Abstract
In order to solve optimization problems, this paper introduces a new metaheuristic algorithm called the Numeric Crunch Algorithm (NCA), which employs the distribution behaviour of the population members and a novel hyperbolic acceleration function for convergence. Each generation's search space exploration and exploitation are ensured by the population's distribution behaviour around its members and their adaptively diversified boundaries, respectively. The convergence of the search solutions in the NCA was also accelerated by the random, adaptive parameters and hyperbolic function. A set of 68 test benchmark functions with (30, 100, 500, and 1000) dimensions was used to examine the NCA's effectiveness in terms of exploration, exploitation, local optimality avoidance, population fitness enhancement, and convergence rate. Firstly, the proposed NCA's behaviour is examined using a collection of 23 standard well-known benchmark functions, including unimodal, multimodal, and fixed-dimensional functions. Secondly, the proposed NCA's superiority is examined using the IEEE CEC-2015 and IEEE CEC-2017 benchmark suites. In addition to qualitatively examine NCA's superiority over other metaheuristics, Friedman and Wilcoxon rank-sum tests are performed. In terms of performance metrics, NCA ranked first. For application perspective, the NCA is tested on eight real-world constrained and unconstrained engineering design problems from IEEE CEC-2020 real-world optimization benchmark suits. The NCA algorithm's performance on benchmark functions and engineering design problems indicates that it can handle constrained and uncertain search spaces in real-world scenarios. The source code of the NCA algorithm is publicly available at https://github.com/Shivankur07/Numeric-Crunch-Algorithm.git.
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Data availability
The source code of the proposed algorithm NCA with 23 standard benchmark test functions (as listed in Appendix A) and 42 standard extra supplementary functions (as listed in Appendix B) and 7 constrained and unconstrained test functions are publicly available at https://drive.google.com/drive/folders/16wUSaIq9-7Z6a9tob_MhGoLpn9BAeD3R?usp=share_link or https://github.com/Shivankur07/Numeric-Crunch-Algorithm.git.
Abbreviations
- ACO:
-
Ant Colony Optimization
- GWO:
-
Grey Wolf Optimization
- PSO:
-
Particle Swarm Optimization
- GTO:
-
Gorilla Troops Optimizer
- SCA:
-
Sine–Cosine Algorithm
- CSA:
-
Cuckoo Search Algorithm
- TSA:
-
Tree Seed Optimizer
- MVO:
-
Multi-verse Optimizer
- WOA:
-
Whale Optimization Algorithm
- MFO:
-
Moth Flame Optimization
- FP:
-
Flower Pollination
- PGO:
-
Plant Growth Optimization
- SFO:
-
Sun Flower Optimization
- GA:
-
Genetics Algorithm
- PBIL:
-
Probability-based Incremental Learning
- BBO:
-
Biogeography-based Optimizer
- FSO:
-
Fish Swarm Optimization
- CSO:
-
Cat Swarm Optimization
- BCO:
-
Big Crunch Optimization
- ASO:
-
Atom Search Optimization
- RO:
-
Ray Optimization
- CFO:
-
Central Force Optimization
- SA:
-
Simulated Annealing
- GLSA:
-
Gravitational Search Algorithm
- GSA:
-
Gravitational Search Algorithm
- CSS:
-
Charged System Search
- ACROA:
-
Artificial Chemical Reaction Optimization Algorithm
- BHOA:
-
Black Hole Optimization Algorithm
- SWOA:
-
Small-World Optimization Algorithm
- GBSA:
-
Galaxy-Based Search Algorithm
- CSO:
-
Curved Space Optimization
- SGA:
-
Fashion Search Group Algorithm
- SLC:
-
Soccer League Competition
- GTO:
-
Group Teaching Optimization
- KIA:
-
Kidney-Inspired Algorithm
- TLBO:
-
Teaching–Learning-based Optimizer
- QPSO:
-
Quantum-behaved PSO
- SPSO:
-
Simplified PSO
- BBPSO:
-
Bare-bones PSO
- CPSO:
-
Chaotic PSO
- FPSO:
-
Fuzzy PSO
- PSOTVAC:
-
PSO with TVAC
- OPSO:
-
Opposition-based PSO
References
Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609. https://doi.org/10.1016/j.cma.2020.113609
Abualigah L, Yousri D, Elaziz AM, Ewees AA, Al-qaness MAA, Gandomi AH (2021) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250. https://doi.org/10.1016/j.cie.2021.107250
Abualigah L, Elaziz MA, Sumari P, Geem ZW, Gandomi AH (2022) Reptile Search Algorithm (RSA): a nature-inspired meta-heuristic optimizer. Expert Syst Appl 191:116158. https://doi.org/10.1016/j.eswa.2021.116158
Agushaka JO, Ezugwu AE, Olaide ON, Akinola O, Zitar RA, Abualigah L (2022) Improved dwarf mongoose optimization for constrained engineering design problems. Bionic J Eng. https://doi.org/10.1007/s42235-022-00316-8
Ahmad MF (2022) MF Ahmad, NAM Isa, Lim WH, Ang KM 2022 Differential evolution: a recent review based on state-of-the-art works. Alexandria Eng J 61(5):3831–3872. https://doi.org/10.1016/j.aej.2021.09.013
Ahmadianfar I, Heidari AA, Gandomi AH, Chu X, Chen H (2021) RUN beyond the metaphor: an efficient optimization algorithm based on Runge Kutta method. Expert Syst Appl 181:115079. https://doi.org/10.1016/j.eswa.2021.115079
Ahmadianfar I, Heidari AA, Noshadian S, Chen H, Gandomi AH (2022) INFO: an efficient optimization algorithm based on weighted mean of vectors. Expert Syst Appl 195:116516. https://doi.org/10.1016/j.eswa.2022.116516
Akyol S, Alatas B (2017) Plant intelligence based metaheuristic optimization algorithms. Artif Intell Rev 47(4):417–462. https://doi.org/10.1007/s10462-016-9486-6
Alabool HM, Alarabiat D, Abualigah L, Heidari AA (2021) Harris hawks optimization: a comprehensive review of recent variants and applications. Neural Comput Appl 33(15):8939–8980. https://doi.org/10.1007/s00521-021-05720-5
Alatas B, Bingol H (2020) Comparative assessment of light-based intelligent search and optimization algorithms. Light Eng. https://doi.org/10.33383/2019-029
Arora S, Singh S (2019) Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23(3):715–734. https://doi.org/10.1007/s00500-018-3102-4
Askari Q, Saeed M, Younas I (2020) Heap-based optimizer inspired by corporate rank hierarchy for global optimization. Expert Syst Appl 161:113702. https://doi.org/10.1016/j.eswa.2020.113702
Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: 2007 IEEE congress on evolutionary computation, pp 4661–4667. https://doi.org/10.1109/CEC.2007.4425083.
Ayyarao LTSV et al (2022) War strategy optimization algorithm: a new effective metaheuristic algorithm for global optimization. IEEE Access 10:25073–25105. https://doi.org/10.1109/ACCESS.2022.3153493
Babu AH, Naresh P, Madhava V, Reddy MS (2016) Minimum weight optimization of a gear train by using GA. IJETAS 1:43–50
Bäck T, Schwefel H-P (1993) An overview of evolutionary algorithms for parameter optimization. Evol Comput 1(1):1–23. https://doi.org/10.1162/evco.1993.1.1.1
Bhandari AK, Singh VK, Kumar A, Singh GK (2014) Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur’s entropy. Expert Syst Appl 41(7):3538–3560. https://doi.org/10.1016/j.eswa.2013.10.059
Bogere P, Akol R, Butime J (2015) Optimization of frequency modulation band for terrestrial radio broadcasting: the case of Uganda. https://doi.org/10.1109/COMCAS.2015.7360389
Braik M, Hammouri A, Atwan J, Al-Betar MA, Awadallah MA (2022) White shark optimizer: a novel bio-inspired meta-heuristic algorithm for global optimization problems. Knowl Based Syst 243:108457. https://doi.org/10.1016/j.knosys.2022.108457
Celik Y, Kutucu H (2018) Solving the tension/compression spring design problem by an improved firefly algorithm. In: IDDM
Dehghani M, Hubálovský Š, Trojovský P (2022) Tasmanian devil optimization: a new bio-inspired optimization algorithm for solving optimization algorithm. IEEE Access 10:19599–19620. https://doi.org/10.1109/ACCESS.2022.3151641
Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70. https://doi.org/10.1016/j.advengsoft.2017.05.014
Dorigo M, Birattari M, Stützle T (2006) Ant colony optimization. Comput Intell Mag IEEE 1:28–39. https://doi.org/10.1109/MCI.2006.329691
Eberhart, Shi Y (2001a) Particle swarm optimization: development, applications and resources. In: Proceedings of the IEEE conference on evolutionary computation, ICEC, Sep 2001a, vol 1, pp 81–86. https://doi.org/10.1109/CEC.2001.934374
Eberhart, Shi Y (2001) Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546), 2001, vol 1, pp 81–86. https://doi.org/10.1109/CEC.2001.934374
Erdoğan Yildirim A, Karci A (2018) Application of three bar truss problem among engineering design optimization problems using artificial atom algorithm. pp 1–5. https://doi.org/10.1109/IDAP.2018.8620762
Ezugwu AE, Agushaka JO, Abualigah L, Mirjalili S, Gandomi AH (2022) Prairie dog optimization algorithm. Neural Comput Appl 34(22):20017–20065. https://doi.org/10.1007/s00521-022-07530-9
Faramarzi A, Heidarinejad M, Mirjalili S (2020) and Gandomi AH 2020 Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst Appl 152:113377. https://doi.org/10.1016/j.eswa.2020.113377
Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020b) Equilibrium optimizer: a novel optimization algorithm. Knowledge-Based Syst 191:105190. https://doi.org/10.1016/j.knosys.2019.105190
Fister Jr I, Fister I, X.-S. Yang, Fong S, Zhuang Y (2014) Bat algorithm: recent advances. In: CINTI 2014—15th IEEE International Symposium on Computational Intelligence and Informatics, Proceedings, pp 163–167, https://doi.org/10.1109/CINTI.2014.7028669.
Hashim FA, Hussien AG (2022) Snake optimizer: a novel meta-heuristic optimization algorithm. Knowl Based Syst 242:108320. https://doi.org/10.1016/j.knosys.2022.108320
Hashim FA, Houssein EH, Hussain K, Mabrouk MS, Al-Atabany W (2022) Honey Badger Algorithm: new metaheuristic algorithm for solving optimization problems. Math Comput Simul 192:84–110. https://doi.org/10.1016/j.matcom.2021.08.013
Henderson D, Jacobson S, Johnson A (2006) The theory and practice of simulated annealing. In: Handbook of metaheuristics, pp 287–319. https://doi.org/10.1007/0-306-48056-5_10.
Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evol Comput 44:148–175. https://doi.org/10.1016/j.swevo.2018.02.013
Johari N, Zain A, Mustaffa N, Udin A (2013) Firefly algorithm for optimization problem. Appl Mech Mater. https://doi.org/10.4028/www.scientific.net/AMM.421.512
Joshi AS, Kulkarni O, Kakandikar G, Nandedkar V (2017) Cuckoo search optimization—a review. Mater Today Proc 4:7262–7269. https://doi.org/10.1016/j.matpr.2017.07.055
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
Kim JH (2016) Harmony search algorithm: a unique music-inspired algorithm. Procedia Eng 154:1401–1405. https://doi.org/10.1016/j.proeng.2016.07.510
Kiran MS (2015) TSA: tree-seed algorithm for continuous optimization. Expert Syst Appl 42(19):6686–6698. https://doi.org/10.1016/j.eswa.2015.04.055
Krishnamoorthy D, Fjalestad K, Skogestad S (2019) Optimal operation of oil and gas production using simple feedback control structures. Control Eng Pract 91:104107. https://doi.org/10.1016/j.conengprac.2019.104107
Kumar V, Chhabra JK, Kumar D (2015) Differential search algorithm for multiobjective problems. Procedia Comput Sci 48:22–28. https://doi.org/10.1016/j.procs.2015.04.105
Lin M-H, Tsai J-F, Hu N-Z, Chang S-C (2013) Design optimization of a speed reducer using deterministic techniques. Math Probl Eng 2013:1–7. https://doi.org/10.1155/2013/419043
Man KF, Tang KS, Kwong S (1996) Genetic algorithms: concepts and applications [in engineering design]. IEEE Trans Ind Electron 43(5):519–534. https://doi.org/10.1109/41.538609
Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowledge-Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006
Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008
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
Mirjalili S, Mirjalili S, Hatamlou A (2015) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl. https://doi.org/10.1007/s00521-015-1870-7
Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002
Mohamed AW, Hadi AA, Mohamed AK (2020) Gaining-sharing knowledge based algorithm for solving optimization problems: a novel nature-inspired algorithm. Int Mach J Learn Cybern 11(7):1501–1529. https://doi.org/10.1007/s13042-019-01053-x
Oyelade ON, Ezugwu AE-S, Mohamed TIA, Abualigah L (2022) Ebola optimization search algorithm: a new nature-inspired metaheuristic optimization algorithm. IEEE Access 10:16150–16177. https://doi.org/10.1109/ACCESS.2022.3147821
Pierezan J, Dos Santos Coelho L (2018) Coyote optimization algorithm: a new metaheuristic for global optimization problems. In: 2018 IEEE congress on evolutionary computation (CEC), 2018, pp 1–8.https://doi.org/10.1109/CEC.2018.8477769
Rao VR, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems. Comput Des 43(3):303–315. https://doi.org/10.1016/j.cad.2010.12.015
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci (NY) 179(13):2232–2248. https://doi.org/10.1016/j.ins.2009.03.004
Sachidananda HK, Prasant, D (2019) Design and analysis of pressure vessel. Int J Mech Prod Eng Res Dev 9(5):125–136. https://doi.org/10.24247/ijmperdoct201912
Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713. https://doi.org/10.1109/TEVC.2008.919004
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. Glob J Optim 11(4):341–359. https://doi.org/10.1023/A:1008202821328
Sun Y, Wierstra D, Schaul T, Schmidhuber J (2009) Efficient natural evolution strategies. In: Proceedings of the 11th annual conference on genetic and evolutionary computation
Willis MJ, Hiden H., Marenbach P, McKay B, Montague GA (1997) Genetic programming: an introduction and survey of applications. In: Second international conference on genetic algorithms in engineering systems: innovations and applications. IET, pp 314–319
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82. https://doi.org/10.1109/4235.585893
Yang X-S (2009) Firefly algorithms for multimodal optimization. In: Stochastic algorithms: foundations and applications, pp 169–178
Zhao W, Wang L, Zhang Z (2019a) Supply-demand-based optimization: a novel economics-inspired algorithm for global optimization. IEEE Access 7:73182–73206. https://doi.org/10.1109/ACCESS.2019.2918753
Zhao W, Wang L, Zhang Z (2019b) Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl Based Syst 163:283–304. https://doi.org/10.1016/j.knosys.2018.08.030
Zhao W, Zhang Z, Wang L (2020) Manta ray foraging optimization: An effective bio-inspired optimizer for engineering applications. Eng Appl Artif Intell 87:103300. https://doi.org/10.1016/j.engappai.2019.103300
Zhong C, Li G, and Meng Z, “Beluga whale optimization: A novel nature-inspired metaheuristic algorithm,” Knowledge-Based Syst., vol. 251, p. 109215, 2022, https://doi.org/10.1016/j.knosys.2022.109215.
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The first author wishes to express his gratitude to Doon University in Uttarakhand, India, for providing all of the essential resources for this study.
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Appendices
Appendix 1
See Table 26.
Appendix 2
See Fig. 20.
Surface plot for 23 benchmark functions
Appendix 3
See Table 27.
Appendix 4
See Table 28.
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Thapliyal, S., Kumar, N. Numeric Crunch Algorithm: a new metaheuristic algorithm for solving global and engineering optimization problems. Soft Comput 27, 16611–16657 (2023). https://doi.org/10.1007/s00500-023-08925-z
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DOI: https://doi.org/10.1007/s00500-023-08925-z