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Recent Trends in Communication and Intelligent Systems
Harish Sharma · Aditya Kumar Singh Pundir ·Neha Yadav · Ajay Sharma ·Swagatam Das Editors
Proceedings of ICRTCIS 2019
Algorithms for Intelligent SystemsSeries Editors: Jagdish Chand Bansal · Kusum Deep · Atulya K. Nagar
Algorithms for Intelligent Systems
Series Editors
Jagdish Chand Bansal, Department of Mathematics, South Asian University,New Delhi, Delhi, IndiaKusum Deep, Department of Mathematics, Indian Institute of Technology Roorkee,Roorkee, Uttarakhand, IndiaAtulya K. Nagar, Department of Mathematics and Computer Science,Liverpool Hope University, Liverpool, UK
This book series publishes research on the analysis and development of algorithmsfor intelligent systems with their applications to various real world problems. Itcovers research related to autonomous agents, multi-agent systems, behavioralmodeling, reinforcement learning, game theory, mechanism design, machinelearning, meta-heuristic search, optimization, planning and scheduling, artificialneural networks, evolutionary computation, swarm intelligence and other algo-rithms for intelligent systems.
The book series includes recent advancements, modification and applicationsof the artificial neural networks, evolutionary computation, swarm intelligence,artificial immune systems, fuzzy system, autonomous and multi agent systems,machine learning and other intelligent systems related areas. The material will bebeneficial for the graduate students, post-graduate students as well as theresearchers who want a broader view of advances in algorithms for intelligentsystems. The contents will also be useful to the researchers from other fields whohave no knowledge of the power of intelligent systems, e.g. the researchers in thefield of bioinformatics, biochemists, mechanical and chemical engineers,economists, musicians and medical practitioners.
The series publishes monographs, edited volumes, advanced textbooks andselected proceedings.
More information about this series at http://www.springer.com/series/16171
Harish Sharma • Aditya Kumar Singh Pundir •
Neha Yadav • Ajay Sharma • Swagatam DasEditors
Recent Trendsin Communicationand Intelligent SystemsProceedings of ICRTCIS 2019
123
EditorsHarish SharmaDepartment of Computer Scienceand EngineeringRajasthan Technical UniversityKota, Rajasthan, India
Aditya Kumar Singh PundirDepartment of Electronics andCommunication EngineeringArya College of Engineering & ITKukas, Rajasthan, India
Neha YadavDepartment of MathematicsNational Institute of TechnologyHamirpur, Himachal Pradesh, India
Ajay SharmaDepartment of Electrical EngineeringGovernment Engineering CollegeJhalawar, Rajasthan, India
Swagatam DasElectronics and CommunicationSciences UnitIndian Statistical InstituteKolkata, West Bengal, India
ISSN 2524-7565 ISSN 2524-7573 (electronic)Algorithms for Intelligent SystemsISBN 978-981-15-0425-9 ISBN 978-981-15-0426-6 (eBook)https://doi.org/10.1007/978-981-15-0426-6
© Springer Nature Singapore Pte Ltd. 2020This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721,Singapore
Jointly Organized By
Publication Partner
Supported By
Organizing Committee
International Advisory Committee
Dr. Bimal K. Bose, University of Tennessee, USADr. S. Ganesan, Oakland University, USADr. L. M. Patnaik, IISc Bangalore, IndiaDr. Ramesh Agarwal, Washington University, St. LouisDr. Vincenzo Piuri, University of Milan, ItalyDr. Ashoka Bhat, University of Victoria, CanadaProf. Akhtar Kalam, Victoria University, AustraliaDr. M. H. Rashid, University of West Florida, USADr. Fushuan Wen, Zhejiang University, ChinaIr. Dr. N. A. Rahim, UM, Kuala Lumpur, MalaysiaDr. Tarek Bouktir, University of Setif, Algeria
National Advisory Committee
Dr. S. N. Joshi, CSIR-CEERI, PilaniDr. Vineet Sahula, MNIT Jaipur, IndiaDr. K. J. Rangra, CSIR-CEERI, Pilani, IndiaDr. R. K. Sharma, CSIR-CEERI, Pilani, IndiaDr. Vijay Janyani, MNIT Jaipur, IndiaDr. K. R. Niazi, MNIT Jaipur, IndiaDr. V. K. Jain, DRDO, IndiaDr. Manoj Kr. Patairiya, NISCAIR, IndiaDr. Sanjeev Mishra, RTU, KotaProf. Harpal Tiwari, MNIT JaipurDr. S. Gurunarayanan, BITS, PilaniDr. Ghanshyam Singh, MNIT Jaipur
vii
Prof. Satish Kumar, CSIR-CSIO, ChandigarhDr. Kota Srinivas, CSIR-CSIO, Chennai CentreSh. Anand Pathak, SSME, IndiaSh. Ulkesh Desai, SSME, IndiaSh. Ashish Soni, SSME, IndiaSh. R. M. Shah, SSME, IndiaAch. (Er.) Daria S. Yadav, ISTE Rajasthan and Haryana SectionEr. Sajjan Singh Yadav, IEI, JaipurEr. Gautam Raj Bhansali, IEI, JaipurDr. J. L. Sehgal, IEI, JaipurSmt. Annapurna Bhargava, IEI, JaipurSmt. Jaya Vajpai, IEI, JaipurDr. Hemant Kumar Garg, IEI, JaipurEr. GunjanSaxena, IEI, JaipurEr. Sudesh Roop Rai, IEI, JaipurDr. Manish Tiwari, IETE Rajasthan Centre, JaipurDr. Ashish Ghunawat, MNIT JaipurDr. Dinesh Yadav, IETE Rajasthan Centre, JaipurDr. Jitendra Kr. Deegwal, Government Women Engineering College, Ajmer
Organizing Committee
Chief Patron
Prof. (Dr.) Neelima Singh, HVC, RTU, Kota
Patrons
Smt. Madhu Malti Agarwal, Chairperson, Arya GroupEr. Anurag Agarwal, Group ChairmanProf. Dhananjay Gupta, Chairman, Governing Body
General Chair
Dr. Swagatam Das, ISI KolkattaDr. Neha Yadav, NIT HamirpurDr. Vibhakar Pathak, ACEIT, Jaipur
Conveners
Dr. D. K. Sambariya, RTU, KotaDr. Kirti Vyas, ACEIT, JaipurDr. Ajay Sharma, GECJ, JhalawarEr. Ankit Gupta, ACEIT, JaipurEr. Vivek Upadhyaya, ACEIT, Jaipur
viii Organizing Committee
Organizing Chair
Dr.Rahul Srivastava, ACEIT, JaipurDr. Harish Sharma, RTU, KotaDr. S. D. Purohit, RTU, KotaDr. Ramesh C. Poonia, Amity University, Jaipur
Organizing Secretaries
Dr. Aditya Kr S. Pundir, ACEIT, JaipurDr. Sandeep Kumar, Amity University, Jaipur
Special Session Chair
Dr. Anupam Yadav, NIT JalandharDr. Sarabani Roy, Jadavpur University, KolkataDr. Nirmala Sharma, RTU, KotaDr. IrumAlvi, RTU, KotaDr. S. Mekhilef, University of Malaya, Malaysia
Local Organizing Committee Chairs
Prof. Manu Gupta, ACEIT, JaipurProf. Arun Kr Arya, ACEIT, JaipurProf. Akhil Pandey, ACEIT, JaipurProf. Prabhat Kumar, ACEIT, JaipurProf. Shalani Bhargava, ACEIT, JaipurDr. Pawan Bhambu, ACEIT, JaipurShri Ramcharan Sharma, ACEIT, Jaipur
Organizing Committee ix
Preface
This volume comprises papers presented at the TEQIP-III RTU (ATU) sponsoredFirst International Conference on Recent Trends in Communication & IntelligentSystems (ICRTICS) held on 8–9 June 2019. These presented papers cover a widerrange of selected topics related to intelligent systems and communication networks,including Intelligent Computing & Converging Technologies, IntelligentSystem Communication and Sustainable Design and Intelligent Control,Measurement & Quality Assurance. The volume Recent Trends inCommunication and Intelligent System (ICRTICS 2019) of algorithms for intelli-gent systems brings 27 of the presented papers. Each of them presents newapproaches and/or evaluates methods to real-world problems and exploratoryresearch that describes novel approaches in the field of intelligent systems.ICRTICS 2019 has received (all tracks) 272 submissions, 70 of them were acceptedfor presentation, and 27 papers have been presented. The salient feature ofICRTCIS 2019 is to promote research with a view to bring academia and industrycloser. The Advisory Committee of ICRTCIS 2019 comprises senior scientists,scholars and professionals from the reputed institutes, laboratories and industriesaround the world. The technical sessions will have peer-reviewed paper presenta-tions. In addition, keynote addresses by eminent research scholars and invited talksby technocrats will be organized during the conference. The conference is stronglybelieved to result in igniting the minds of the young researchers for undertakingmore interdisciplinary and collaborative research. The editors trust that this volumewill be useful and interesting to readers for their own research work.
Kota, India Harish SharmaKukas, India Aditya Kumar Singh PundirHamirpur, India Neha YadavJhalawar, India Ajay SharmaKolkata, India Swagatam DasAugust 2019
xi
About Arya College of Engineering & IT
Arya College of Engineering & IT was established under the aegis of All IndiaArya Samaj Society of Higher & Technology Education, in the year 2000, by LateEr. T. K. Agarwal Ji, Founder Honourable Chairman. Arya has made a strongstand among the topmost private engineering institutes in the state of Rajasthan.This group is a blend of innovation, perfection, and creation. The college is spreadover a splendid 25 acres of land area, providing a state-of-the-art infrastructure withwell-equipped laboratories, modern facilities and finest education standards.
The Arya College 1st Old Campus for a decade is known to create a bench-mark with its specialized excellence, innovative approach, participative culture andacademic rigour. The Management of Arya College is having the right bent ofinnovation and has the accurate knack to get these innovative ideas implemented.Globally accredited for its professional emergence towards technical education,Arya College makes special efforts to recruit trained faculty and stirring admissionprocedures to select potential prospects across the country, which are then trained toturn into a pool of skilled intellectual capital for the nation. This helps in a healthyand dynamic exchange which incubates leader in the corporate world. The strongindustry linkages ultimately go along the way in providing a holistic approach toresearch and education.
Arya College is the pioneer in the field of technical education and was the firstengineering college in the city of Jaipur, Rajasthan. Arya College of Engineering& ITwas the first college to start regular M.Tech. in the state of Rajasthan in the year 2006.
Arya College of Engineering & IT (ACEIT), Kukas, Jaipur, Established inYear 2000, is among the foremost of institutes of national significance in highertechnical education and approved by AICTE, New Delhi, and affiliated withRajasthan Technical University, Kota, in Rajasthan. It is commonly known as“ARYA 1st OLD CAMPUS” and “ARYA 1st”. The institute ranks amongst thebest technological institutions in the state and has contributed to all sectors oftechnical and professional development. It has also been considered a leading lightin the area of education and research.
xiii
Contents
1 Fast Convergent Gravitational Search Algorithm . . . . . . . . . . . . . . 1Pragya Rawal, Harish Sharma and Nirmala Sharma
2 An Experimental Perusal of Impedance Plethysmographyfor Biomedical Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Ramesh Kumar, Aditya Kumar Singh Pundir, Raj Kr Yadav,Anup Kumar Sharma and Digambar Singh
3 Compressive Sensing: An Efficient Approach for ImageCompression and Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Vivek Upadhyaya and Mohammad Salim
4 Optimal Location of Renewable Energy Generatorin Deregulated Power Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Digambar Singh, Ramesh Kumar Meena and Pawan Kumar Punia
5 A Genetic Improved Quantum Cryptography Modelto Optimize Network Communication . . . . . . . . . . . . . . . . . . . . . . . 47Avinash Sharma, Shivani Gaba, Shifali Singla, Suneet Kumar,Chhavi Saxena and Rahul Srivastava
6 Neural Networks-Based Framework for Detecting ChemicallyRipened Banana Fruits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55R. Roopalakshmi, Chandan Shastri, Pooja Hegde, A. S. Thaizeeraand Vishal Naik
7 Low Power CMOS Low Transconductance OTAfor Electrocardiogram Applications . . . . . . . . . . . . . . . . . . . . . . . . 63Gaurav Kumar Soni and Himanshu Arora
8 Spiral Resonator Microstrip Patch Antenna with Metamaterialon Patch and Ground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Akshta Kaushal and Gaurav Bharadwaj
xv
9 A Packet Fluctuation-Based OLSR and EfficientParameters-Based OLSR Routing Protocols for UrbanVehicular Ad Hoc Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Kirti Prakash, Prinu C. Philip, Rajeev Paulus and Anil Kumar
10 Evaluation of Similarity Measure to Find Coherence . . . . . . . . . . . 89Mausumi Goswami and B. S. Purkayastha
11 Bagged Random Forest Approach to Classify SentimentsBased on Technical Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Sweety Singhal, Saurabh Maheshwari and Monalisa Meena
12 Healthcare Services Customers’ ICT-Related Expectationsand Experiences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Anamika Sharma and Irum Alvi
13 Variation Measurement of SNR and MSE for MusicalInstruments Signal Compressed Using Compressive Sensing . . . . . 123Preeti Kumari, Gajendra Sujediya and Vivek Upadhyaya
14 A Framework to Impede Phishing Activities Using Neural Netand Website Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Srushti S. Patil and Sudhir N. Dhage
15 Overcoming the Security Shortcomings Between Open vSwitchand Network Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Milind Gupta, Shivangi Kochhar, Pulkit Jain, Manu Singhand Vishal Sharma
16 An Incremental Approach Towards Clustering Short-LengthBiological Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Neeta Maitre
17 A Novel Approach to Localized a Robot in a Given Mapwith Optimization Using GP-GPU . . . . . . . . . . . . . . . . . . . . . . . . . 157Rohit Mittal, Vibhakar Pathak, Shweta Goyal and Amit Mithal
18 Area-Efficient Splitting Mechanism for 2D Convolutionon FPGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165Shashi Poddar, Sonam Rani, Bipin Koli and Vipan Kumar
19 Neural Network Based Modeling of Radial DistortionThrough Synthetic Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Ajita Bharadwaj, Divya Mehta, Vipan Kumar, Vinod Kararand Shashi Poddar
20 A Stylistic Features Based Approach for Author Profiling . . . . . . . 185Karunakar Kavuri and M. Kavitha
xvi Contents
21 Load Balancing in Cloud Through Task Scheduling . . . . . . . . . . . 195Tarandeep and Kriti Bhushan
22 Empirical Modeling and Multi-objective Optimization of 7075Metal Matrix Composites on Machining of ComputerizedNumerical Control Wire Electrical Discharge MachiningProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205Atmanand Mishra, Dinesh Kumar Kasdekar and Sharad Agrawal
23 Identification of Rumors on Twitter . . . . . . . . . . . . . . . . . . . . . . . . 219Richa Anant Patil, Kiran Gawande and Sudhir N. Dhage
24 Brain Tumor Detection and Classification Using MachineLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227Pritanjli and Amit Doegar
25 Design of DGS-Enabled Simple UWB MIMO Antenna HavingImprovement in Isolation for IoT Applications . . . . . . . . . . . . . . . . 235Manisha Kumawat, Kirti Vyas and Rajendra Prasad Yadav
26 Concatenated Polar Code Design Aspects for 5G New Radio . . . . . 245Arti Sharma, Mohammad Salim and Vivek Upadhyay
27 Protection of Six-Phase Transmission Line Using HaarWavelet Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255Gaurav Kapoor
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Contents xvii
About the Editors
Harish Sharma is an Associate Professor at Rajasthan Technical University, Kota,in the Department of Computer Science & Engineering. He has worked atVardhaman Mahaveer Open University, Kota, and Government EngineeringCollege, Jhalawar. He received his B.Tech. and M.Tech. degree in ComputerEngineering from Government Engineering College, Kota, and Rajasthan TechnicalUniversity, Kota, in 2003 and 2009, respectively. He obtained his Ph.D. fromABV-Indian Institute of Information Technology and Management, Gwalior, India.He is secretary and one of the founder members of Soft Computing ResearchSociety of India. He is a life-time member of Cryptology Research Society of India,ISI, Kolkata. He is an associate editor of “International Journal of SwarmIntelligence (IJSI)” published by Inderscience. He has also edited special issuesof the journals “Memetic Computing” and “Journal of Experimental andTheoretical Artificial Intelligence”. His primary area of interest is nature-inspiredoptimization techniques. He has contributed in more than 45 papers published invarious international journals and conferences.
Dr. Aditya Kumar Singh Pundir has received B.E. degree in Electronics &Communication Engineering from University of Rajasthan, M.Tech. degree inVLSI Design Engineering from Rajasthan Technical University, Kota, India, andPh.D. in VLSI Testing and Embedded System Design from Poornima University,Jaipur. He is currently working as a Professor in the Department of Electronics andCommunication Engineering at Arya College of Engineering & IT, Jaipur. Hiscurrent research interests are memory testing and built-in self-testing usingembedded system design. He is a member of IEEE Electron Device Society andprofessional member of ACM, life member of ISTE, life member of CSI, India.
Dr. Neha Yadav received her Ph.D. in Mathematics from Motilal Nehru NationalInstitute of Technology, (MNNIT) Allahabad, India, in the year 2013. She com-pleted her postdoctorate from Korea University, Seoul, South Korea. She is receiverof Brain Korea (BK-21) Postdoctoral Fellowship given by Government of Republicof Korea. Prior to joining NIT Hamirpur, she taught courses and conducted research
xix
at BML Munjal University, Gurugram, Korea University Seoul, S. Korea, and TheNorthCap University, Gurugram. Her major research area includes numericalsolution of boundary value problems, artificial neural networks, and optimization.
Dr. Ajay Sharma did his B.E. from Government Engineering College, Kota(University of Rajasthan), and M.Tech. and Ph.D. from Rajasthan TechnicalUniversity, Kota. He is presently working as an Assistant Professor in theDepartment of Electrical Engineering, Government Engineering College, Jhalawar,with more than 12 years of teaching experience. His research area includes softcomputing techniques for engineering optimization problems. He has publishedmore than 30 international journals/conference papers and has delivered more than20 invited talks at the various institutes of repute. He is a life-time member ofInstitution of Engineers India.
Swagatam Das received the B.E. Tel.E., M.E. Tel.E (Control Engineering spe-cialization) and Ph.D. degrees, all from Jadavpur University, India, in 2003, 2005,and 2009, respectively.
Swagatam Das is currently serving as an Associate Professor at the Electronicsand Communication Sciences Unit of the Indian Statistical Institute, Kolkata, India.His research interests include evolutionary computing, pattern recognition,multi-agent systems, and wireless communication. Dr. Das has published oneresearch monograph, one edited volume, and more than 200 research articles inpeer-reviewed journals and international conferences. He is the foundingco-editor-in-chief of Swarm and Evolutionary Computation, an international journalfrom Elsevier. He has also served as or is serving as the associate editor of the IEEETransactions on Systems, Man, and Cybernetics: Systems, IEEE ComputationalIntelligence Magazine, IEEE Access, Neurocomputing (Elsevier), EngineeringApplications of Artificial Intelligence (Elsevier), and Information Sciences(Elsevier). He is an editorial board member of Progress in Artificial Intelligence(Springer), PeerJ Computer Science, International Journal of Artificial Intelligenceand Soft Computing, and International Journal of Adaptive and AutonomousCommunication Systems. Dr. Das has 15000+ Google Scholar citations and anH-index of 60 till date. He has been associated with the international programcommittees and organizing committees of several regular international conferencesincluding IEEE CEC, IEEE SSCI, SEAL, GECCO, and SEMCCO. He has acted asguest editor for special issues in journals like IEEE Transactions on EvolutionaryComputation and IEEE Transactions on SMC, Part C. He is the recipient of the2012 Young Engineer Award from the Indian National Academy of Engineering(INAE). He is also the recipient of the 2015 Thomson Reuters Research ExcellenceIndia Citation Award as the highest cited researcher from India in Engineering andComputer Science category between 2010 and 2014.
xx About the Editors
Chapter 1Fast Convergent Gravitational SearchAlgorithm
Pragya Rawal, Harish Sharma and Nirmala Sharma
1 Introduction
Nature-inspired algorithms (NIAs) provide many effective ways for solving complexproblems. Evolutionary algorithms (EAs) and swarm intelligence (SI) based algo-rithms are two main population-based stochastic approaches. By the gravitationalforce, individuals attract each other and stimulate according to the gravity forceemployed on individuals. As contrasted to high masses individuals, lower massesindividuals have low attraction power. This attraction strength of individuals respon-sible for lower masses individuals moves quickly in comparison to higher massesindividuals. GSA [11] provides proper balancing between exploration and exploita-tion. Here individuals of lighter masses are responsible for exploration while individ-ual having higher masses responsible for exploitation in the search space. When theprocess begins, first the exploration is carried out by the lighter masses individualswith high step size and after that, exploitation is executed by the heavier massesindividuals with small step size. Researchers are regularly working in this domainto improve the fulfillment of the GSA [3–5, 7].
In this article, an improved stochastic population-based search algorithm isdesigned, namely, fast convergent gravitational search algorithm (FCGSA) to enhancethe convergence rate as well as the exploitation capabilities of the GSA algorithm.Here, a sigmoidal function is used to control the number of agents that employ theforce to another agent in the search space.
P. Rawal (B) · H. Sharma · N. SharmaRajasthan Technical University, Kota, Indiae-mail: [email protected]
H. Sharmae-mail: [email protected]
N. Sharmae-mail: [email protected]
© Springer Nature Singapore Pte Ltd. 2020H. Sharma et al. (eds.), Recent Trends in Communication and Intelligent Systems,Algorithms for Intelligent Systems,https://doi.org/10.1007/978-981-15-0426-6_1
1
2 P. Rawal et al.
Further, description of the article is as follows: Sect. 2 describes the GSA algo-rithm; FCGSA is proposed in Sect. 3; Sect. 4 includes experimental results and dis-cussion; Sect. 5 concludes this article.
2 Gravitational Search Algorithm
The intelligent behavior of gravitational search algorithm (GSA) depends on New-ton’s gravitational law and movement [6]. According to Newton’s gravitation law,objects accelerate toward each other in the universe by the gravitational force whichis exactly corresponding to the multiplication of masses of these particles and con-versely corresponding to the square of the separation between them. This gravita-tional force is responsible for the global action of all objects toward the heaviest massobject. The achievement of these objects is marked in expressions of their masses.
Now, assume an n-dimensional space with J agents. Each individualUi in searchregion is explained below.
Ui = (u1i , . . . , udi , . . . , u
ni ) for i = 1, 2, . . . , J (1)
Here, udi represents the location of i th agent in d dimensional area.As the performance of each individual is measured by gravitational masses, which
is dependent on the fitness of individuals, the fitness of each agent is estimated. Bythese fitness values the worst and best fitness are determined as follows:
• Best and worst fitness for minimization problems are [6]:
best(q) = min f i t j (q) j ∈ 1, . . . , P (2)
worst(q) = max f i t j (q) j ∈ 1, . . . , P (3)
• Best and worst fitness for maximization problems are [6]:
best(q) = max f i t j (q) j ∈ 1, . . . , P (4)
worst(q) = min f i t j (q) j ∈ 1, . . . , P (5)
where the maximum and minimum fitness is represented by max f i t j (q) andmin f i t j (q) of the i th and j th agents, respectively, during the iteration q.
After the computation of individual’s fitness, masses, i.e., inertial, active, and pas-sive gravitational masses are calculated. Experimentally, inertial and gravitationalmasses are same in GSA. Heavier masses agents are more considered due to theirhigh attraction power and slow movement. Gravitational masses of individuals arecalculated as
Maj = Mpi = Mii = Mi , i = l, 2, . . . , N . (6)
1 Fast Convergent Gravitational Search Algorithm 3
mi (q) = f i t i − worst(q)
best(q) − worst(q)(7)
Mi = mi (q)∑J
j=1 m j (q)(8)
whereMaj ,Mpi , andMii are active, passive gravitationalmasses, and inertialmasses,respectively. f i t i and Mi are the fitness value and gravitational agent’s mass i ,respectively. worst(q) and best(q) are worst and best fitness values.
The gravitational constant G(q) is calculated as follows:
G(q) = G0e(−αq/T ) (9)
Here, G0 and α are constants and initialized before the process begins. G(q)
reduces exponentially with time [1]. The acceleration of i th agent is determined as
adi (q) = Fdi (q)
Mi (q)(10)
where Fdi (q) is the randomly weighted sum of the forces applied from other agents
and Mi (q) is gravitational mass. Fdi (q) is calculated through the following expres-
sion:Fdi (q) =
∑
j∈Kbest, j �=i
rand j Fdi j (q) (11)
where Kbest is calculated as follows:
Kbest = f inalper + (1 − q
T) · (P − f inalper) (12)
Kbest = round
(
P × Kbest
100
)
(13)
Here, f inalper is the constant value. It represents only 2 percent of agents whichapply force toward each others in the last iteration. P defines the whole populationin the search region. Kbest is the initial P individuals having the best fitness valueand the highest mass.
Fdi j (q) in Eq. (11) is Newton’s gravitational force, defined as force acting on i th
agent mass by the j th agent mass in the qth iteration and is computed using thefollowing equation:
Fdi j (q) = G(q) · Mpi (q) · Maj (q)
Ri j (q) + ε· (xdj (q) − xdi (q)) (14)
4 P. Rawal et al.
Here, Maj (q) and Mpi (q) are active or passive gravitational masses of j th and i thindividuals subsequently. Ri j (q) is the euclidian distance between i th and j th indi-viduals.
ε is a constant and G(q) is the gravitational constant computed through Eq. (9).Due to this gravitational force, globalmovement of objects takes place.Agents updatetheir velocity and position according to the following equations:
vdi (q + 1) = randi × vd
i (q) + adi (q) (15)
xdi (q + 1) = xdi (q) + vdi (q + 1) (16)
where rand is uniformly randomized variable lies in range [0, 1]. It gives randomizedcharacteristics for searching operation. adi (q) is the acceleration of i th agent in ddimension space during iteration q. vd
i (q) and vdi (q + 1) are velocities of i th agent
at the q and (q + 1) iterations, respectively. While xdi (q) and xdi (q + 1) are thepositions of i th agent at the q and (q + 1) iterations, respectively. Each mass in theGSA is a solution and the optimum solution of the search space is represented bythe heaviest mass.
3 Fast Convergent Gravitational Search Algorithm
Exploration and exploitation play a vital role in any population-based optimizationalgorithm. Exploration is for probing an enlarging part of search regionwith the crav-ing of discovering other encouraging individual that are to be characterized, whereasthe exploitation is for investigating a optimum solution of the search region with thepassion of encouraging a assuring solution with the previously visited search space.GSA investigates the search region to find the excellent solution. After the few slipby of iterations, GSA exploits the search space. For better execution, it is essentialto keep an appropriate balance among exploration and exploitation capabilities. Toachieve exploration, individuals should make high step size, whereas in later iter-ations, individuals should make small step size. It is obvious, that performance ofGSA is greatly influenced by its parameters. In GSA, Kbest control the count ofagents that employ the power to other agent in search space. Almost all agents applyforce to other agents through preceding iterations, to restrict trape in local optima,while at the last iteration, there is only one agent that applys force to another. As itis clear from Eq. (12), Kbest is linearly reduced to improve in Kbest a little as thecount of iterations increments. So to enhance the convergence speed, a new strategyis introduced named as fast convergent gravitational search algorithm (FCGSA). Inthe FCGSA, a new Kbest is proposed as demonstrated as follows:
Kbest ′ = f inalper + 1
1 + e(αq/T )· (P − f inalper) (17)
1 Fast Convergent Gravitational Search Algorithm 5
Here, f inalper and α are constants and q and T are contemporary iteration andhighest count of iterations consequently. A sigmoidal function is embedded withKbest in Eq. (17), which is decreased exponentially in every iteration.
Further, position update process in Eq. (9), performs a huge role for the step size ofindividual. From the position update process, we can simply conclude that positiondepends on the velocity. When the velocity of individual is large, acceleration ofindividual is large, which leads to large step size, that helps in exploration, while lowacceleration will result in less step size, which helps in search region’s exploitation.Therefore, in this article, location modification equation is modified as follows:
xdi (q + 1) = xdi (q) + vdi (q + 1) · e(−α0q/T ) (18)
Here, α is constant, q and T are the current iterations and highest count of iteration,respectively. From the Eq. (18), it is clear that impetus in initial iteration is high,which results in high acceleration and step size will be large. Velocity exponentiallydecreases through the iteration, which controls the step size of individual. So thepropose strategy organizes a decent balance between diversification and intensifica-tion knowledge as the count of iteration increases. The pseudocode of FCGSA isdepicted in Algorithm 1.
Algorithm 1 FCGSA AlgorithmIdentify the initial population of the search space.Creating a randomly dispersed set of individuals.while Stopping criteria is not filled doEvaluate fitness for each individuals.Calculate gravitational mass by Eqs. (7) and (8) for each individual.Evaluate gravitational constant (G) by equation (9).Calculate Kbest by Eqs. (17) and (13).Calculate the acceleration (a) for every individual by Eq. (10).modify velocities and location of the individuals by Eqs. (15) and (18).
end while
4 Experimental Results and Discussion
4.1 Test Problems Under Consideration
To investigate the pursuance of the introduced FCGSA mechanism, 15 benchmarkfunctions are chosen as shown in Table1.
6 P. Rawal et al.
Table1
Testproblems,S:
dimension,A
E:acceptableerror
Testproblem
Objectiv
efunctio
nSearch
range
Optim
umvalue
SAE
Griew
ank
f 1(u
)=
1+
140
00
∑D i=
1u2 i−
∏D i=
1cos(
u i √ i)
[−600,
600]
f(0)
=0
301.0E
−05
Zakharov
f 2(u
)=
∑D i=
1u i
2+
(∑D i=
1iu
i 2)2
+(∑
D i=1iu
1 2)4
[−5.12,5.12]
f(0)
=0
301.0E
−02
Cigar
f 3(u
)=
u02+
100000
∑D i=
1u i
2[−
10,10
]f(0)
=04
301.0E
−05
Sum
ofdifferentp
owers
f 4(u
)=
∑D i=
1|u i
|i+1
[−11
]f(0)
=0
301.0E
−05
Bealefunctio
nf 5
(u)=
[1.5
−u1(1
−u2)]2
+[2.
25−
u1(1
−u2 2)]2
+[2.
625
−u1(1
−u3 2)]2
[−4.5,4.5]
f(3,0.5)
=0
21.0E
−05
Colville
f 6(u
)=
100[u
2−
u2 1]2
+(1
−u1)2
+90
(u4−
u2 3)2
+(1
−u3)2
+10
.1[(u
2−
1)2+
(u4−
1)2]+
19.8
(u2
−1)
(u4−
1)[−
10,10
]f(1)
=0
41.0E
−05
Branins’sfunctio
nf 7
(u)=
a(u2
−bu
2 1+
cu1−
d)2
+e(1
−f)
cosx 1
+e
−5≤
u1
≤10
,0
≤u2
≤15
f(−π
,12
.275
)=
0.3979
21.0E
−05
Kow
alik
f 8(u
)=
∑11 i=
1[a i
−u1(b
2 i+b
iu2)
b2 i+b
iu3+u
4]2
[−5,5]
f(0.192833
,0.190836
,0.12311,
0.135766
)=
0.000307486
41.0E
−04
Geartrainprob
lem
f 9(u
)=
(1
6.93
1−
u1u2
u3u4
)2
[12,60
]f(19
,16
,43
,49
)=
−1.0316
41.0E
−15
Six-hu
mpcamelback
f 10(u
)=
(4−
2.1u
2 1+
u4 1/3)u2 1
+u1u2+
(−4
+4u
2 2)u
2 2[−
5,5]
f(−0
.0898,0.7126
)=
−1.0316
21.0E
−05
Easom
’sfunctio
nf 11(u
)=
−cosu
1
cosu
2e(
(−(u
1−π
)2−(
u2−π
)2))
[−100,
100]
f(π,π
)=
−12
1.0E
−13
DekkersandAarts
f 12(u
)=
105u2 1+i2 2
−(u
2 1+
u2 2)2
+10
−5(u
2 1+
u2 2)4
[−20
,20
]f(0,
15)=
f(0,
−15)
=−2
4777
25.0E
−01
Hosakip
roblem
f 13
=(1
−8u
1+
7u2 1−
7/3u
3 1+
1/4u
4 1)u
2 2exp(
−u2)
[0,5],[0,6]
−2.3458
21.0E
−05
McC
ormick
f 14(u
)=
sin(u1+
u2)+
(u1−
u2)2
−3 2u1+
5 2u2+
1−1
.5≤
u1
≤4,
−3≤
u2
≤3
f(−0
.547,−
1.547)
=−1
.9133
301.0E
−04
Temp
f 15(u
)=
u2 1+
u2 2
[−5,5]
f(0)
=0
21.0E
−5
1 Fast Convergent Gravitational Search Algorithm 7
Fig. 1 Effect of α and α0 on success rate
4.2 Experimental Setting
To attest the fulfillment of the introduced algorithm GSA, a comparable estima-tion is done among FCGSA, GSA [6], FBGSA [4], BBO [10], and SMO [2]. Theexperimental setting is as follows:
• The count of runs = 30,• Population size = 50,• G0 = 100• α = 20,• The Parameter perception for GSA [6], FBGSA [4], BBO [10], and SMO [2] aretaken from their original research,
• The validity of FCGSA is analyzed for examined test problems over distinct valuesof α and α0. The estimation of α and α0 is set through sensitive investigationregarding success rate (SR) and results are appeared in Fig. 1. Figure1 proves thathigest value of sum of success, i.e., best outcome is achieved by taking α = 20and α0 = 7.
4.3 Results Comparison
Experimental outcomes are appeared inTable2 for the considered algorithms. Table2shows the analysis of average count of function evaluations (AFEs),mean error (ME),standard deviation (SD), and success rate (SR). The results shows the hight efficiencyand accuracy level of FCGSA as compared to GSA [6], FBGSA [4], BBO [10], andSMO [2].
A comparison is also performed between the considered algorithms for the AFEsthrough the analysis of boxplots. The boxplot is a graphical representation of data, inwhich rectangle is drawn to represent the interquartile with a vertical line indicating
8 P. Rawal et al.
Table 2 Comparison results of test problem, TP
TF Algorithm SD ME AFEs SR
f1 FCGSA 8.06052E–07 9.20853E–06 37108.33333 30
GSA 7.37634E–07 8.92957E–06 37148.33333 30
FBGSA 0.03891712 0.865277098 200000.0000 0
BBO 1.45446E–06 8.92554E–06 23176.66667 30
SMO 1.84E–03 5.20E–04 85981.60000 27
f2 FCGSA 0.000372323 0.009592798 56746.66667 30
GSA 2.597485864 5.068510743 200000.0000 0
FBGSA 8.652301498 40.38870689 200000.0000 0
BBO 0.785070093 0.988277042 200000.0000 0
SMO 7.93E–04 9.14E–03 131681.7000 30
f3 FCGSA 4.5719E–07 9.53292E–06 171578.3333 30
GSA 9.788438037 8.780742862 200000.0000 0
FBGSA 9.811033166 10.82059429 200000.0000 0
BBO 2.60599E–06 7.72803E–06 55525.00000 30
SMO 7.74E–07 8.93E–06 22581.90000 30
f4 FCGSA 1.84074E–06 7.56839E–06 21205.00000 30
GSA 2.51821E–06 6.96522E–06 37470.00000 30
FBGSA 1.89628E–06 7.4215E–06 57345.00000 30
BBO 1.05776E–05 1.06609E–05 58341.66667 23
SMO 1.73E–06 7.98E–06 5181.000000 30
f5 FCGSA 2.90255E–06 5.99934E–06 35346.66667 30
GSA 2.96856E–06 4.82759E–06 55576.66667 30
FBGSA 2.83446E–06 5.3857E–06 70070.00000 30
BBO 0.228618561 0.07621397 36078.33333 27
SMO 3.01E–06 5.52E–06 1640.100000 30
f6 FCGSA 0.000246749 0.000605967 53436.66667 30
GSA 0.156289433 0.031365194 128590.0000 27
FBGSA 0.372881454 0.099248862 200000.0000 0
BBO 2.754500971 2.68777526 200000.0000 0
SMO 2.48E–04 7.44E–04 48452.70000 30
f7 FCGSA 2.90316E–05 4.62067E–05 24695.00000 30
GSA 2.74336E–05 4.61824E–05 31956.66667 30
FBGSA 3.24517E–05 4.31121E–05 38440.00000 30
BBO 2.11049E–05 7.90241E–05 55346.66667 30
SMO 6.83E–06 5.99E–06 42765.83333 27
PSO 3.72E–06 5.14E–06 22480.00000 27
f8 FCGSA 0.000117784 0.000188932 65.00000000 30
GSA 7.97953E–05 0.000239179 78.33333333 30
FBGSA 7.81274E–05 0.000247513 63.33333333 30
BBO 7.16167E–05 0.000267026 108.3333333 30
SMO 9.46E–06 9.29E–05 37906.76667 30
(continued)
1 Fast Convergent Gravitational Search Algorithm 9
Table 2 (continued)
TF Algorithm SD ME AFEs SR
f9 FCGSA 7.35101E–13 1.93583E–12 12460.00000 30
GSA 7.49274E–13 1.81189E–12 17951.66667 30
FBGSA 7.80543E–13 1.89104E–12 21995.00000 30
BBO 4.97212E–13 2.19232E–12 1750.000000 30
SMO 1.42E–14 2.7E–12 415647.0667 0
f10 FCGSA 1.22148E–05 1.35309E–05 32006.66667 30
GSA 1.18518E–05 1.30128E–05 40371.66667 30
FBGSA 1.19628E–05 1.22282E–05 47368.33333 30
BBO 0.360911475 0.217643947 69625.00000 22
SMO 1.42E–05 1.69E–05 222537.4000 14
f11 FCGSA 0.179498873 0.033332104 163100.0000 29
GSA 0.208447215 0.1 137431.6667 27
FBGSA 2.70435E–14 5.3435E–14 155450.0000 30
BBO 0.299974022 0.099996837 193430.0000 1
SMO 2.71E–14 4.18E–14 11959.2000 30
f12 FCGSA 5513.426617 6807.452936 330.0000000 30
GSA 6115.568355 8014.527136 533.3333333 30
FBGSA 4961.479556 5963.045707 683.3333333 30
BBO 6652.02535 5259.95564 890.0000000 30
SMO 4.90E–03 4.88E–01 1230.90000 30
f13 FCGSA 5.99309E–06 5.88909E–06 28421.66667 30
GSA 6.39726E–06 5.76948E–06 35351.66667 30
FBGSA 6.24228E–06 6.28523E–06 36780.00000 30
BBO 0.49872928 1.518751054 200000.0000 0
SMO 2.13E–06 1.12E–05 402717.8667 1
f14 FCGSA 5.80666E–06 8.99053E–05 26213.33333 30
GSA 7.08747E–06 8.8465E–05 38666.66667 30
FBGSA 5.65863E–06 8.89199E–05 41330.00000 30
BBO 6.29432E–06 9.15118E–05 12386.66667 30
SMO 6.76E–06 8.74E–05 702.9000000 30
f15 FCGSA 2.95213E–06 4.87418E–06 32386.66667 30
GSA 3.16689E–06 4.72873E–06 37408.33333 30
FBGSA 2.63159E–06 4.03363E–06 42641.66667 30
BBO 2.78005E–06 4.76596E–06 750.0000000 30
SMO 2.74E–06 4.62E–06 726.0000000 30
10 P. Rawal et al.
Fig. 2 Boxplots graphs (average number of function evaluation)
the median value. The boxplot analysis of the respective algorithms with FCGSA isshown in Fig. 2. The outcomes demonstrate that interquartile pasture and medians ofFCGSA are low in the correlation of GSA, FBGSA, BBO, and SMO.
Further, Mann-Whitney U rank sum test (MWUR) [9] is performed at 5% level ofexceptional (α = 0.05) between FCGSA–GSA, FCGSA–FBGSA, FCGSA–BBO,and FCGSA–SMO. Table3 shows the compared results of mean function evaluationandMann-Whitney test for 30 runs. In this test, wewatch the extraordinary differencebetween two informational sets. If the remarkable difference is not seen then “=”symbol shows up and when a remarkable difference is watched, then an examinationis performed as far as the AFEs. We utilize “+” and “−” symbol, “+” speaks to thatthe FCGSA is finer than the analyzed methods and “−” speaks to that the method issubordinate. The last row in Table3, authorizes the superiority of FCGSA over GSA,FBGSA, BBO, and SMO. To confirm the convergence power of modified methodwe use acceleration rate (AR) [8] which is represented as follows:
AR = AFEcompareAlgo
AFEFCGSA(19)
Here compareAlgo ∈ (GSA, FBGSA, BBO SMO) and AR > 1 means FCGSA isquicker than the other comparative methods. Table4 demonstrated that convergencespeed of LEGSA is superior than the other analyzed methods.
1 Fast Convergent Gravitational Search Algorithm 11
Table 3 Comparison based on MWUR test at significance level α = 0.05 and mean functionevaluations
Test problems FCGSA versusGSA
FCGSA versusFBGSA
FCGSA versusBBO
FCGSA versusSMO
f1 + + − +f2 + + + +f3 + + − −f4 + + + −f5 + + + +f6 + + + −f7 + − + +f8 + + + +f9 + + − +f10 + + + +f11 − − + −f12 + + + +f13 + + + +f14 + + − −f15 + + − −Total no. of + sign 14 13 10 9
Table 4 Test problems: TP, acceleration rate (AR) of FCGSA compare to the standard GSA,BBO
TP GSA FBGSA BBO SMO
f1 1.001077925 5.389624972 0.624567707 2.317042893
f2 3.52443609 3.52443609 3.524436090 2.320518679
f3 1.165648344 1.165648344 0.323613121 0.131612772
f4 1.767036076 2.704315020 2.751316513 0.244329168
f5 1.572331195 1.982365145 1.020699735 1.020699735
f6 2.406400099 3.742748425 3.742748424 0.906731333
f7 1.294054127 1.556590403 2.241209421 1.556590403
f8 1.205128205 0.974358974 1.666666666 583.1810257
f9 1.440743713 1.765248796 0.140449438 33.35851257
f10 1.261351802 1.479952093 2.175328056 6.95284524
f11 0.842622113 0.95309626 1.185959534 0.073324341
f12 1.616161616 2.070707071 2.696969696 3.73000000
f13 1.243828065 1.294083152 7.036885004 14.16939659
f14 1.475076297 1.576678535 0.472533062 0.026814598
f15 1.15505352 1.316642651 0.023157678 0.022416632
