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Unknown area exploration for robots with energy constraints using a modified Butterfly Optimization Algorithm

Soft Computing volume 27, pages 3785–3804 (2023)Cite this article

Abstract

Butterfly Optimization Algorithm (BOA) is a recent metaheuristic that has been used in several optimization problems. In this paper, we propose a new version of the algorithm (xBOA) based on the crossover operator and compare its results to the original BOA and 3 other variants recently introduced in the literature. We also proposed a framework for solving the unknown area exploration problem with energy constraints using metaheuristics in both single- and multi-robot scenarios. This framework allowed us to benchmark the performances of different metaheuristics for the robotics exploration problem. We conducted several experiments to validate this framework and used it to compare the effectiveness of xBOA with well-known metaheuristics used in the literature through 5 evaluation criteria. Although BOA and xBOA are not optimal in all these criteria, we found that BOA can be a good alternative to many metaheuristics in terms of the exploration time, while xBOA is more robust to local optima; has better fitness convergence; and achieves better exploration rates than the original BOA and its other variants.

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Data availability

Data and code are available at the following link: https://github.com/amineHorseman/butterfly-optimization-algorithms.

References

  • Abualigah L, Diabat A, Mirjalili S et al (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376(113):609

    MathSciNet  MATH  Google Scholar 

  • Abualigah L, Yousri D, Abd Elaziz M et al (2021) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157(107):250

    Google Scholar 

  • Abualigah L, Abd Elaziz M, Sumari P et al (2022) Reptile search algorithm (rsa): a nature-inspired meta-heuristic optimizer. Expert Syst Appl 191(116):158

    Google Scholar 

  • Agushaka JO, Ezugwu AE, Abualigah L (2022) Dwarf mongoose optimization algorithm. Comput Methods Appl Mech Eng 391(114):570

    MathSciNet  MATH  Google Scholar 

  • Ahmadi S, Kebriaei H, Moradi H (2018) Constrained coverage path planning: evolutionary and classical approaches. Robotica 36:1–21. https://doi.org/10.1017/S0263574718000139

    Article  Google Scholar 

  • Al khawaldah M, Nuchter A, (2015) Enhanced frontier-based exploration for indoor environment with multiple robots. Adv Robot 29. https://doi.org/10.1080/01691864.2015.1015443

  • Arora S, Anand P (2019) Binary butterfly optimization approaches for feature selection. Expert Syst Appl 116:147–160

    Article  Google Scholar 

  • Arora S, Singh S (2015) Butterfly algorithm with levy flights for global optimization. In: 2015 International conference on signal processing, computing and control (ISPCC), IEEE, pp 220–224

  • Arora S, Singh S (2016) An improved butterfly optimization algorithm for global optimization. Adv Sci Eng Med 8(9):711–717

    Article  Google Scholar 

  • Arora S, Singh S (2019) Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23(3):715–734

    Article  Google Scholar 

  • Arora S, Singh S, Yetilmezsoy K (2018) A modified butterfly optimization algorithm for mechanical design optimization problems. J Braz Soc Mech Sci Eng 40(1):1–17

    Article  Google Scholar 

  • Assiri AS (2021) On the performance improvement of butterfly optimization approaches for global optimization and feature selection. PLoS One 16(1):e0242,612

  • Azizi M (2021) Atomic orbital search: a novel metaheuristic algorithm. Appl Math Model 93:657–683

    Article  MathSciNet  MATH  Google Scholar 

  • Bautin A, Simonin O, Charpillet F (2012) Minpos : a novel frontier allocation algorithm for multi-robot exploration. pp 496–508. https://doi.org/10.1007/978-3-642-33515-0_49

  • Beazley D (2010) Understanding the python gil. In: PyCON Python Conference. Atlanta, Georgia

  • Bergstra J, Yamins D, Cox DD, et al. (2013) Hyperopt: a python library for optimizing the hyperparameters of machine learning algorithms. In: Proceedings of the 12th Python in science conference, Citeseer, p 20

  • Biscani F, Izzo D (2020) A parallel global multiobjective framework for optimization: pagmo. J Open Source Softw 5(53):2338. https://doi.org/10.21105/joss.02338

    Article  Google Scholar 

  • Choset H, Pignon P (1998) Coverage path planning: the boustrophedon cellular decomposition. In: Field and service robotics, Springer, pp 203–209

  • Dakulović M, Horvatić S, Petrović I (2011) Complete coverage d* algorithm for path planning of a floor-cleaning mobile robot. IFAC Proc Vol 44(1):5950–5955. https://doi.org/10.3182/20110828-6-IT-1002.03400

    Article  Google Scholar 

  • Dosovitskiy A, Ros G, Codevilla F, et al (2017) Carla: an open urban driving simulator. In: Conference on robot learning, PMLR, pp 1–16

  • Elfes A (1989) Using occupancy grids for mobile robot perception and navigation. Computer 22(6):46–57

    Article  Google Scholar 

  • Fan Y, Shao J, Sun G, et al. (2020) A self-adaption butterfly optimization algorithm for numerical optimization problems. IEEE Access 8:88,026–88,041

  • Fong S, Deb S, Chaudhary A (2015) A review of metaheuristics in robotics. Comput Electr Eng 43:278–291

    Article  Google Scholar 

  • García M, Puig D, Wu L, et al (2007) Voronoi-based space partitioning for coordinated multi-robot exploration. JoPha: J Phys Agents, ISSN 1888-0258, Vol 1, No 1, 2007, p 37-44. https://doi.org/10.14198/JoPha.2007.1.1.05

  • Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New York

    MATH  Google Scholar 

  • Guo Y, Liu X, Chen L (2021) Improved Butterfly Optimisation Algorithm based on guiding weight and population restart. J Exp Theor Artif Intell 33(1):127–145

    Article  Google Scholar 

  • Hansen N, Müller S, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (cma-es). Evol Comput 11:1–18. https://doi.org/10.1162/106365603321828970

    Article  Google Scholar 

  • Hart PE, Nilsson NJ, Raphael B (1968) A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Syst Sci Cybern 4(2):100–107. https://doi.org/10.1109/TSSC.1968.300136

    Article  Google Scholar 

  • Holz D, Basilico N, Amigoni F, et al. (2010) Evaluating the efficiency of frontier-based exploration strategies. pp 1 – 8

  • Hoshino S, Takahashi K (2019) Dynamic partitioning strategies for multi-robot patrolling systems. J Robot Mech 31(4):535–545

    Article  Google Scholar 

  • Jalali SMJ, Ahmadian S, Kebria PM, et al (2019) Evolving artificial neural networks using butterfly optimization algorithm for data classification. In: International conference on neural information processing, Springer, pp 596–607

  • Kamalova A, Navruzov S, Qian D et al (2019) Multi-robot exploration based on multi-objective grey wolf optimizer. Appl Sci 9:2931. https://doi.org/10.3390/app9142931

    Article  Google Scholar 

  • Kamalova A, Kim KD, Lee SG (2020) Waypoint mobile robot exploration based on biologically inspired algorithms. IEEE Access 8:190,342–190,355

  • Karaboga D (2005) An idea based on honey bee swarm for numerical optimization, technical report - tr06. Technical Report, Erciyes University

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95 - International Conference on Neural Networks, vol 4, pp 1942–1948. https://doi.org/10.1109/ICNN.1995.488968

  • Koenig N, Howard A (2004) Design and use paradigms for gazebo, an open-source multi-robot simulator. In: 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)(IEEE Cat. No. 04CH37566), IEEE, pp 2149–2154

  • Li AQ (2020) Exploration and mapping with groups of robots: recent trends. Curr Robot Rep pp 1–11

  • Li G, Shuang F, Zhao P et al (2019) An improved butterfly optimization algorithm for engineering design problems using the cross-entropy method. Symmetry 11(8):1049

    Article  Google Scholar 

  • Luperto M, Antonazzi M, Amigoni F et al (2020) Robot exploration of indoor environments using incomplete and inaccurate prior knowledge. Robot Auton Syst 133(103):622

    Google Scholar 

  • Masehian E, Amin-Naseri M (2004) A voronoi diagram-visibility graph-potential field compound algorithm for robot path planning. J Robot Syst 21(6):275–300

    Article  Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  • Pavai G, Geetha T (2016) A survey on crossover operators. ACM Comput Surveys (CSUR) 49(4):1–43

    Article  Google Scholar 

  • Rohmer E, Singh SP, Freese M (2013) V-rep: a versatile and scalable robot simulation framework. In: 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE, pp 1321–1326

  • Sharma S, Saha AK, Majumder A, et al (2021) Mpboa-a novel hybrid butterfly optimization algorithm with symbiosis organisms search for global optimization and image segmentation. Multimed Tools Appl 80(8):12,035–12,076

  • Shen Z, Wilson JP, Gupta S (2020) \(\epsilon ^{\star }+\): an online coverage path planning algorithm for energy-constrained autonomous vehicles. In: Global Oceans 2020: Singapore, U.S. Gulf Coast, pp 1–6. https://doi.org/10.1109/IEEECONF38699.2020.9389353

  • Shrestha R, Tian FP, Feng W, et al (2019) Learned map prediction for enhanced mobile robot exploration. In: 2019 International Conference on Robotics and Automation (ICRA), IEEE, pp 1197–1204

  • Song J, Gupta S (2018) \(\epsilon *\): an online coverage path planning algorithm. IEEE Trans Robot 34:526–533. https://doi.org/10.1109/TRO.2017.2780259

    Article  Google Scholar 

  • Ström DP, Bogoslavskyi I, Stachniss C (2017) Robust exploration and homing for autonomous robots. Robot Auton Syst 90:125–135

    Article  Google Scholar 

  • Tai L, Liu M (2016) A robot exploration strategy based on q-learning network. In: 2016 IEEE international conference on real-time computing and robotics (RCAR), IEEE, pp 57–62

  • Tubishat M, Alswaitti M, Mirjalili S, et al. (2020) Dynamic butterfly optimization algorithm for feature selection. IEEE Access 8:194,303–194,314

  • Wang Z, Luo Q, Zhou Y (2021) Hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism for global optimization problems. Eng Comput 37(4):3665–3698

    Article  Google Scholar 

  • Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  • Xiao B, Su H, Zhao Y et al (2013) Ant colony optimisation algorithm-based multi-robot exploration. Int J Model Identif Control 18(1):41–46

    Article  Google Scholar 

  • Xie L, Han T, Zhou H, et al (2021) Tuna swarm optimization: a novel swarm-based metaheuristic algorithm for global optimization. Comput Intell Neurosci 2021

  • Yamauchi B (1997) A frontier-based approach for autonomous exploration. In: Proceedings 1997 IEEE International Symposium on Computational Intelligence in Robotics and Automation CIRA’97. ’Towards New Computational Principles for Robotics and Automation’, pp 146–151. https://doi.org/10.1109/CIRA.1997.613851

  • Yamauchi B (1998) Frontier-based exploration using multiple robots. pp 47–53, https://doi.org/10.1145/280765.280773

  • Yang XS (2012) Flower pollination algorithm for global optimization. In: International conference on unconventional computing and natural computation, Springer, pp 240–249

  • Zhang M, Long D, Qin T, et al. (2020) A chaotic hybrid butterfly optimization algorithm with particle swarm optimization for high-dimensional optimization problems. Symmetry 12(11):1800

  • Zhou Y, Xiao K, Wang Y et al (2013) A pso-inspired multi-robot map exploration algorithm using frontier-based strategy. Int J Syst Dyn Appl 2:1–13. https://doi.org/10.4018/ijsda.2013040101

    Article  Google Scholar 

  • Zounemat-Kermani M, Mahdavi-Meymand A, Hinkelmann R (2021) Nature-inspired algorithms in sanitary engineering: modelling sediment transport in sewer pipes. Soft Comput 25(8):6373–6390

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  1. Signal-Image-Parole (SIMPA) Laboratory, Computer Science Department, Université des Sciences et de la Technologie d’Oran Mohamed Boudiaf, El Mnaouar, BP 1505, Bir El Djir, 31000, Oran, Algeria

    Amine Bendahmane & Redouane Tlemsani

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  1. Amine Bendahmane
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  2. Redouane Tlemsani
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Correspondence to Amine Bendahmane.

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Bendahmane, A., Tlemsani, R. Unknown area exploration for robots with energy constraints using a modified Butterfly Optimization Algorithm. Soft Comput 27, 3785–3804 (2023). https://doi.org/10.1007/s00500-022-07530-w

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Keywords

  • Robotics
  • Exploration
  • Butterfly Optimization Algorithm
  • Crossover operator
  • Metaheuristics
  • Multi-robot systems