β-Chaotic map enabled Grey Wolf Optimizer

Abstract The diversification (exploration) and intensification (exploitation) are two main attributes of any population-based metaheuristic algorithm. It is essential for any algorithm that in exploration phase the search space is utilized and explored properly through random behavior, on the other hand, the progression of the search in a viable direction to obtain global minima, should be performed through strategic behavior in exploitation phase. A proper balance between these two can be achieved by an adaptive mechanism in every algorithm. Robustness of an algorithm is judged by the efficacy of these two attributes along with the efficiency of the bridging mechanism. In literature, the positive impact of inculcation of chaotic sequences on the efficacy of these attributes has been reported. With this motivation, the paper presents an adaptive bridging mechanism based on β -chaotic sequence for the improvement of Grey Wolf Optimizer (GWO). The control vector of classical GWO is integrated with the β -chaotic sequence for better exploration and exploitation virtues. The new variant β -GWO is benchmarked on two benchmark suites 1 and 2 that include 12 shifted and biased functions and 29 Congress on Evolutionary Computation-2017 (CEC-2017) functions. Sensitivity Dependence of Initial Conditions (SDIC) is performed for tuning the initial parameters. The comparison of the proposed variant with other contemporary algorithms is carried out and different statistical tests are performed to judge the efficacy of the proposed variant. Further, the applicability of the proposed variant is checked with two real engineering problems namely frequency modulated sound waves parameter estimation problem and strategic bidding in the energy market. Results reveal that the proposed chaotic variant exhibits better exploration and exploitation qualities.

[1]  Konstantinos G. Margaritis,et al.  On benchmarking functions for genetic algorithms , 2001, Int. J. Comput. Math..

[2]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[3]  Radu-Emil Precup,et al.  Grey Wolf Optimizer Algorithm-Based Tuning of Fuzzy Control Systems With Reduced Parametric Sensitivity , 2017, IEEE Transactions on Industrial Electronics.

[4]  Y. Baghzouz,et al.  Genetic-Algorithm-Based Optimization Approach for Energy Management , 2013, IEEE Transactions on Power Delivery.

[5]  Harish Sharma,et al.  Spider Monkey Optimization algorithm for numerical optimization , 2014, Memetic Computing.

[6]  Rafik Hamza,et al.  A novel pseudo random sequence generator for image-cryptographic applications , 2017, J. Inf. Secur. Appl..

[7]  Xiaosong Hu,et al.  Charging optimization in lithium-ion batteries based on temperature rise and charge time , 2017 .

[8]  Xin-She Yang,et al.  Firefly Algorithms for Multimodal Optimization , 2009, SAGA.

[9]  Xin‐She Yang,et al.  Appendix A: Test Problems in Optimization , 2010 .

[10]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[11]  Edward N. Lorenz The Butterfly Effect , 2000 .

[12]  Kusum Deep,et al.  A novel Random Walk Grey Wolf Optimizer , 2019, Swarm Evol. Comput..

[13]  Andrew Lewis,et al.  Biogeography-based optimisation with chaos , 2014, Neural Computing and Applications.

[14]  Amir Hossein Gandomi,et al.  Chaotic gravitational constants for the gravitational search algorithm , 2017, Appl. Soft Comput..

[15]  Hossein Nezamabadi-pour,et al.  GSA: A Gravitational Search Algorithm , 2009, Inf. Sci..

[16]  Zhaolu Guo,et al.  Enhancing social emotional optimization algorithm using local search , 2017, Soft Comput..

[17]  Xin-She Yang,et al.  Cuckoo Search via Lévy flights , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[18]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[19]  F. Wilcoxon Individual Comparisons by Ranking Methods , 1945 .

[20]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[21]  Sankalap Arora,et al.  Chaotic grey wolf optimization algorithm for constrained optimization problems , 2018, J. Comput. Des. Eng..

[22]  Bijaya K. Panigrahi,et al.  Binary Grey Wolf Optimizer for large scale unit commitment problem , 2018, Swarm Evol. Comput..

[23]  Jun Wang,et al.  Chaotic direct sequence spread spectrum for secure underwater acoustic communication , 2016 .

[24]  R. Coppinger,et al.  Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations , 2011, Behavioural Processes.

[25]  Zhaolu Guo,et al.  Adaptive harmony search with best-based search strategy , 2018, Soft Comput..

[26]  Amir Hossein Gandomi,et al.  Chaotic bat algorithm , 2014, J. Comput. Sci..

[27]  Aboul Ella Hassanien,et al.  Feature selection via a novel chaotic crow search algorithm , 2017, Neural Computing and Applications.

[28]  Jianjun Jiao,et al.  A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems , 2017, Neural Computing and Applications.

[29]  Dan Simon,et al.  Biogeography-Based Optimization , 2022 .

[30]  Xin-She Yang,et al.  Firefly algorithm with chaos , 2013, Commun. Nonlinear Sci. Numer. Simul..

[31]  T. Jayabarathi,et al.  Economic dispatch using hybrid grey wolf optimizer , 2016 .

[32]  Annapurna Bhargava,et al.  Modified Grey Wolf Optimization Algorithm for Transmission Network Expansion Planning Problem , 2017, Arabian Journal for Science and Engineering.

[33]  Chokri Ben Amar,et al.  Beta wavelets. Synthesis and application to lossy image compression , 2005, Adv. Eng. Softw..

[34]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

[35]  Urvinder Singh,et al.  Modified Grey Wolf Optimizer for Global Engineering Optimization , 2016, Appl. Comput. Intell. Soft Comput..

[36]  Andrew Lewis,et al.  Grasshopper Optimisation Algorithm: Theory and application , 2017, Adv. Eng. Softw..

[37]  Rajesh Kumar,et al.  Intelligent Grey Wolf Optimizer - Development and application for strategic bidding in uniform price spot energy market , 2018, Appl. Soft Comput..

[38]  N. Maletic,et al.  Random Binary Sequences in Telecommunications , 2013 .

[39]  Rim Zahmoul,et al.  Image encryption based on new Beta chaotic maps , 2017 .

[40]  Andrew Lewis,et al.  Grey Wolf Optimizer , 2014, Adv. Eng. Softw..

[41]  Anders Lagerkvist,et al.  Stabilization of Pb- and Cu-contaminated soil using coal fly ash and peat. , 2007, Environmental pollution.

[42]  Alex S. Fukunaga,et al.  Evaluating the performance of SHADE on CEC 2013 benchmark problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[43]  Provas Kumar Roy,et al.  Oppositional based grey wolf optimization algorithm for economic dispatch problem of power system , 2017, Ain Shams Engineering Journal.

[44]  Nantiwat Pholdee,et al.  Optimal reactive power dispatch problem using a two-archive multi-objective grey wolf optimizer , 2017, Expert Syst. Appl..

[45]  Xin-She Yang,et al.  Flower Pollination Algorithm for Global Optimization , 2012, UCNC.

[46]  Rajesh Kumar,et al.  Application and Development of Enhanced Chaotic Grasshopper Optimization Algorithms , 2018 .

[47]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[48]  Akash Saxena,et al.  Grey wolf optimizer based regulator design for automatic generation control of interconnected power system , 2016 .

[49]  Alex S. Fukunaga,et al.  Improving the search performance of SHADE using linear population size reduction , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[50]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[51]  Aboul Ella Hassanien,et al.  Binary grey wolf optimization approaches for feature selection , 2016, Neurocomputing.

[52]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[53]  Wen-Tsao Pan,et al.  A new Fruit Fly Optimization Algorithm: Taking the financial distress model as an example , 2012, Knowl. Based Syst..

[54]  Edward J. Anderson,et al.  Estimation of Electricity Market Distribution Functions , 2003, Ann. Oper. Res..

[55]  S.N. Singh,et al.  Fuzzy Adaptive Particle Swarm Optimization for Bidding Strategy in Uniform Price Spot Market , 2007, IEEE Transactions on Power Systems.

[56]  Ibrahim Eksin,et al.  A new optimization method: Big Bang-Big Crunch , 2006, Adv. Eng. Softw..

[57]  Akash Saxena,et al.  Ambient Air Quality Classification by Grey Wolf Optimizer Based Support Vector Machine , 2017, Journal of environmental and public health.

[58]  Alireza Askarzadeh,et al.  A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm , 2016 .

[59]  Tao Yu,et al.  Grouped grey wolf optimizer for maximum power point tracking of doubly-fed induction generator based wind turbine , 2017 .

[60]  Xin-She Yang,et al.  Chaos-enhanced accelerated particle swarm optimization , 2013, Commun. Nonlinear Sci. Numer. Simul..

[61]  Anil Kumar,et al.  Electrocardiogram Signal Compression Using Beta Wavelets , 2012, J. Math. Model. Algorithms.

[62]  Abdolreza Hatamlou,et al.  Black hole: A new heuristic optimization approach for data clustering , 2013, Inf. Sci..