MotionEncoded Electric Charged Particles Optimization for Moving Target Search Using Unmanned Aerial Vehicles
Abstract
:1. Introduction
 
 The formulation of the optimization problem with a suitable objective function and the required constraints represents the targeted problem accurately.
 
 The use of motionencoding mechanism with ECPO to increase the efficacy of the algorithm. This duo has neither been tried before in the literature nor in solving any optimization problems.
 
 Comparing the proposed mechanism with 10 commonly used metaheuristic optimization algorithms strengthens the logic of using it in moving target search applications. It is also compared with MPSO, used in a recently published research paper to solve a similar optimization problem.
 
 The presentation of the convergence curves for all the used optimization methods in a single plot to ease the comparison of their performance.
2. Problem Formulation
2.1. Target Model
2.2. Sensor Model
2.3. Belief Map Update
2.4. Objective Function
3. MotionEncoded Electric Charged Particles Optimization (ECPOME) Algorithm
3.1. Description
 nECP: the total number of ECPs,
 MaxITER: the maximum number of iterations,
 nECPI: the number of ECPs which are interacting with themselves in one of the three strategies,
 naECP: the archive pool size.
3.2. Pseudocode
Algorithm 1 ECPO pseudocode 

3.3. Algorithm
3.3.1. Initialization
3.3.2. Archive Pool
3.3.3. Selection
3.3.4. Interaction
Strategy 1
Strategy 2
Strategy 3
3.3.5. Checking the Bounds
3.3.6. Diversification
3.3.7. Diversification
Algorithm 2 Pseudocode for the diversification phase 
1 For$\mathrm{i}=1:\mathrm{newECP}$ 2 For$\mathrm{j}=1:\text{}\mathrm{ProblemSize}$ 3 $\mathrm{I}\mathrm{f}\text{}\mathrm{rand}\mathrm{Pd}$ 4 select a random ECP from the archive pool (k) 5 $\mathrm{newECP}\left(\mathrm{i},\mathrm{j}\right)=\text{}\mathrm{archiveECP}\left(\mathrm{k},\mathrm{j}\right)$ 6 End If 7 End For 
3.3.8. Population Update
3.3.9. Criteria for Termination
3.3.10. Constraint Handling
3.3.11. Motion Encoding (ME)
4. Application, Results, and Discussion
4.1. Scenarios
4.2. Comparing Algorithms
4.3. Results
 
 For Scenario A, the proposed ECPOME algorithm obtained the best results for the ‘BEST’, the ‘MEAN’ and, the ‘MEDIAN values. The TLBO algorithm obtained the highest ‘WORST’ and ‘SD’ Values.
 
 For Scenario B, the TLBO obtained a slightly better value than the ECPOME in terms of the ‘BEST’ values. However, the ECPOME obtained the best results of the ‘MEAN’, the ‘MEDIAN, the ‘WORST’ and the ‘SD’ values compared to the remaining algorithms.
 
 For Scenario C and Scenario D, the proposed ECPOME outperformed the other algorithms in terms of the statistical performance indicators used in this study. It is worth mentioning that the DE achieved equally good results to ECPOME in terms of the ‘BEST’ values.
 
 For Scenario E, the proposed ECPOME showed better performance than all the remaining algorithms in terms of the ‘BEST’, the ‘MEAN’ and the ‘MEDIAN values while the DE achieved better results in terms of the ‘WORST’ and the ‘SD’ values.
 
 For Scenario F, the proposed ECPOME achieved a better result than all the remaining algorithms in terms of the ‘BEST’, the ‘MEDIAN’ and the ‘WORST’ values, while the TLBO was better in terms of the ‘MEAN’ and ‘SD’ values.
 
 All algorithms gave an FR equal to 100, which reflects that all of them could find a solution (i.e., a path) in all the runs and for all the investigated scenarios except for the ABC algorithm for Scenario D (FR = 93.33%).
 
 For scenarios with high probability regions, like Scenario C and Scenario D, the likelihood of finding the target is higher because there is no need to divide or spread the chances of finding the target in other areas.
4.4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
References
 Huo, L.; Zhu, J.; Li, Z.; Ma, M. A Hybrid Differential Symbiotic Organisms Search Algorithm for UAV Path Planning. Sensors 2021, 21, 3037. [Google Scholar] [CrossRef] [PubMed]
 Jayaweera, H.M.P.C.; Hanoun, S. UAV Path Planning for Reconnaissance and LookAhead Coverage Support for Mobile Ground Vehicles. Sensors 2021, 21, 4595. [Google Scholar] [CrossRef]
 Behjati, M.; Mohd Noh, A.B.; Alobaidy, H.A.H.; Zulkifley, M.A.; Nordin, R.; Abdullah, N.F. LoRa Communications as an Enabler for Internet of Drones towards LargeScale Livestock Monitoring in Rural Farms. Sensors 2021, 21, 5044. [Google Scholar] [CrossRef]
 Liu, Y.; Qiu, M.; Hu, J.; Yu, H. Incentive UAVEnabled Mobile Edge Computing Based on Microwave Power Transmission. IEEE Access 2020, 8, 28584–28593. [Google Scholar] [CrossRef]
 Ochoa, S.F.; Santos, R. Humancentric wireless sensor networks to improve information availability during urban search and rescue activities. Inf. Fusion 2015, 22, 71–84. [Google Scholar] [CrossRef]
 Bourgault, F.; Furukawa, T.; DurrantWhyte, H.F. Optimal search for a lost target in a Bayesian world. Springer Tracts Adv. Robot. 2006, 24, 209–222. [Google Scholar] [CrossRef]
 Raap, M.; MeyerNieberg, S.; Pickl, S.; Zsifkovits, M. Aerial Vehicle SearchPath Optimization: A Novel Method for Emergency Operations. J. Optim. Theory Appl. 2017, 172, 965–983. [Google Scholar] [CrossRef]
 Lanillos, P.; YañezZuluaga, J.; Ruz, J.J.; BesadaPortas, E. A Bayesian approach for constrained multiagent minimum time search in uncertain dynamic domains. In Proceedings of the GECCO 2013 Genetic and Evolutionary Computation Conference, Amsterdam, The Netherlands, 6–10 July 2013; pp. 391–398. [Google Scholar]
 Chen, S.; Xiong, G.; Chen, H.; Negrut, D. MPCbased path tracking with PID speed control for highspeed autonomous vehicles considering timeoptimal travel. J. Cent. South Univ. 2020, 27, 3702–3720. [Google Scholar] [CrossRef]
 Jiang, K.; Yang, D.; Liu, C.; Zhang, T.; Xiao, Z. A Flexible MultiLayer Map Model Designed for LaneLevel Route Planning in Autonomous Vehicles. Engineering 2019, 5, 305–318. [Google Scholar] [CrossRef]
 Sujit, P.B.; Ghose, D. Self assessmentbased decision making for multiagent cooperative search. IEEE Trans. Autom. Sci. Eng. 2011, 8, 705–719. [Google Scholar] [CrossRef]
 Hu, J.; Xie, L.; Lum, K.Y.; Xu, J. Multiagent information fusion and cooperative control in target search. IEEE Trans. Control Syst. Technol. 2013, 21, 1223–1235. [Google Scholar] [CrossRef]
 Furukawa, T.; Bourgault, F.; Lavis, B.; DurrantWhyte, H.F. Recursive Bayesian searchandtracking using coordinated UAVs for lost targets. In Proceedings of the IEEE International Conference on Robotics and Automation, Orlando, FL, USA, 15–19 May 2006; Volume 2006, pp. 2521–2526. [Google Scholar]
 PerezCarabaza, S.; BesadaPortas, E.; LopezOrozco, J.A.; de la Cruz, J.M. Ant colony optimization for multiUAV minimum time search in uncertain domains. Appl. Soft Comput. J. 2018, 62, 789–806. [Google Scholar] [CrossRef]
 Trummel, K.E.; Weisinger, J.R. Complexity of the optimal searcher path problem. Oper. Res. 1986, 34, 324–327. [Google Scholar] [CrossRef][Green Version]
 Bernstein, D.S.; Givan, R.; Immerman, N.; Zilberstein, S. The complexity of decentralized control of Markov decision processes. Math. Oper. Res. 2002, 27, 819–840. [Google Scholar] [CrossRef]
 Goldberg, D.E.; Holland, J.H. Genetic Algorithms and Machine Learning. Mach. Learn. 1988, 3, 95–99. [Google Scholar] [CrossRef]
 Eagle, J.N.; Yee, J.R. Optimal branchandbound procedure for the constrained path, moving target search problem. Oper. Res. 1990, 38, 110–114. [Google Scholar] [CrossRef][Green Version]
 Lanillos, P.; BesadaPortas, E.; Pajares, G.; Ruz, J.J. Minimum time search for lost targets using cross entropy optimization. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Vilamoura, Algarve, Portugal, 7–12 October 2012; pp. 602–609. [Google Scholar]
 Gan, S.K.; Sukkarieh, S. MultiUAV target search using explicit decentralized gradientbased negotiation. In Proceedings of the IEEE International Conference on Robotics and Automation, Shanghai, China, 9–13 May 2011; pp. 751–756. [Google Scholar]
 Mathews, G.; DurrantWhyte, H.; Prokopenko, M. Asynchronous gradientbased optimisation for team decision making. In Proceedings of the IEEE Conference on Decision and Control, New Orleans, LA, USA, 12–14 December 2007; pp. 3145–3150. [Google Scholar]
 Sarmiento, A.; MurrietaCid, R.; Hutchinson, S. An efficient motion strategy to compute expectedtime locally optimal continuous search paths in known environments. Adv. Robot. 2009, 23, 1533–1560. [Google Scholar] [CrossRef][Green Version]
 Xu, R.; Tang, G.; Xie, D.; Han, L. Threedimensional neural network tracking control of autonomous underwater vehicles with input saturation. J. Cent. South Univ. 2020, 27, 1754–1769. [Google Scholar] [CrossRef]
 Phung, M.D.; Ha, Q.P. Motionencoded particle swarm optimization for moving target search using UAVs. Appl. Soft Comput. 2020, 97, 106705. [Google Scholar] [CrossRef]
 Qiming, Z.; Husheng, W.; Zhaowang, F. A review of intelligent optimization algorithm applied to unmanned aerial vehicle swarm search task. In Proceedings of the 2021 11th International Conference on Information Science and Technology (ICIST), Chengdu, China, 21–23 May 2021; pp. 383–393. [Google Scholar]
 Bouchekara, H.R.E.H. Electric Charged Particles Optimization and Its Application to the Optimal Design of a Circular Antenna Array; Springer: Dordrecht, The Netherlands, 2020; ISBN 0123456789. [Google Scholar]
 Eberhart, R.; Kennedy, J. A new optimizer using particle swarm theory. In Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 4–6 October 1995; pp. 39–43. [Google Scholar]
 Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the ICNN’95International Conference on Neural Networks, Perth, WA, Australia, 27 Novembre–1 December 1995; Volume 4, pp. 1942–1948. [Google Scholar] [CrossRef]
 Bouchekara, H.R.E.H. Most Valuable Player Algorithm: A novel optimization algorithm inspired from sport. Oper. Res. 2017, 20, 139–195. [Google Scholar] [CrossRef]
 Georgioudakis, M.; Plevris, V. A Comparative Study of Differential Evolution Variants in Constrained Structural Optimization. Front. Built Environ. 2020, 6, 102. [Google Scholar] [CrossRef]
 Holland, J.H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence; University of Michigan Press: Massachusetts, MA, USA, 1975. [Google Scholar]
 Bouchekara, H.R.E.H. Electrostatic Discharge Algorithm (ESDA): A Novel NatureInspired Optimization Algorithm and its Application to WorstCase Tolerance Analysis of An EMC Filter. IET Sci. Meas. Technol. 2019, 13, 491–499. [Google Scholar] [CrossRef]
 Simon, D. Biogeographybased optimization. IEEE Trans. Evol. Comput. 2008, 12, 702–713. [Google Scholar] [CrossRef][Green Version]
 Karaboga, D. Artificial bee colony algorithm. Scholarpedia 2010, 5, 6915. [Google Scholar] [CrossRef]
 Mittal, H.; Tripathi, A.; Pandey, A.C.; Pal, R. Gravitational search algorithm: A comprehensive analysis of recent variants. Multimed. Tools Appl. 2020, 80, 7581–7608. [Google Scholar] [CrossRef]
 Rao, R.V.; Savsani, V.J.; Vakharia, D.P. Teaching–learningbased optimization: A novel method for constrained mechanical design optimization problems. Comput. Des. 2011, 43, 303–315. [Google Scholar] [CrossRef]
 Hatamlou, A. Black hole: A new heuristic optimization approach for data clustering. Inf. Sci. 2013, 222, 175–184. [Google Scholar] [CrossRef]
 Bouchekara, H.R.E.H. Optimal power flow using blackholebased optimization approach. Appl. Soft Comput. J. 2014, 24, 879–888. [Google Scholar] [CrossRef]
ECPOME  ECPO  MPSO  MVPA  DE  GA  ESDA  BBO  ABC  GSA  TLBO  BH  

Scenario A  BEST  0.20551  0.20116  0.18138  0.19810  0.20197  0.16030  0.18885  0.19948  0.18511  0.19572  0.20485  0.18101 
MEAN  0.19239  0.16555  0.06021  0.11085  0.18960  0.13368  0.14730  0.17851  0.14966  0.04258  0.19207  0.13570  
MEDIAN  0.19118  0.18091  0.03225  0.12225  0.18942  0.13315  0.15159  0.18132  0.16003  0.00095  0.19115  0.13742  
WORST  0.18209  0.03135  0.00000  0.00002  0.17250  0.10551  0.09942  0.11788  0.00131  0.00000  0.18303  0.06931  
SD  0.00593  0.04174  0.06305  0.06100  0.00630  0.01466  0.02609  0.01696  0.03707  0.06203  0.00587  0.02547  
FR  100  100  100  100  100  100  100  100  100  100  100  100  
Scenario B  BEST  0.27634  0.26252  0.22652  0.26014  0.27466  0.22486  0.23978  0.26156  0.24424  0.18925  0.27689  0.23919 
MEAN  0.25724  0.23126  0.10670  0.17272  0.24516  0.18563  0.18328  0.21522  0.19452  0.05717  0.25216  0.19299  
MEDIAN  0.25820  0.24153  0.11274  0.19613  0.24909  0.18932  0.18379  0.23196  0.20196  0.04139  0.25462  0.19735  
WORST  0.23530  0.14698  0.01105  0.03688  0.14928  0.15175  0.11802  0.11055  0.01471  0.00009  0.22876  0.13430  
SD  0.00964  0.02539  0.05659  0.06069  0.02339  0.01860  0.03786  0.04466  0.04892  0.05281  0.01293  0.02803  
FR  100  100  100  100  100  100  100  100  100  100  100  100  
Scenario C  BEST  0.68662  0.64070  0.58442  0.64361  0.68662  0.54835  0.64221  0.66811  0.61142  0.51114  0.67221  0.60402 
MEAN  0.64158  0.52614  0.30143  0.37015  0.62170  0.46797  0.47561  0.55109  0.49444  0.22860  0.63269  0.49182  
MEDIAN  0.64997  0.55979  0.31420  0.39419  0.63538  0.47210  0.48670  0.59358  0.52423  0.23693  0.63631  0.50913  
WORST  0.57162  0.26147  0.00240  0.01434  0.35432  0.36236  0.27549  0.23189  0.26933  0.00000  0.55967  0.36322  
SD  0.02876  0.10643  0.17289  0.15426  0.06193  0.05306  0.08845  0.10633  0.09406  0.13620  0.03111  0.07498  
FR  100  100  100  100  100  100  100  100  100  100  100  100  
Scenario D  BEST  0.55431  0.49309  0.47090  0.46095  0.55431  0.40220  0.51444  0.50274  0.46497  0.33458  0.53742  0.39930 
MEAN  0.48849  0.38766  0.24390  0.31673  0.45452  0.29675  0.31233  0.35144    0.20418  0.46575  0.28810  
MEDIAN  0.49887  0.38931  0.23998  0.32675  0.44347  0.29698  0.30451  0.33692    0.20486  0.46263  0.27994  
WORST  0.40148  0.26634  0.04982  0.09241  0.32458  0.21807  0.18826  0.22614    0.00002  0.37301  0.18647  
SD  0.03120  0.05620  0.08177  0.09298  0.06339  0.04411  0.07879  0.07564    0.08891  0.04044  0.05650  
FR  100  100  100  100  100  100  100  100  93.33  100  100  100  
Scenario E  BEST  0.20518  0.20358  0.18901  0.18726  0.20477  0.17868  0.18686  0.20130  0.19559  0.17188  0.20518  0.16870 
MEAN  0.19008  0.17367  0.11979  0.13986  0.18615  0.13753  0.14400  0.17809  0.16200  0.07077  0.18893  0.13598  
MEDIAN  0.18870  0.18154  0.12904  0.14625  0.18395  0.14029  0.14865  0.17725  0.16468  0.07634  0.18830  0.13544  
WORST  0.17187  0.11000  0.00021  0.02299  0.17277  0.09305  0.04521  0.15401  0.04478  0.00012  0.16969  0.07844  
SD  0.00801  0.02362  0.05092  0.03505  0.00787  0.01839  0.03434  0.01107  0.02810  0.05553  0.00867  0.02228  
FR  100  100  100  100  100  100  100  100  100  100  100  100  
Scenario F  BEST  0.22728  0.21985  0.16005  0.17661  0.22195  0.16416  0.20217  0.22195  0.20572  0.17721  0.22175  0.18615 
MEAN  0.20007  0.18020  0.07334  0.10851  0.19650  0.10638  0.13038  0.19142  0.15022  0.06385  0.20008  0.13070  
MEDIAN  0.21024  0.18573  0.07296  0.13480  0.20160  0.11310  0.14440  0.20465  0.15892  0.03687  0.20930  0.13941  
WORST  0.16650  0.08188  0.00129  0.00564  0.13640  0.04128  0.03171  0.08111  0.00041  0.00070  0.16648  0.02830  
SD  0.01978  0.03226  0.05025  0.05427  0.02234  0.03378  0.04813  0.03334  0.05207  0.06128  0.01820  0.04135  
FR  100  100  100  100  100  100  100  100  100  100  100  100 
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Alanezi, M.A.; Bouchekara, H.R.E.H.; Shahriar, M.S.; Sha’aban, Y.A.; Javaid, M.S.; Khodja, M. MotionEncoded Electric Charged Particles Optimization for Moving Target Search Using Unmanned Aerial Vehicles. Sensors 2021, 21, 6568. https://doi.org/10.3390/s21196568
Alanezi MA, Bouchekara HREH, Shahriar MS, Sha’aban YA, Javaid MS, Khodja M. MotionEncoded Electric Charged Particles Optimization for Moving Target Search Using Unmanned Aerial Vehicles. Sensors. 2021; 21(19):6568. https://doi.org/10.3390/s21196568
Chicago/Turabian StyleAlanezi, Mohammed A., Houssem R. E. H. Bouchekara, Mohammad S. Shahriar, Yusuf A. Sha’aban, Muhammad S. Javaid, and Mohammed Khodja. 2021. "MotionEncoded Electric Charged Particles Optimization for Moving Target Search Using Unmanned Aerial Vehicles" Sensors 21, no. 19: 6568. https://doi.org/10.3390/s21196568