A grey wolf optimizer using Gaussian estimation of distribution and its application in the multi-UAV multi-target urban tracking problem

Abstract To overcome premature convergence in the grey wolf optimizer (GWO), in this study, a modified GWO integrating the basic GWO with the Gaussian estimation of distribution (GED) strategy, called GEDGWO, is proposed. GEDGWO employs the Gauss probability model to estimate the distribution of the selected superior individuals and shifts the weighted mean to adjust the search directions. Additionally, a Gaussian distribution based inferior solutions repair (ISR) method is introduced to modify the ill-shaped distribution of the population. A disturbed Gaussian random walk method is utilized to strengthen the local exploration ability. The performance of GEDGWO is compared with those of other promising GWO variants and state-of-the-art algorithms on a benchmarking CEC 2014 test suite. Non-parametric Wilcoxon and Friedman tests as well as the post hoc Iman–Davenport test are performed to further verify the efficacy of GEDGWO. Moreover, GEDGWO is applied to solve multi-UAV multi-target urban tracking path planning problem. To overcome the shortcomings of the previous solution model, a new model is described to address this complex real-time engineering optimization problem. The validity and practicability of the problem models as well as the accuracy and efficiency of GEDGWO are demonstrated by the experimental results.

[1]  Narinder Singh,et al.  A New Hybrid Whale Optimizer Algorithm with Mean Strategy of Grey Wolf Optimizer for Global Optimization , 2018 .

[2]  J. Sampson.  Adaptation in Natural and Artificial Systems (John H. Holland) , 1976 .

[3]  Zhou Rui,et al.  Dynamic UCAVs cooperative task allocation based on SAGWO algorithm , 2018 .

[4]  Leandro dos Santos Coelho,et al.  Coyote Optimization Algorithm: A New Metaheuristic for Global Optimization Problems , 2018, 2018 IEEE Congress on Evolutionary Computation (CEC).

[5]  Hossam Faris,et al.  Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems , 2017, Adv. Eng. Softw..

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

[7]  Belkacem Mahdad,et al.  Blackout risk prevention in a smart grid based flexible optimal strategy using Grey Wolf-pattern search algorithms , 2015 .

[8]  Hui Zhao,et al.  A novel nature-inspired algorithm for optimization: Virus colony search , 2016, Adv. Eng. Softw..

[9]  Duangjai Jitkongchuen,et al.  A hybrid differential evolution with grey wolf optimizer for continuous global optimization , 2015, 2015 7th International Conference on Information Technology and Electrical Engineering (ICITEE).

[10]  Chuang Liu,et al.  A hybrid evolutionary algorithm based on tissue membrane systems and CMA-ES for solving numerical optimization problems , 2016, Knowl. Based Syst..

[11]  Fei Su,et al.  Active sensing based cooperative target tracking using UAVs in an urban area , 2010, 2010 2nd International Conference on Advanced Computer Control.

[12]  Xie Ling.  Global Convergence Analysis of Hybrid Optimization Algorithms , 2012 .

[13]  Aboul Ella Hassanien,et al.  New Rough Set Attribute Reduction Algorithm Based on Grey Wolf Optimization , 2015, AISI.

[14]  Himani Joshi,et al.  Enhanced Grey Wolf Optimization Algorithm for Global Optimization , 2017, Fundam. Informaticae.

[15]  Gaige Wang,et al.  Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems , 2016, Memetic Computing.

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

[17]  Srikrishna Subramanian,et al.  Grey wolf optimization for combined heat and power dispatch with cogeneration systems , 2016 .

[18]  Hussain Shareef,et al.  Lightning search algorithm , 2015, Appl. Soft Comput..

[19]  Wei Wang,et al.  A new metaheuristic algorithm: car tracking optimization algorithm , 2017, Soft Computing.

[20]  Ponnuthurai Nagaratnam Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization , 2014 .

[21]  Layak Ali,et al.  Weighted distance Grey wolf optimizer for global optimization problems , 2015, 2015 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC).

[22]  Pinar Civicioglu,et al.  Weighted differential evolution algorithm for numerical function optimization: a comparative study with cuckoo search, artificial bee colony, adaptive differential evolution, and backtracking search optimization algorithms , 2018, Neural Computing and Applications.

[23]  Tal Shima,et al.  Task Assignment and Motion Planning for Multiple UAVs Tracking Multiple Targets in Urban Environments , 2009 .

[24]  Sen Zhang,et al.  Hybrid Grey Wolf Optimizer Using Elite Opposition-Based Learning Strategy and Simplex Method , 2017, Int. J. Comput. Intell. Appl..

[25]  Arit Thammano,et al.  Weighted distance grey wolf optimization with immigration operation for global optimization problems , 2017, 2017 18th IEEE/ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD).

[26]  Huaglory Tianfield,et al.  Biogeography-based learning particle swarm optimization , 2016, Soft Computing.

[27]  Qiang Li,et al.  An Enhanced Grey Wolf Optimization Based Feature Selection Wrapped Kernel Extreme Learning Machine for Medical Diagnosis , 2017, Comput. Math. Methods Medicine.

[28]  Yin Wang,et al.  Unmanned aerial vehicles cooperative path planning for ground target tracking via chemical reaction optimization , 2015 .

[29]  Zhirong He,et al.  Moving target tracking by UAVs in an urban area , 2013, 2013 10th IEEE International Conference on Control and Automation (ICCA).

[30]  A. Kai Qin,et al.  Self-adaptive differential evolution algorithm for numerical optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[31]  Radu-Emil Precup,et al.  An Easily Understandable Grey Wolf Optimizer and Its Application to Fuzzy Controller Tuning , 2017, Algorithms.

[32]  Parham Pahlavani,et al.  An efficient modified grey wolf optimizer with Lévy flight for optimization tasks , 2017, Appl. Soft Comput..

[33]  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.

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

[35]  Hossam Faris,et al.  Grey wolf optimizer: a review of recent variants and applications , 2017, Neural Computing and Applications.

[36]  Leandro dos Santos Coelho,et al.  Earthworm optimisation algorithm: a bio-inspired metaheuristic algorithm for global optimisation problems , 2018, Int. J. Bio Inspired Comput..

[37]  Songfeng Lu,et al.  Chaotic opposition-based grey-wolf optimization algorithm based on differential evolution and disruption operator for global optimization , 2018, Expert Syst. Appl..

[38]  Neeraj Kumar Singh,et al.  A novel hybrid GWO-SCA approach for optimization problems , 2017 .

[39]  Hui Xu,et al.  An improved grey wolf optimizer algorithm integrated with Cuckoo Search , 2017, 2017 9th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS).

[40]  Tal Shima,et al.  UAVs Task and Motion Planning in the Presence of Obstacles and Prioritized Targets , 2015, Sensors.

[41]  Marjan Mernik,et al.  A chess rating system for evolutionary algorithms: A new method for the comparison and ranking of evolutionary algorithms , 2014, Inf. Sci..

[42]  Aboul Ella Hassanien,et al.  A Hybrid Grey Wolf Based Segmentation with Statistical Image for CT Liver Images , 2016, AISI.

[43]  Xia Wang,et al.  A novel hybrid algorithm based on Biogeography-Based Optimization and Grey Wolf Optimizer , 2018, Appl. Soft Comput..

[44]  Marco Dorigo,et al.  Ant colony optimization , 2006, IEEE Computational Intelligence Magazine.

[45]  Honglun Wang,et al.  Distributed trajectory optimization for multiple solar-powered UAVs target tracking in urban environment by Adaptive Grasshopper Optimization Algorithm , 2017 .

[46]  G. M. Komaki,et al.  Grey Wolf Optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time , 2015, J. Comput. Sci..

[47]  S. B. Singh,et al.  Hybrid Algorithm of Particle Swarm Optimization and Grey Wolf Optimizer for Improving Convergence Performance , 2017, J. Appl. Math..

[48]  Hui Zhao,et al.  Cognitive behavior optimization algorithm for solving optimization problems , 2016, Appl. Soft Comput..

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

[50]  Oscar Castillo,et al.  A Study of Parameters of the Grey Wolf Optimizer Algorithm for Dynamic Adaptation with Fuzzy Logic , 2017, Nature-Inspired Design of Hybrid Intelligent Systems.

[51]  Hongxia Ji,et al.  Multi-UAVs tracking target in urban environment by model predictive control and Improved Grey Wolf Optimizer , 2016 .

[52]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[53]  Long Li,et al.  Differential evolution based on covariance matrix learning and bimodal distribution parameter setting , 2014, Appl. Soft Comput..

[54]  Wei Pan,et al.  Grey wolf optimizer for unmanned combat aerial vehicle path planning , 2016, Adv. Eng. Softw..

[55]  Seyed Mohammad Mirjalili,et al.  Evolutionary population dynamics and grey wolf optimizer , 2015, Neural Computing and Applications.

[56]  Tal Shima,et al.  Cooperative UAV Tracking Under Urban Occlusions and Airspace Limitations , 2008 .

[57]  Francisco Herrera,et al.  Since CEC 2005 competition on real-parameter optimisation: a decade of research, progress and comparative analysis’s weakness , 2017, Soft Comput..

[58]  Alex S. Fukunaga,et al.  Success-history based parameter adaptation for Differential Evolution , 2013, 2013 IEEE Congress on Evolutionary Computation.

[59]  Mohd Herwan Sulaiman,et al.  LS-SVM hyper-parameters optimization based on GWO algorithm for time series forecasting , 2015, 2015 4th International Conference on Software Engineering and Computer Systems (ICSECS).

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

[61]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[62]  Zhenxing Zhang,et al.  A novel atom search optimization for dispersion coefficient estimation in groundwater , 2019, Future Gener. Comput. Syst..

[63]  Tal Shima,et al.  Unmanned Aerial Vehicles Cooperative Tracking of Moving Ground Target in Urban Environments , 2008 .

[64]  Michal Pluhacek,et al.  Success-history based adaptive differential evolution algorithm with multi-chaotic framework for parent selection performance on CEC2014 benchmark set , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[65]  Mohamed A. Tawhid,et al.  A Hybrid grey wolf optimizer and genetic algorithm for minimizing potential energy function , 2017, Memetic Computing.

[66]  Soheila Ghambari,et al.  An improved artificial bee colony algorithm and its application to reliability optimization problems , 2018, Appl. Soft Comput..

[67]  Eid Emary,et al.  A Hybrid Grey Wolf-Bat Algorithm for Global Optimization , 2018, AMLTA.

[68]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.