25.3 Theoretical Framework

25.4 Methodology

25.5 Results and Discussions

25.6 Conclusion

References

26 Design and Implementation of Control for Nonlinear Active Suspension System

26.1 Introduction

26.2 Mathematical Model of Quarter Car Suspension System

26.3 Conclusion

References

27 A Study of Various Peak to Average Power Ratio (PAPR) Reduction Techniques for 5G Communication System (5G-CS)

27.1 Introduction

27.2 Literature Review

27.3 Overview of 5G Cellular System

27.4 PAPR

27.5 Factors on which PAPR Reduction Depends

27.6 PAPR Reduction Technique

27.7 Limitation of OFDM

27.8 Universal Filter Multicarrier (UMFC) Emerging Technique to Reduce PAPR in 5G

27.9 Comparison Between Various Techniques

27.10 Conclusion

References

28 Investigation of Rebound Suppression Phenomenon in an Electromagnetic V-Bending Test

28.1 Introduction

28.2 Investigation

28.3 Mathematical Evaluation

28.4 Modeling for Material

28.5 Conclusion

References

29 Quadratic Spline Function Companding Technique to Minimize Peak-to-Average Power Ratio in Orthogonal Frequency Division Multiplexing System

29.1 Introduction

29.2 OFDM System

29.3 Companding Technique

29.4 Numerical Results and Discussion

29.5 Conclusion

Acknowledgment

References

30 A Novel MCGDM Approach for Supplier Selection in a Supply Chain Management

30.1 Introduction

30.2 Proposed Algorithm

30.3 Illustrative Example

30.4 Conclusions

References

Index

Also of Interest

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Description of Unimodal Benchmark Problems with the Performance of GWO [7] and Improved GWOLF.

Table 1.2 Description of multimodal, high dimension benchmark problems with the performance of GWO [7] and improved GWOLF.

Table 1.3 Description of multimodal, low dimension benchmark problem with performance of GWO [7] and improved GWOLF.

Table 1.4 Power generated by 15 generators for 24 hours for EPRI load.

Table 1.5 Power generated by 15 generators for 24 hours for off-peak load.

Table 1.6 Power generated by 15 generators for 24 hours for stochastic load.

Table 1.7 Cost incurred by 15 generators for meeting different load distribution.

Appendix I Parameters of optimizers.

Appendix II Best solution and rank of LEVY variant for benchmark function.

Chapter 2

Table 2.1 Comparison of YOLO and Faster R-CNN.

Chapter 4

Table 4.1 Parameters of boost converter.

Chapter 5

Table 5.1 Fuzzy rule base.

Chapter 6

Table 6.1 Applications of PSO.

Chapter 7

Table 7.1 Simulation results.

Table 7.2 Component wise reliability of transformer.

Chapter 8

Table 8.1 Model parameters of linear regression ML model.

Table 8.2 Model parameters of random forests ML model.

Table 8.3 XGboost model parameters.

Table 8.4 SVM model parameters.

Table 8.5 KPIs of the training phase.

Table 8.6 Testing metrics.

Table 8.7 K cross-fold validation of R

2

.

Table 8.8 K cross-fold validation of negative mean squared error.

Table 8.9 K cross-fold actual validation of Metric negative root mean squared error.

Chapter 9

Table 9.1 Paired t-test for significance of precision value.

Chapter 10

Table 10.1 Simulation parameters.

Chapter 11

Table 11.1 Evaluation metrics for logistic regression with L1.

Table 11.2 Evaluation metrics for logistic regression with L2.

Table 11.3 Evaluation metrics for SVM with L1.

Table 11.4 Evaluation metrics for SVM with L2.

Table 11.5 Evaluation metrics for random forest.

Table 11.6 Evaluation metrics for XGBoost.

Table 11.7 Heatmap for accuracies of different classifiers with different featurization.

Table 11.8 Heatmap for f-measure of different classifiers with different featurization.

Chapter 12

Table 12.1 Pareto optimal solution and corresponding decision variables.

Chapter 14

Graph 1 Frequency error minimization by NARMA-L2 controller.

Graph 2 Frequency error minimization by PID controller.

Graph 3 Frequency error minimization by PI controller.

Graph 4 Frequency error minimization by P controller.

Chapter 15

Table 15.1 Decision matrix and weight matrix.

Table 15.2 Decision matrix in TFNs.

Table 15.3 Weighted normalized decision matrix.

Table 15.4 Ranking of NPITs based on BNP value of S

i

.

Table 15.5 Ranking of NPITs based on BNP value of .

Table 15.6 Ranking of NPITs based on BNF value of .

Chapter 17

Table 17.1 Demographic characteristic of farmer (n = 53) shown.

Table 17.2 Stress levels of farmers (n = 53) shown.

Table 17.3 Identification of risk factors and key objective shown.

Table 17.4 Initial decision matrix given away.

Table 17.5 Normalized decision matrix given away.

Table 17.6 Weighted normalized decision matrix given away.

Table 17.7 Concord set and discordance set given away.

Table 17.8 Concord matrix given away.

Table 17.9 Discordance matrix given away.

Table 17.10 Concord dominance matrix given away.

Table 17.11 Discordance dominance matrix given away.

Table 17.12 Aggregate dominance matrix given away.

Table 17.13 Ranking (higher value in final solutions have higher ranking) given away.

Chapter 18

Table 18.1 Linguistic variables, acronyms and TFN for performance rating.

Table 18.2 Linguistic variables, acronym and TFNs for criteria weights.

Table 18.3 Decision matrix in terms of both crisp numbers and linguistic variables.

Table 18.4 Decision matrix in terms of both crisp and fuzzy numbers.

Table 18.5 Decision matrix in terms of crisp numbers.

Table 18.6 Decision matrix in terms of normalized performance ratings.

Table 18.7 Fuzzy weights matrix in terms of TFNs by decision makers.

Table 18.8 Fuzzy weight matrix in terms of TFNs.

Table 18.9 Mean weights of criteria.

Table 18.10 Weighted normalized performance ratings.

Table 18.11 Performance score, relative performance index and ranking order.

Chapter 19

Table 19.1 Results of average worker productivity study and S/N ratio.

Chapter 20

Table 20.1 Identified key influencing factors of the rural tourism.

Table 20.2 The fundamental scale developed by Saaty (AHP).

Table 20.3 Saaty Scale for Random Index.

Table 20.4 Pair wise comparison matrix of factors.

Table 20.5 Criteria weightage and ranking of factors.

Table 20.6 Pairwise comparison matrix of subfactors (cultural factors).

Table 20.7 Pairwise comparison matrix of subfactors (heritage factor) with ranking.

Table 20.8 Pair wise comparison matrix of subfactor (local quality factor).

Table 20.9 Ranking through global and local weight of factors and subfactors.

Chapter 21

Table 21.1 Observed data set.

Table 21.2 Optimal solution of the SC model under various approaches.

Table 21.3 Sensitivity Analysis on fuzzy deviation parameters of the proposed model.

Chapter 22

Table 22.1 Satty preference scale.

Table 22.2 Pairwise comparison matrix of the criterion.

Table 22.3 Normalized matrix.

Table 22.4 Pairwise matrix of the alternate providers w.r.t G.

Table 22.4.1 Normalised matrix.

Table 22.5 Pairwise matrix of the alternate providers w.r.t L.

Table 22.5.1 Normalized matrix.

Table 22.6 Pairwise matrix of the alternate providers w.r.t H.

Table 22.6.1 Normalized matrix.

Table 22.7 Pairwise matrix of the alternate providers w.r.t N.

Table 22.7.1 Normalized matrix.

Table 22.8 Calculation of final provider priorities.

Chapter 23

Table 23.1 Review of literature on e-waste mmanagement.

Table 23.2 List of challenges.

Table 23.3 Scale of relative importance.

Table 23.4 Pairwise comparison matrix.

Table 23.5 Normalized pairwise comparison matrix.

Table 23.6 Ranking of the challenges.

Chapter 24

Table 24.1 Analysis of variance.

Table 24.2 Clusters and distances of the states from the centroids.

Chapter 25

Table 25.1 Parameter value settings.

Chapter 26

Table 26.1 Quarter car suspension system syllables.

Table 26.2 Parameters of the quarter car suspension system.

Chapter 27

Table 27.1 Comparison of the parameter.

Chapter 28

Table 28.1 Characteristics of al alloy (2024-T3).

Table 28.2 Coil parameters.

Table 28.3 Depiction of values of various parameters.

Chapter 29

Table 29.1 Simulation parameters.

Table 29.2 PAPR for various b and c parameter.

Chapter 30

Table 30.1 Decision matrix comprising of performance ratings of the alternative suppliers.

Table 30.2 Weight matrix consisting the weights of the criteria and subcriteria.

Table 30.3 Normalized performance rating of the alternative suppliers.

Table 30.4 Weighted normalized performance ratings for suppliers with respect to subcriteria.

Table 30.5 Weighted normalized performance ratings of the suppliers for each criteria.

Table 30.6 Absolute weighting ratings (AWR) for the alternative suppliers.

Table 30.7 Performance score and ranking order of the suppliers.

List of Illustrations

Chapter 1

Figure 1.1 Charging probability distribution by different profiles.

Figure 1.2 Social Hierarchy of wolves and their characteristics in improved GWOLF.

Figure 1.3 Flowchart for improved grey wolf optimizer with levy flight.

Figure 1.4 Random walk by Levy distribution for Levy probability distribution.

Appendix I Parameters of optimizers.

Appendix II Best solution and rank of LEVY variant for benchmark function.

Chapter 2

Figure 2.1 Architecture of inception model.

Figure 2.2 Architecture of inception model.

Figure 2.3 Input and output of Max pool layer.

Figure 2.4 Input and output of average layer.

Figure 2.5 Fundamental inception block.

Figure 2.6 YOLO output after first stage detection, prior non-max suppression. Training parameters of YOLO:

Figure 2.7 Global steps per second.

Figure 2.8 Classification and localization loss.

Figure 2.9 RPN and total loss.

Figure 2.10 Test image for YOLO.

Figure 2.11 Test image for faster R-CNN 1.

Figure 2.12 Test image for faster R-CNN 2.

Chapter 3

Figure 3.1 Block diagram of proposed system.

Figure 3.2 Simulation diagram using MATLAB.

Figure 3.3 Output voltage and current.

Figure 3.4 Power factor output.

Chapter 4

Figure 4.1 Block diagram.

Figure 4.2 (a) Variable irradiance vs voltage. (b) Variable irradiance vs current. (c) Variable irradiance vs power.

Figure 4.3 (a) Voltage vs current. (b) Voltage vs power.

Figure 4.4 Basic structure of ANN.

Figure 4.5 SIMULINK structure of ANN.

Figure 4.6 Output of trained NN.

Figure 4.7 Closed loop control of cascaded boost converter using ANN-based MPPT.

Figure 4.8 Input and output power of the NN-based boost converter for various irradiations.

Figure 4.9 PV voltage of NN-based boost converter for various irradiations.

Figure 4.10 Output voltage and output current of proposed system for change in irradiations.

Figure 4.11 Output voltage and output current of proposed system for change in temperature.

Figure 4.12 Output voltage and output current for change in load condition.

Chapter 5

Figure 5.1 The proportionate circuit of a solar cell.

Figure 5.2 Similar circuit for multijunction solar PV cell.

Figure 5.3 Flowchart of P&O algorithm.

Figure 5.4 Membership function patterns for (a) input

1

(b) input

2

(c) output.

Figure 5.5 P-V behavioral patterns of single-junction solar PV cell.

Figure 5.6 V-I behavioral patterns of single-junction solar PV cell.

Figure 5.7 V-I behavioral patterns of single-junction solar PV cell at different temperatures (°C).

Figure 5.8 V-I behavioral patterns of single-junction solar PV cell at different irradiance levels (W/m

2

).

Figure 5.9 V-I behavioral patterns of single-junction solar PV cell at different series resistance (Ω).

Figure 5.10 V-I behavioral patterns of single-junction solar PV cell at different shunt resistance (Ω).

Figure 5.11 P-V behavioral patterns of multijunction solar cell.

Figure 5.12 V-J behavioral patterns of multijunction solar cell.

Figure 5.13 V-J behavioral patterns of multijunction solar cell at different irradiance levels (W/cm

2

).

Figure 5.14 V-J behavioral patterns of triple-junction solar cell at different temperatures (K).

Figure 5.15 V-J behavioral patterns of all junctions individually.

Figure 5.16 P-V behavioral patterns of 1-, 2-, and 3-junction solar cell.

Figure 5.17 Power obtained by P&O-based MPPT scheme at different temperatures (K).

Figure 5.18 Power curve obtained by P&O-based MPPT scheme at different irradiance levels (W/cm

2

).

Figure 5.19 Power curve obtained by FLA-based MPPT scheme at different temperatures (K).

Figure 5.20 Power curve obtained by FLA-based MPPT scheme at different irradiance levels (W/cm

2

).

Figure 5.21 Comparative study of power obtained by conventional, P&O-, and FLA-based MPPT.

Chapter 6

Figure 6.1 Flowchart of PSO algorithm.

Chapter 7

Figure 7.1 Hundred random node topologies.

Figure 7.2 Chain creation in the first cluster.

Figure 7.3 Chain creation in the second cluster.

Figure 7.4 Chain creation in the third cluster.

Figure 7.5 Chain creation in the fourth cluster.

Figure 7.6 Chain formation in the 5th cluster.

Figure 7.7 Results of applications of GAs.

Figure 7.8 Coverage with 100 iterations.

Figure 7.9 Coverage with several nodes.

Figure 7.10 Coverage vs. number of iterations.

Figure 7.11 Coverage vs. number of iterations (with 20 numbers of nodes).

Figure 7.12 GA.

Chapter 8

Figure 8.1 Proposed methodology block diagram.

Figure 8.2 Training all machine learning algorithms on the train data set.

Figure 8.3 Testing all machine learning algorithms on the test data set.

Chapter 9

Figure 9.1 Proposed technique.

Figure 9.2 Image dataset.

Figure 9.3 Output images state-of-the-art vs proposed techniques.

Figure 9.4 Comparison of similarity index of outputs of both methods vs ground truth value.

Chapter 10

Figure 10.1 SIC process in downlink NOMA transmission with N users.

Figure 10.2 Near far user pairing in NOMA.

Figure 10.3 User pairing for 12 users.

Figure 10.4 Sum rate vs transmission power.

Figure 10.5 Energy efficiency vs transmission power.

Figure 10.6 Energy efficiency vs spectral efficiency.

Chapter 11

Figure 11.1 Flow diagram for the proposed method.

Figure 11.2 Snippet of code for featurization using average of word2vec.

Figure 11.3 Snippet of code for featurization using combination of TF-IDF and word2vec.

Chapter 12

Figure 12.1 Framework of GA.

Figure 12.2 Best fitness plot for main cutting force.

Figure 12.3 Best fitness plot for feed force.

Figure 12.4 Variation of cutting forces with respect to rake angle.

Figure 12.5 Variation of cutting forces with respect to entering angle.

Figure 12.6 Variation of cutting forces with respect to cutting speed.

Figure 12.7 Pareto front for the optimal solutions.

Chapter 13

Figure 13.1 GA-based distinctive phonetic features recognition.

Chapter 14

Figure 14.1 Block diagram of PI controller.

Figure 14.2 Block diagram of PI controller.

Figure 14.3 Block diagram of P controller.

Figure 14.4 Simulink model of single-area thermal power plant.

Graph 1 Frequency error minimization by NARMA-L2 controller.

Graph 2 Frequency error minimization by PID controller.

Graph 3 Frequency error minimization by PI controller.

Graph 4 Frequency error minimization by P controller.

Chapter 15

Figure 15.1 Membership Function of a TFN .

Figure 15.2 BNP of fuzzy Q value.

Figure 15.3 Comparison of ranking order based on BNP of fuzzy S, R, and Q values.

Chapter 17

Figure 17.1 Steps in this research work.

Figure 17.2 Procedural steps of ELECTRE method.

Chapter 18

Figure 18.1 Relative performance index of the alternative material handling systems.

Figure 18.2 Ranking order of the alternative material handling systems.

Chapter 19

Figure 19.1 Experimental layout.

Figure 19.2 Figure showing variation of WBGT temperature with S/N ratio.

Figure 19.3 Figure showing variation of relative humidity with S/N ratio.

Figure 19.4 Figure showing variation of illuminance with S/N ratio.

Figure 19.5 Figure showing variation of average productivity with S/N ratio.

Chapter 20

Figure 20.1 AHP-based model for ranking the key influential factors for sustainable growth of rural tourism.

Chapter 21

Figure 21.1 Pollution generating model at ith production process.

Figure 21.2 Variation of order quantity with respect to cycle time.

Figure 21.3 Variation of average inventory cost due to pollution index.

Figure 21.4 Variation of order quantity with respect to pollution index.

Chapter 24

Figure 24.1 Primary energy HCEs of states by fuel type (2015).

Figure 24.2 Total primary energy HCEs by fuel type.

Figure 24.3 Total primary energy household emissions of LPG, kerosene, diesel by CH

4

and N

2

O.

Figure 24.4 Dendrogram.

Figure 24.5 Cluster centers by fuel type and gas type.

Figure 24.6 Population (2015) by states and clusters.

Chapter 25

Figure 25.1 CSTM experimental setup.

Figure 25.2 Air layer and without air layer.

Figure 25.3 Electric field against the offset with and without hydrocarbon for a 100-m to 500-m depth of seawater.

Figure 25.4 Hydrocarbon with airwaves.

Figure 25.5 Hydrocarbon without airwaves.

Figure 25.6 Hydrocarbon with filtered airwaves.

Chapter 26

Figure 26.1 Quarter car suspension system.

Figure 26.2 Sprung mass velocity.

Figure 26.3 Suspension deflection.

Figure 26.4 Sprung mass velocity.

Figure 26.5 Suspension deflection.

Figure 26.6 Sprung mass velocity.

Figure 26.7 Suspension deflection.

Chapter 27

Figure 27.1 Application of 5G Cellular System (Source: Ericsson white-papers/5g-wireless-access-an-overview).

Figure 27.2 SLM-OFDM transmitter.

Figure 27.3 PTS-OFDM transmitter.

Figure 27.4 Basic block diagram for UMFC transceiver.

Chapter 28

Figure 28.1 Figure showing schematic of die.

Figure 28.2 Schematic showing forming result of part.

Figure 28.3 Figure showing variation of measured coil current.

Figure 28.4 Figure showing flowchart for the strategy.

Figure 28.5 Showing the final shape of part (EMF removal).

Figure 28.6 Current pulse excitation showing the final shape of the part.

Figure 28.7 Graph depicting the fluctuation of current, displacement, and EMF over time.

Figure 28.8 Figure showing Fz1 and Fz2 positioning.

Figure 28.9 Electromagnetic strength and sequence strategy for coupling.

Figure 28.10 (a) Depiction of X-component of EMF. (b) Depiction of Z-component of EMF.

Chapter 29

Figure 29.1 Block diagram of an OFDM system using quadratic spline technique.

Figure 29.2 Approximation of the nonlinear optimal compressor function (NOCF) using the quadratic spline function (QSF).

Figure 29.3 CCDF of PAPR OFDM system the quadratic spline companding for various values of c parameter.

Figure 29.4 The BER of the quadratic spline companding for various values of c parameter.

Chapter 30

Figure 30.1 Performance score of the suppliers.

Figure 30.2 Ranking order of the suppliers.

Guide

Cover Page

Series Page

Title Page

Copyright Page

Dedication Page

Contents

Preface

Acknowledgments

Begin Reading

Index

Also of Interest

End User License Agreement

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Optimization Techniques in Engineering

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Preface

Optimization is a precise method that allows the planner to identify the best solution to a problem by using design restrictions and criteria. Optimization techniques have been used to solve a variety of practical problems in a variety of fields. These optimization methods have existed since the time of Newton, Lagrange and Cauchy. The contributions of Leibnitz and Newton to calculus are responsible for the growth of differential calculus approaches for optimization. Optimization techniques are useful tools for obtaining the required design parameters and operational conditions. They direct the experimental effort and lower the design and operations risk and cost. Finding the values of decision variables that correspond to and give the maximum or minimum of one or more specified objectives is referred to as optimization. An optimization algorithm is a process that compares numerous solutions iteratively until an optimum or satisfying solution is identified. Thus, optimization has become a feature of computer-aided design activities since the invention of computers. The formulation of goal functions and the optimization technique chosen determine the reliability of optimal solutions. A mathematical model that characterizes and predicts the process behavior is required for optimization. An optimization search could aid in the estimation of unknown parameters in complex nonlinear processes. In dynamic processes, robust optimization can be used to find uncertainty variables. Optimization can also be used to aid in the development of scale-up methodologies and the design of multiphase reactors and flow systems. Manufacturing and engineering activities currently being used will not be as efficient until design and operations are optimized. The purpose of design optimization might simply be to reduce production costs or to increase production efficiency. Optimization is particularly important in companies since it helps to cut costs, which can lead to increased earnings and success in a competitive environment.

There are two types of optimization approaches used: traditional and soft computing-based. Traditional optimization techniques can be used to identify the best solution or unconstrained maxima and minima of continuous and differentiable functions. These are mathematical methods that use differential calculus to get the best solution. Optimization can decrease readability and introduce code that is only needed to boost performance. This might make programs or systems more difficult to maintain and debug. As a result, performance tweaking or optimization is frequently done near the conclusion of the development stage. Customer experience optimization is critical since it boosts customer satisfaction and helps organizations improve their key performance indicators. More revenue and growth are frequently associated with satisfied customers and improved key performance indicators. Performance optimization is the practice of altering how a system functions to increase its efficiency and effectiveness. Debugging the optimization solution is more complex than debugging the rule-based simulation solution. It could be a mix of numerous limitations and input data from multiple places and time steps. Many fields have used optimization theory and methodologies to solve various practical challenges. Soft computing is the application of approximation computations to difficult computer problems to produce “mushy” but usable outcomes. The method produces results for issues that are either unsolvable or take too long to solve using traditional methods.

An optimization algorithm is a process that compares numerous solutions iteratively until an optimum or satisfying one is identified. It follows particular rules when moving from one solution to the next. Many fields of study employ optimization methods to find solutions that maximize or minimize certain study parameters, such as minimizing expenses in the manufacture of a thing or service, maximizing earnings, minimizing raw materials in the development of a good, or maximizing productivity.

The goal of optimizing an objective function is to identify a set of inputs that results in a maximum or minimal function evaluation. Many machine learning algorithms, from fitting logistic regression models to training artificial neural networks, are based on this concept. The purpose of the optimization process is to find choice variable values that result in an objective function’s maximum or minimum. Optimization issues are characterized as linear, nonlinear, geometric, or quadratic programming problems based on the nature of the expressions for the objective function and constraints. An optimization model is a representation of the key features of the business problem being addressed. The objective function, decision variables, and business constraints are the three components of the model.

The purpose of optimization is to find the best design possible based on a set of prioritized criteria or constraints. These include, among other things, boosting productivity, strength, reliability, lifetime, efficiency, and utilization. Many fields have used optimization theory and methodologies to solve various practical challenges; and optimization techniques have become increasingly important and popular in various engineering applications as computing systems have advanced.

The aim of this book is to present some of the recent developments in the area of optimization theory, methods, and applications in engineering. It focuses on the metaphor of the inspired system and how to configure and apply the various algorithms. The book is organized into two parts: Part I – Soft Computing and Evolutionary-Based Optimization; and Part II – Decision Science and Simulation-Based Optimization, which contains application-based chapters. A brief description of each of the chapters is presented below:

Part I: Soft Computing and Evolutionary-Based Optimization

Chapter 1

attempts to realistically represent the existing grey wolf optimizer in order to increase the algorithm’s efficiency. Unlike grey wolf optimizers, the modeling of prey in this study is considered dynamic. To solve a dynamic economic dispatch problem with electric vehicle profiles, dynamism is added to the prey using the Levy flight distribution function.

Chapter 2

presents an object detection approach devised for detecting plastics. To apply transfer learning, the algorithm is written in tensor flow. The two most commonly used object identification approaches, YOLO and Faster R-CNN, are compared.

Chapter 3

strives to increase the use of real power in relation to reactive power in order to improve the power factor. The power factor is corrected closer to unity with the help of a smart power factor correction device. The power factor controller swaps the appropriate capacitor blocks in steps depending on the load and power factor of the network to raise the power factor to almost 0.95. MATLAB software is used to simulate the system.

Chapter 4

focuses on the design and analysis of a solar-fed cascaded boost converter with a maximum power point tracking (MPPT) algorithm based on neural networks (NN), which is used for electric vehicle (EV) applications.

Chapter 5

proposes modeling of a single and multi-junction solar cell with maximum power point tracking (MPPT) using an intelligent fuzzy logic algorithm (FLA) for maximum productivity.

Chapter 6

discusses the utility of particle swarm optimization (PSO), as well as the weaknesses in the algorithm. The latest developments and improvements to the PSO parameters are also highlighted. Finally, it explores its hybridization with other notable algorithms and applications in a variety of disciplines and contexts during the last few decades.

Chapter 7

delves into the uniformity subfields of sensor networks, as well as energy-efficient sensor networks, which actively investigate the use of genetic algorithms (GAs) as a fundamental component in developing deployment strategies and routing protocols. Since manual garbage collection is a time-consuming technique that cannot keep up with the ever-increasing demands of city rubbish, sensor networks can be used in garbage collection as the first step toward proper plastics treatment and recycling for a more environmentally friendly future.

Chapter 8

presents several machine learning methods, such as random forests, linear regression, XGBoost, and support vector machine (SVM), that aid in the estimation of delamination factor based on known inputs such as feed rate, point angle, and spindle speed.

Chapter 9

attempts using a differential evolutionary algorithm to perform sand elevation categorization of sand deposits acquired with a drone camera in a desert location. However, the results are unsatisfactory, prompting the development of an evolutionary algorithm-based contour identification approach for accurate elevation categorization.

Chapter 10

mainly discusses promoting energy efficiency while maintaining a sustainable minimum spectral efficiency requirement. By obtaining the Pareto optimal solution set, the joint user clustering and multi-objective particle swarm optimization (MOPSO) method has been proposed for downlink non-orthogonal multiple access (NOMA). The simulation results reveal that the proposed MOPSO approach outperforms the existing systems in terms of parametric efficiency.

Chapter 11

uses the Amazon fine food reviews dataset to automatically analyze product reviews and classify them as good or terrible. Four distinct types of classifiers were employed to identify the reviews as positive or negative: logistic regression, support vector machine (SVM), random forest, and XGBoost.

Chapter 12

primarily determines the best cutting conditions for turning operations. Rake angle, entry angle, and cutting speed were used as cutting parameters during the turning operation in this investigation. Different cutting forces, such as primary cutting force and feed force, have been used as machining variables at the same time. A variety of cutting settings were chosen as inputs, and all machining variables were monitored as outputs. With the use of Minitab software, the effects of cutting parameters on cutting forces were identified as a regression equation. In this chapter, single objective optimization and multi-objective optimization approaches have been used for optimization. For optimization, a genetic algorithm (GA) has been applied as an evolutionary computation approach.

Chapter 13

uses a genetic algorithm (GA) with modified mutation and crossover to address the classification problem on the hate speech detection problem in social media.

Chapter 14

investigates load frequency control (LFC) based on a neural network for increasing the power system dynamic performance of a single area thermal power plant.

Part II: Decision Science and Simulation-Based Optimization

Chapter 15

uses the Fuzzy VIKOR (VIse Kriterijumska Optimizacija I Kompromisno Resenje) method to choose non-powered industrial trucks based on several conflicting criteria. Subjective weighting of criteria and alternative performance ratings are made based on the experience, perception, and opinion of experts and decision makers participating in the process.

Chapter 16

introduces new concepts for continuous function in neutrosophic topological spaces.

Chapter 17

identifies mental health risk factors, such as the unique stressors that farmers face, based on an exhaustive assessment of the literature and discussions with farmers and agricultural professionals. Then, the ELECTRE technique, one of the most recent multi-criteria decision-making techniques, was chosen to address the increased concern over farmers’ mental health issues.

Chapter 18

proposes a scientific and mathematically based multiple objective and subjective criteria evaluation technique (MOSCET) to assist decision makers in industrial organizations in making the most appropriate decision based on objective and subjective criteria in situations where the human brain is incapable of finding the right solution.

Chapter 19

employs an analysis of variance (ANOVA) measure of signal-to-noise ratio (S/N ratio) to see if environmental variables such as lighting, humidity, and other elements had a significant impact on worker output in an Indian manufacturing plant.

Chapter 20

focuses on rural tourism in an attempt to identify critical characteristics that could help India’s rural tourism grow. Sub-determinants of the top three primary factors were also ranked in order to learn more about contributing sub-factors by allocating both local and global weights to the success of rural tourism. Several factors and sub-factors were found and prioritized using the analytic hierarchy process (AHP).

Chapter 21

uses a cost minimization technique to construct an economic order quantity (EOQ) model based on environmental contamination. By mixing the demand rate and all cost elements of the inventory management system as triangle dense fuzzy numbers, the fuzzy model parameters create a triangular dense fuzzy mathematical model.

Chapter 22

considers a total of ten major factors responsible for aging and uses the analytic hierarchy process (AHP) to sift through and choose the best of these factors based on their priority order, which are extremely, strongly, and least accountable for aging.

Chapter 23

uses the analytic hierarchy process (AHP) in an attempt to identify and rank e-waste management concerns according to their importance.

Chapter 24

suggests employing the k-means method to identify different groupings of primary energy household emissions in Indian states.

Chapter 25

proposes using the fast Fourier transform (FFT) algorithm to detect and remove the noise from the transmitted signal to reduce misinterpretation in the exploration of hydrocarbon in shallow water environments.

Chapter 26

explores the linear and nonlinear portions of an active suspension system using a quarter vehicle model. Nonlinearity in the plant must be considered to ensure resilience of the specified control technique in various operating situations. Proportional–integral–derivative (PID) and state feedback methodologies are used to investigate the performance of the suggested quarter vehicle model. The simulation results for a passive, active, and linearized quarter vehicle system are compared.

Chapter 27

examines various peak-to-average power ratio (PAPR) reduction techniques for 5G communication systems.

Chapter 28

explores the rebound phenomena for an electromagnetic V-bending test based on the time-bearing disparity between the sheet metal displacement and the power amplitude. The loose coupling strategy is studied using a numerical simulation method.

Chapter 29

presents a new class of compandors-based peak-to-average power ratio (PAPR) reduction approach. Nonlinear compandors are applied to orthogonal frequency division multiplexing (OFDM) signals to attenuate the high signal peaks more than the rest of the signal, lowering the PAPR.

Chapter 30

proposes a novel multi-criteria group decision-making approach for supplier selection. This method can take into account various subjective criteria and their subcriteria that are in conflict.

The Editors

February 2023

Acknowledgments

The editors would like to thank everyone who helped them edit this book by providing vital feedback, support, constructive recommendations, and assistance.

The editors would like to express their gratitude to all of the authors for their outstanding contributions to the book’s intellectual substance.

Simple words cannot describe the editors’ thanks to Scrivener Publishing’s complete editing and production teams, notably Mr. Martin Scrivener, for his unwavering support, encouragement, and direction throughout the publishing process. Without his enormous contributions, this work would not have been feasible.

The editors want to express their gratitude to the reviewers who generously donated their time and expertise to help shape such a high-quality book on such a topical issue.

During the book’s preparation, the editors would like to thank their families for their love, understanding, and support.

Finally, the editors would like to thank all of the readers for their support and hope that this book will continue to inspire and guide them in their future endeavours.

The Editors

Part 1SOFT COMPUTING AND EVOLUTIONARY-BASED OPTIMIZATION

1Improved Grey Wolf Optimizer with Levy Flight to Solve Dynamic Economic Dispatch Problem with Electric Vehicle Profiles

Anjali Jain1*, Ashish Mani1 and Anwar S. Siddiqui2

1Department of Electrical and Electronics Engineering, Amity University Uttar Pradesh, Noida, Uttar Pradesh, India

2Department of Electrical and Electronics Engineering, Jamia Milia Islamia, Delhi, India

Abstract

Meta-heuristic algorithm plays an important role in solving nonconvex, nondifferentiable complex problems. One such complex problem in the power system is dynamic economic dispatch (DED), which is difficult to solve while considering transmission losses and ramp-rate limits. The purpose of dynamic economic dispatch is to find power generated by different generating units for the given specified load while fulfilling the operational constraints along with ramp rate limit and also optimizing the cost of generation as well. Moreover, the problem considered in this chapter is of 15 generator test cases for 24 hours along with three distinct profiles of electric vehicles. Here, in this chapter, an improved version of the Grey wolf optimizer is utilized to optimize the cost objective function. In this variant, grey wolf optimizer prey position is modeled with the help of Levy probability distribution, which makes the modeling of prey dynamic in nature and, hence, showcases the more realistic modeling of the grey wolf hunting process. The selection of parameters for Levy flight is done with the help of experimentation conducted on different benchmark functions. After finalizing the parameters for Levy flight, an improved grey wolf optimizer with Levy flight demonstrated its efficacy for nonconvex and nondifferentiable functions. The numerical results shown with the help of Benchmark solution and 15 bus generators showcase the efficiency of the algorithm. The results produced by this algorithm are compared with other state-of-the-art algorithms, which prove that the algorithm is giving either better or competitive results.

Keywords: Charging scenario, electric vehicle profile, dynamic economic dispatch, Levy flight, probability distribution function

1.1 Introduction

Static economic dispatch problem determines the optimal schedule of the different committed units to meet the load demand at the given time with minimum operating cost while meeting the operational cost. On the other hand, dynamic economic dispatch is defined to schedule the generators in such a way for the given time taking into consideration of operational constraints along with ramp rate limits. It can be understood in this way that the DED problem is dividing the dispatch period into smaller time intervals wherein the SED problem is just to find the power generated by each unit in such an individual interval. Hence, we can say, DED is an extension of the SED problem.

DED problem has been noticed by many researchers in the 1980s, wherein several algorithms have been proposed by different researchers from time to time. DED problem has been discussed for various test cases in Jain et al. [1]. Chen et al. [2] showed its application to analyze both distribution and transmission systems. The classical methods to solve such problems are Lambda iterative method [3], Lagrangian method [4] and interior point method [5]. But this type of methods does not work well for the nonsmooth and nonconvex objective function. Hence, these solutions do not work for DED objective function, which itself is a nonsmooth and nonconvex optimization problem. To overcome this problem, evolutionary algorithms are proposed from time to time to solve DED problems.

Some of the meta-heuristic techniques, which have been explored to find the solution for such a nonsmooth and nonconvex optimization problem are genetic algorithm [6], grey wolf optimizer [7], biogeography based optimization [8], differential evolution [9], simulated annealing [10], gravitational search algorithm [11], firefly algorithm [12], self-learning teaching learning-based algorithm [13], etc. These algorithms utilize an initially generated population of individuals, which represents the solution for the said problem and then iterated and evolved to find the better solution.

Moreover, the trend of using a single heuristic technique has been shifted to a hybrid meta-heuristic, so that the hybrid solution will be able to give better results by mitigating its limitations and employing its strengths. The authors from time to time used a hybrid algorithm to solve complex problems [14, 15].

Here, in the proposed work, an effort has been made to realistically model the existing grey wolf optimizer so that the efficiency of the algorithm is improved. The modeling of prey in this work is considered to be dynamic, unlike grey wolf optimizers. The dynamism has been added to the prey with the help of the Levy flight distribution function. Also, the tuning of parameters of probability distribution has been done with the help of experimentation by taking a different combination of variable parameters. The performance of the different parameters is tested on different benchmark function, and hence, the optimum variables are selected as per their performance. Since it is the improved version of grey wolf optimizer, and it is utilizing Levy flight probability distribution function for modeling of prey position, hence, the name proposed for the algorithm is improved grey wolf optimizer with Levy flight, i.e., improved GWOLF. The algorithm is modeled using the MATLAB platform and is run for a 15-unit DED problem without electric vehicles and with electric vehicles for different load profiles.

Dynamic economic dispatch problem is itself a complex problem, wherein the inclusion of renewable energy sources will further make the power system more dynamic. The intermittent power generated by renewable energy sources can be taken care of with the help of plug-in electric vehicles. Moreover, the charging of electric vehicles adds to increased load in the grid. Three different profiles of plug-in electric vehicles have been used to analyze the performance of improved GWO to solve the DED problem. The charging probability distribution of these electric vehicle profiles has been shown in Figure 1.1. The different profiles considered in this chapter are EPRI, off-peak, and stochastic profiles [13].

Section 1.2 discusses problem formulation of DED problem, Section 1.3 elaborates the proposed algorithm, i.e., improved grey wolf optimizer with Levy flight along with the brief introduction to grey wolf optimizer. Section 1.4 talks about simulation and results, and the chapter is concluded in Section 1.5.

1.2 Problem Formulation

Dynamic economic dispatch (DED) is a well-known power system complex problem. The mathematical modeling of the cost function is considering the cost of thermal generators along with valve-point effect [1] as under,

(1.1)

Here in Eq (1.1), ai, bi and ci are the fuel coefficients, ei and fi represents valve point parameters to model the ripples produced in the cost curve. Ng represents the maximum number of generating units in the test case, T is the total time interval in hours for which objective function is calculated, Pi min is the minimum powergeneration by ith generator and is the power generation by ith generator in tth interval

The different constraints accompanying DED are [1]:

1.2.1 Power Output Limits

Power generated by a specific unit should be within its minimum and maximum limits.

(1.2)

where Pi min, Pi max are the minimum and maximum of power generation bygenerator.

1.2.2 Power Balance Limits

Power generated must be equal to the algebraic sum of power demand and losses at all times. Since in the test case, we have electric vehicles as well, which are also acting as the load for the system. Hence, the power balance equation is written as

(1.3)

Here, PD,t is the power demand in tth interval, t is the time interval, PL,t is the transmission losses in tth interval and Lpev,t is load added because of charge probability distribution given by different electric vehicle profiles. Transmission losses are defined with the help of Kron’s formula,

(1.4)

where loss coefficients are defined as Bij, B0i, and B00

1.2.3 Ramp Rate Limits

The change in power generation during any time interval cannot occur abruptly. Hence the change in power is defined with the ramp rate limits as under,

(1.5)

URi and DRi represents the ramp-up and ramp-down rate limit of the ith generator respectively. Pi,t of the ith generator in the tth time interval should be limited by the previously dispatched power Pi,t-1 of the ith generator in the (t − 1)th time interval within ramp-up and ramp-down rate limits URi and DRi.

1.2.4 Electric Vehicles

Greenhouse gas emission by conventional locomotives is the main reason for the increased use of electric vehicles. The increased use of electric vehicles leads to added load on the generators. Hence, these electric vehicles in this chapter are treated as load and the profile for different test cases such as EPRI, off-peak and stochastic are considered in this chapter [13].

Figure 1.1 represents the charging probability distribution function of different electric vehicle profiles. These profiles are adding extra load Lpev,t to the system, and this has been shown in Eq. (1.3).

Figure 1.1 Charging probability distribution by different profiles.

1.3 Proposed Algorithm

1.3.1 Overview of Grey Wolf Optimizer

The behavior of Canis lupus wolves is the source of inspiration to model the grey wolf optimization algorithm. This algorithm is modeled based on the social hierarchy and hunting behavior followed by different wolves in the pack [7]. The alpha (α) wolves are at the top of the pack and are considered to be leaders of the pack. Beta (β) wolves act as the advisors of α wolves wherein δ wolves are following α and β wolves. Omega (ω) wolves have the function of scapegoats only. The positions vectors of different wolves are updated to model the encircling behavior of the wolves in the (t + 1)th iteration as under,

(1.6)

where

: position vector of a

Canis lupus

wolf in iteration

t

: the index for the current iteration

: position vector of the prey

(1.7)

(1.8)

(1.9)

where

: coefficient vectors

: random vectors lies in [0, 1]

: parameter from 2 to 0 over the course of iterations,

MaxIter

: maximum number of iterations.

The positions of the other wolves are updated according to the positions of α, β, and δ as follows [7]:

(1.10)

(1.11)

(1.12)

where

: position of

α

wolves,

: position of

β

wolves,

: position of

δ

wolves

The next generation will be generated as under,

(1.13)

1.3.2 Improved Grey Wolf Optimizer with Levy Flight

The Exploratiρn andρexploiρation behavior of the algorithm is defined by the values of and [7]. lies in [−2a, 2a], where the elements are linearly decreasing from 2 to 0. Grey wolf optimizer is modified by adding one more hierarchal level, which leads to better exploitation capability and modeling prey position with the help of Levy flight distribution, which improves the exploration capability.

Addition of one more level of hierarchy

The exploitation capabilities of GWO is enhanced by adding one more hierarchal level comprised of Kappa (say κ wolves). One more level is added in Canis lupus hierarchy as shown in (1.14)