Improved Energy Valley Optimizer with Levy Flight for Optimization Problems

Nabila H Shikoun; Islam S Fathi

doi:10.61927/igmin172

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André Mampuya Nzita, Edmond Phuku Phuati, Robert Muanda Ngimbi, Guyh Dituba Ngoma and Nathanaël Masiala Mavungu

Technology Group Research Article Article ID: igmin172

Improved Energy Valley Optimizer with Levy Flight for Optimization Problems

Data Science Machine Learning Data Mining

Nabila H Shikoun ^1,2 and

Islam S Fathi ^* ¹

Affiliation

Department of Information Systems, Al Alson Higher Institute, Cairo 11762, Egypt | Department of Systems and Computer Engineering, Faculty of Engineering, Alazhar University, Cairo, Egypt

Department of Information Systems, Al Alson Higher Institute, Cairo 11762, Egypt

DOI10.61927/igmin172 Fulltext HTML Fulltext PDF Cite this article

Abstract

Energy Valley Optimizer (EVO) is one of the recent metaheuristic algorithms. It draws inspiration from advanced principles in physics related to particle stability and decay modes. This paper presents a new Energy Valley Optimizer (EVO) and levy flights that are hybrid to improve the EVO in solving optimization problems. Levy flight is one of the most important randomization techniques. Fifteen mathematical test functions (five unimodal functions, four multimodal functions, and six composite functions) are solved with the proposed algorithm. We also compare our results with previous results of metaheuristic algorithms. The statistical results show that the results of the Levy Energy Valley Optimizer (LEVO) outperform other algorithms in almost all mathematical test functions.

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References

Azizi M, Aickelin U, A Khorshidi H, Baghalzadeh Shishehgarkhaneh M. Energy valley optimizer: a novel metaheuristic algorithm for global and engineering optimization. Sci Rep. 2023 Jan 5;13(1):226. doi: 10.1038/s41598-022-27344-y. PMID: 36604589; PMCID: PMC9816156.
Boussaïd I, Lepagnot J, and Siarry P, A survey on optimization metaheuristics. Inform Sci. 2013; 237: 82–117.
Holland JH, Reitman JS. Cognitive systems based on adaptive algorithms. ACM SIGART Bull. 1977; 49–49.
Colorni A, Dorigo M, Maniezzo V. Distributed optimization by ant colonies. In: Proceedings of the first European conference on artificial life. 1991; 134–42.
Eberhart RC, Kennedy J. A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science. 1995; 39–43.
Karaboga D, Basturk B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim. 2007; 39:459–71.
Rajabioun R. Cuckoo optimization algorithm. Appl Soft Comput. 2011; 11:5508–18.
Yang X-S. Firefly algorithm, Levy flights and global optimization. In: Research and development in intelligent systems XXVI. Springer. 2010; 209–18.
Seyedali M, Mohammad MS, Andrew L. Grey wolf optimizer. Adv Eng Software. 2014; 69:46–61.
Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S. Equilibrium optimizer: A novel optimization algorithm. Knowl.-Based Syst. 2020; 191:
MiarNaeimi F, Azizyan G, Rashki M. ‘Horse herd optimization algorithm: A nature-inspired algorithm for high-dimensional optimization problems.’ Knowl.-Based Syst. 2021; 213: 106711.
Trojovská E, Dehghani M, Leiva V. Drawer Algorithm: A New Metaheuristic Approach for Solving Optimization Problems in Engineering. Biomimetics. 2023; 8: 239.
Trojovský P, Dehghani M. A new bio‑inspired metaheuristic algorithm for solving optimization problems based on walruses behavior. Scientific Reports. 2023; 13: 8775.
Elmanakhly DA. An Improved Equilibrium Optimizer Algorithm for Features Selection: Methods and Analysis. IEEE Access; 9, 2021.
Yilmaz S, Kucuksille E. A New Modification Approach on Bat Algorithm for Solving Optimization Problems. Applied Soft Computing Journal.
Chechkin A, Gonchar V, klafter J, Metzler R. Fundomentals of Lévy Flight processes. Adv Chem Phys. 2006; 133B: 439.
Fathi S, Makhlouf MAA, Osman E, Ahmed MA. An Energy-Efficient Compression Algorithm of ECG Signals in Remote Healthcare Monitoring Systems. IEEE Access. 2022; 10: 39129-39144.
ELmanakhly DA. BinHOA: Efficient Binary Horse Herd Optimization Method for Feature Selection: Analysis and Validations. IEEE ACCESS. 2022; 10.
Scharf I, Ovadia O. Factors influencing site abandonment and site selection in a sit-and-wait predator: a review of pit-building antlion larvae. J Insect Behav. 2006; 19:197–218.
Grzimek B, Schlager N, Olendorf D, McDade MC. Grzimek’s animal life encyclopedia. Michigan: Gale Farmington Hills. 2004.
Yang XS. Nature-Inspired Metaheuristic Algorithms second edition.
Brown CT, Liebovitch LS, Glendon R, Lévy Flights in Dobe Ju/’hoansi Foraging Patterns. Hum Ecol. 2007; 35:129-138.
Cuevas E, Echavarría A, Ramírez-Ortegón MA. An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation. Applied Intelligence. 2014; 40(2): 256-272.
Yang XS. A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer; 2010; 65–74.
Yang XS. Flower pollination algorithm for global optimization. In: Unconventional computation and natural computation. 2012; 240–9.
Yang XS, Deb S. Cuckoo search via Lévy flights. In: World congress on nature & biologically inspired computing. 2009. NaBIC 2009; 210–4.

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[1] Azizi M, Aickelin U, A Khorshidi H, Baghalzadeh Shishehgarkhaneh M. Energy valley optimizer: a novel metaheuristic algorithm for global and engineering optimization. Sci Rep. 2023 Jan 5;13(1):226. doi: 10.1038/s41598-022-27344-y. PMID: 36604589; PMCID: PMC9816156.

[2] Boussaïd I, Lepagnot J, and Siarry P, A survey on optimization metaheuristics. Inform Sci. 2013; 237: 82–117.

[3] Holland JH, Reitman JS. Cognitive systems based on adaptive algorithms. ACM SIGART Bull. 1977; 49–49.

[4] Colorni A, Dorigo M, Maniezzo V. Distributed optimization by ant colonies. In: Proceedings of the first European conference on artificial life. 1991; 134–42.

[5] Eberhart RC, Kennedy J. A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science. 1995; 39–43.

[6] Karaboga D, Basturk B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim. 2007; 39:459–71.

[7] Rajabioun R. Cuckoo optimization algorithm. Appl Soft Comput. 2011; 11:5508–18.

[8] Yang X-S. Firefly algorithm, Levy flights and global optimization. In: Research and development in intelligent systems XXVI. Springer. 2010; 209–18.

[9] Seyedali M, Mohammad MS, Andrew L. Grey wolf optimizer. Adv Eng Software. 2014; 69:46–61.

[10] Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S. Equilibrium optimizer: A novel optimization algorithm. Knowl.-Based Syst. 2020; 191:

[11] MiarNaeimi F, Azizyan G, Rashki M. ‘Horse herd optimization algorithm: A nature-inspired algorithm for high-dimensional optimization problems.’ Knowl.-Based Syst. 2021; 213: 106711.

[12] Trojovská E, Dehghani M, Leiva V. Drawer Algorithm: A New Metaheuristic Approach for Solving Optimization Problems in Engineering. Biomimetics. 2023; 8: 239.

[13] Trojovský P, Dehghani M. A new bio‑inspired metaheuristic algorithm for solving optimization problems based on walruses behavior. Scientific Reports. 2023; 13: 8775.

[14] Elmanakhly DA. An Improved Equilibrium Optimizer Algorithm for Features Selection: Methods and Analysis. IEEE Access; 9, 2021.

[15] Yilmaz S, Kucuksille E. A New Modification Approach on Bat Algorithm for Solving Optimization Problems. Applied Soft Computing Journal.

[16] Chechkin A, Gonchar V, klafter J, Metzler R. Fundomentals of Lévy Flight processes. Adv Chem Phys. 2006; 133B: 439.

[17] Fathi S, Makhlouf MAA, Osman E, Ahmed MA. An Energy-Efficient Compression Algorithm of ECG Signals in Remote Healthcare Monitoring Systems. IEEE Access. 2022; 10: 39129-39144.

[18] ELmanakhly DA. BinHOA: Efficient Binary Horse Herd Optimization Method for Feature Selection: Analysis and Validations. IEEE ACCESS. 2022; 10.

[19] Scharf I, Ovadia O. Factors influencing site abandonment and site selection in a sit-and-wait predator: a review of pit-building antlion larvae. J Insect Behav. 2006; 19:197–218.

[20] Grzimek B, Schlager N, Olendorf D, McDade MC. Grzimek’s animal life encyclopedia. Michigan: Gale Farmington Hills. 2004.

[21] Yang XS. Nature-Inspired Metaheuristic Algorithms second edition.

[22] Brown CT, Liebovitch LS, Glendon R, Lévy Flights in Dobe Ju/’hoansi Foraging Patterns. Hum Ecol. 2007; 35:129-138.

[23] Cuevas E, Echavarría A, Ramírez-Ortegón MA. An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation. Applied Intelligence. 2014; 40(2): 256-272.

[24] Yang XS. A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer; 2010; 65–74.

[25] Yang XS. Flower pollination algorithm for global optimization. In: Unconventional computation and natural computation. 2012; 240–9.

[26] Yang XS, Deb S. Cuckoo search via Lévy flights. In: World congress on nature & biologically inspired computing. 2009. NaBIC 2009; 210–4.