Arithmetic optimization algorithm (AOA) is a newly proposed meta-heuristic method which is inspired by the arithmetic operators in mathematics. However, the AOA has the weaknesses of insufficient exploration capability and is likely to fall into local optima. To improve the searching quality of original AOA, this paper presents an improved AOA (IAOA) integrated with proposed forced switching mechanism (FSM). The enhanced algorithm uses the random math optimizer probability (RMOP) to increase the population diversity for better global search. And then the forced switching mechanism is introduced into the AOA to help the search agents jump out of the local optima. When the search agents cannot find better positions within a certain number of iterations, the proposed FSM will make them conduct the exploratory behavior. Thus the cases of being trapped into local optima can be avoided effectively. The proposed IAOA is extensively tested by twenty-three classical benchmark functions and ten CEC2020 test functions and compared with the AOA and other well-known optimization algorithms. The experimental results show that the proposed algorithm is superior to other comparative algorithms on most of the test functions. Furthermore, the test results of two training problems of multi-layer perceptron (MLP) and three classical engineering design problems also indicate that the proposed IAOA is highly effective when dealing with real-world problems.
Citation: Rong Zheng, Heming Jia, Laith Abualigah, Qingxin Liu, Shuang Wang. An improved arithmetic optimization algorithm with forced switching mechanism for global optimization problems[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 473-512. doi: 10.3934/mbe.2022023
Arithmetic optimization algorithm (AOA) is a newly proposed meta-heuristic method which is inspired by the arithmetic operators in mathematics. However, the AOA has the weaknesses of insufficient exploration capability and is likely to fall into local optima. To improve the searching quality of original AOA, this paper presents an improved AOA (IAOA) integrated with proposed forced switching mechanism (FSM). The enhanced algorithm uses the random math optimizer probability (RMOP) to increase the population diversity for better global search. And then the forced switching mechanism is introduced into the AOA to help the search agents jump out of the local optima. When the search agents cannot find better positions within a certain number of iterations, the proposed FSM will make them conduct the exploratory behavior. Thus the cases of being trapped into local optima can be avoided effectively. The proposed IAOA is extensively tested by twenty-three classical benchmark functions and ten CEC2020 test functions and compared with the AOA and other well-known optimization algorithms. The experimental results show that the proposed algorithm is superior to other comparative algorithms on most of the test functions. Furthermore, the test results of two training problems of multi-layer perceptron (MLP) and three classical engineering design problems also indicate that the proposed IAOA is highly effective when dealing with real-world problems.
| [1] |
L. Abualigah, Multi-verse optimizer algorithm: A comprehensive survey of its results, variants, and applications, Neural Comput. Appl., 32 (2020), 12381–12401. doi: 10.1007/s00521-020-04839-1. doi: 10.1007/s00521-020-04839-1
|
| [2] |
K. Hussain, M. N. Mohd Salleh, S. Cheng, Y. Shi, Metaheuristic research: a comprehensive survey, Artif. Intell. Rev., 52 (2019), 2191–2233. doi: 10.1007/s10462-017-9605-z. doi: 10.1007/s10462-017-9605-z
|
| [3] |
L. B. Booker, D. E. Goldberg, J. H. Holland, Classifier systems and genetic algorithms, Artif. Intell., 40 (1989), 235-282. doi: 10.1016/0004-3702(89)90050-7. doi: 10.1016/0004-3702(89)90050-7
|
| [4] | J. R. Koza, J. P. Rice, Automatic programming of robots using genetic programming, in Proceedings Tenth National Conference on Artificial Intelligence, (1992), 194–201. |
| [5] |
S. Das, P. N. Suganthan, Differential evolution: a survey of the state-of-the-art, IEEE Trans. Evol. Comput., 15 (2011), 4–31. doi: 10.1109/TEVC.2010.2059031. doi: 10.1109/TEVC.2010.2059031
|
| [6] | J. Kennedy, R. Eberhart, Particle swarm optimization, in Proceedings of ICNN'95-International Conference on Neural Networks, 4 (1995), 1942–1948. doi: 10.1109/ICNN.1995.488968. |
| [7] |
S. Mirjalili, S. M. Mirjalili, A. Lewis, Grey Wolf Optimizer, Adv. Eng. Softw., 69 (2014), 46–61. doi: 10.1016/j.advengsoft.2013.12.007. doi: 10.1016/j.advengsoft.2013.12.007
|
| [8] |
D. Zhao, L. Liu, F. H. Yu, A. A. Heidari, M. J. Wang, G. X. Liang, et al., Chaotic random spare ant colony optimization for multi-threshold image segmentation of 2D Kapur entropy, Knowl. Based Syst., 216 (2020), 106510. doi: 10.1016/j.knosys.2020.106510. doi: 10.1016/j.knosys.2020.106510
|
| [9] |
D. Karaboga, B. Basturk, On the performance of artificial bee colony (ABC) algorithm, Appl. Soft. Comput., 8 (2008), 687–697. doi: 10.1016/j.asoc.2007.05.007. doi: 10.1016/j.asoc.2007.05.007
|
| [10] |
S. Mirjalili, A. Lewis, The whale optimization algorithm, Adv. Eng. Softw., 95 (2016), 51–67. doi: 10.1016/j.advengsoft.2016.01.008. doi: 10.1016/j.advengsoft.2016.01.008
|
| [11] |
S. M. Li, H. L. Chen, M. J. Wang, A. A. Heidari, S. Mirjalili, Slime mould algorithm: a new method for stochastic optimization, Futur. Gener. Comput. Syst., 111 (2020), 300–323. doi: 10.1016/j.future.2020.03.055. doi: 10.1016/j.future.2020.03.055
|
| [12] |
A. Faramarzi, M. Heidarinejad, S. Mirjalili, A. H. Gandomi, Marine predators algorithm: a nature-inspired metaheuristic, Expert Syst. Appl., 152 (2020), 113377. doi: 10.1016/j.eswa.2020.113377. doi: 10.1016/j.eswa.2020.113377
|
| [13] |
H. M. Jia, X. X. Peng, C. B. Lang, Remora optimization algorithm, Expert Syst. Appl., 185 (2021), 115665. doi: 10.1016/j.eswa.2021.115665. doi: 10.1016/j.eswa.2021.115665
|
| [14] |
C. R. Hwang, Simulated annealing: Theory and applications, Acta. Appl. Math., 12 (1988), 108–111. doi: 10.1016/0378-4754(88)90023-7. doi: 10.1016/0378-4754(88)90023-7
|
| [15] |
E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, GSA: a gravitational search algorithm, Inf. Sci., (Ny) 179 (2009), 2232–2248. doi: 10.1016/j.ins.2009.03.004. doi: 10.1016/j.ins.2009.03.004
|
| [16] |
S. Mirjalili, S. M. Mirjalili, A. Hatamlou, Multi-verse optimizer: a nature-inspired algorithm for global optimization, Neural Comput. Appl., 27 (2015), 495–513. doi: 10.1007/s00521-015-1870-7. doi: 10.1007/s00521-015-1870-7
|
| [17] |
F. Asef, V. Majidnezhad, M. R. Feizi-Derakhshi, S. Parsa, Heat transfer relation-based optimization algorithm (HTOA), Soft. Comput., 25 (2021), 8129–8158. doi: 10.1007/s00500-021-05734-0. doi: 10.1007/s00500-021-05734-0
|
| [18] |
B. Alatas, ACROA: Artificial Chemical Reaction Optimization Algorithm for global optimization, Expert Syst. Appl., 38 (2011), 13170–13180. doi: 10.1016/j.eswa.2011.04.126. doi: 10.1016/j.eswa.2011.04.126
|
| [19] | F. F. Moghaddam, R. F. Moghaddam, M. Cheriet, Curved Space Optimization: A Random Search based on General Relativity Theory, preprint, arXiv: 1208.2214. |
| [20] |
Z. W. Geem, J. H. Kim, G. Loganathan, A new heuristic optimization algorithm: harmony search, Simulation, 76 (2001), 60–68. doi: 10.1177/003754970107600201. doi: 10.1177/003754970107600201
|
| [21] |
R. V. Rao, V. J. Savsani, D. P. Vakharia, Teaching-Learning-Based optimization: an optimization method for continuous non-linear large scale problems, Inf. Sci., 183 (2012), 1–15. doi: 10.1016/j.ins.2011.08.006. doi: 10.1016/j.ins.2011.08.006
|
| [22] |
R. V. Rao, V. J. Savsani, D. P. Vakharia, Teaching-Learning-Based Optimization: A novel method for constrained mechanical design optimization problems, Computer-Aided Des., 43 (2011), 303–15. doi: 10.1016/j.cad.2010.12.015. doi: 10.1016/j.cad.2010.12.015
|
| [23] |
F. Ramezani, S. Lotfi, Social-Based Algorithm (SBA), Appl. Soft. Comput., 13 (2013), 2837–2856. doi: 10.1016/j.asoc.2012.05.018. doi: 10.1016/j.asoc.2012.05.018
|
| [24] |
Q. Fan, Z. J. Chen, Z. Li, Z. H. Xia, J. Y. Yu, D. Z. Wang, A new improved whale optimization algorithm with joint search mechanisms for high-dimensional global optimization problems, Eng. Comput., 37 (2021), 1851–1878. doi: 10.1007/s00366-019-00917-8. doi: 10.1007/s00366-019-00917-8
|
| [25] |
A. Abbasi, B. Firouzi, P. Sendur, A. A. Heidari, H. L. Chen, R. Tiwari, Multi-strategy Gaussian Harris hawks optimization for fatigue life of tapered roller bearings, Eng. Comput., 2021 (2021). doi: 10.1007/s00366-021-01442-3. doi: 10.1007/s00366-021-01442-3
|
| [26] |
Y. Li, Y. Zhao, J. Liu, Dynamic sine cosine algorithm for large-scale global optimization problems, Expert Syst. Appl., 173 (2021), 114950. doi: 10.1016/j.eswa.2021.114950. doi: 10.1016/j.eswa.2021.114950
|
| [27] |
C. Y. Yu, A. A. Heidari, X. Xue, L. J. Zhang, H. L. Chen, W. B. Chen, Boosting Quantum Rotation Gate Embedded Slime Mould Algorithm, Expert Syst. Appl., 181 (2021), 115082. doi: 10.1016/j.eswa.2021.115082. doi: 10.1016/j.eswa.2021.115082
|
| [28] |
Q. S. Fan, H. S. Huang, Q. P. Chen, L. G. Yao, D. Huang, A modified self-adaptive marine predators algorithm: framework and engineering applications, Eng. Comput., 2021 (2021). doi: 10.1007/s00366-021-01319-5. doi: 10.1007/s00366-021-01319-5
|
| [29] |
D. H. Wolpert, W. G. Macready, No free lunch theorems for optimization, IEEE Trans. Evol. Comput., 1 (1997), 67–82. doi: 10.1109/4235.585893 doi: 10.1109/4235.585893
|
| [30] |
L. Abualigah, A. Diabat, S. Mirjalili, M. A. Elaziz, A. H. Gandomi, The arithmetic optimization algorithm, Comput. Methods Appl. Mech. Eng., 376 (2021), 113609. doi: 10.1016/j.cma.2020.113609. doi: 10.1016/j.cma.2020.113609
|
| [31] |
S. Mirjalili, Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm, Knowl.-Based Syst., 89 (2015), 228–249. doi: 10.1016/j.knosys.2015.07.006. doi: 10.1016/j.knosys.2015.07.006
|
| [32] |
P. Manoharan, P. Jangir, D. S. Kumar, S. Ravichandran, S. Mirjalili, A new arithmetic optimization algorithm for solving real-world multiobjective CEC-2021 constrained optimization problems: diversity analysis and validations, IEEE Access, 9 (2021), 84263–84295. doi: 10.1109/ACCESS.2021.3085529. doi: 10.1109/ACCESS.2021.3085529
|
| [33] |
A. Žilinskas, J. Calvin, Bi-objective decision making in global optimization based on statistical models, J. Glob. Optim., 74 (2018), 599–609. doi: 10.1007/s10898-018-0622-5. doi: 10.1007/s10898-018-0622-5
|
| [34] |
L. Abualigah, A. Diabat, P. Sumari, A. H. Gandomi, A novel evolutionary arithmetic optimization algorithm for multilevel thresholding degmentation of COVID-19 CT images, Processes, 9 (2021), 1155. doi: 10.3390/pr9071155. doi: 10.3390/pr9071155
|
| [35] |
S. Khatir, S. Tiachacht, C. L. Thanh, E. Ghandourah, M. A. Wahab, An improved artificial neural network using arithmetic optimization algorithm for damage assessment in FGM composite plates, Compos. Struct., 273 (2021), 114287. doi: 10.1016/j.compstruct.2021.114287. doi: 10.1016/j.compstruct.2021.114287
|
| [36] |
J. G. Digalakis, K. G. Margaritis, On benchmarking functions for genetic algorithms, Int. J. Comput. Math., 77 (2001), 481–506. doi: 10.1080/00207160108805080. doi: 10.1080/00207160108805080
|
| [37] | C. T. Yue, K. V. Price, P. N. Suganthan, J. J. Liang, M. Z. Ali, B. Y. Qu, et al., Problem definitions and evaluation criteria for the CEC 2020 special session and competition on single objective bound constrained numerical optimization, (2020). |
| [38] |
S. García, A. Fernández, J. Luengo, F. Herrera, Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power, Inf. Sci. (Ny), 180 (2010), 2044–2064. doi: 10.1016/j.ins.2009.12.010 doi: 10.1016/j.ins.2009.12.010
|
| [39] |
E. Theodorsson-Norheim, Friedman and Quade tests: BASIC computer program to perform nonparametric two-way analysis of variance and multiple comparisons on ranks of several related samples, Comput. Biol. Med., 17 (1987), 85–99. doi: 10.1016/0010-4825(87)90003-5. doi: 10.1016/0010-4825(87)90003-5
|
| [40] |
S. Mirjalili, SCA: a sine cosine algorithm for solving optimization problems, Knowl. Based Syst., 96 (2016), 120–133. doi: 10.1016/j.knosys.2015.12.022. doi: 10.1016/j.knosys.2015.12.022
|
| [41] |
S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, S. M. Mirjalili, Salp swarm algorithm: a bio-inspired optimizer for engineering design problems, Adv. Eng. Softw., 114 (2017), 163–191. doi: 10.1016/j.advengsoft.2017.07.002. doi: 10.1016/j.advengsoft.2017.07.002
|
| [42] |
S. K. Wang, K. J. Sun, W. Y. Zhang, H. M. Jia, Multilevel thresholding using a modified ant lion optimizer with opposition-based learning for color image segmentation, Math. Biosci. Eng., 18 (2021), 3092–3143. doi: 10.3934/mbe.2021155. doi: 10.3934/mbe.2021155
|
| [43] |
W. Long, J. J. Jiao, X. M. Liang, S. H. Cai, M. Xu, A Random Opposition-Based Learning Grey Wolf Optimizer, IEEE Access, 7 (2019), 113810–113825. doi: 10.1109/ACCESS.2019.2934994. doi: 10.1109/ACCESS.2019.2934994
|
| [44] |
A. Seyyedabbasi, R. Aliyev, F. Kiani, M. U. Gulle, H. Basyildiz, M. A. Shah, Hybrid algorithms based on combining reinforcement learning and metaheuristic methods to solve global optimization problems, Knowl. Based Syst., 223 (2021), 107044. doi: 10.1016/j.knosys.2021.107044. doi: 10.1016/j.knosys.2021.107044
|
| [45] |
R. Zheng, H. M. Jia, L. Abualigah; Q. X. Liu, S. Wang, Deep Ensemble of Slime Mold Algorithm and Arithmetic Optimization Algorithm for Global Optimization, Processes, 9 (2021), 1774. doi: 10.3390/pr9101774. doi: 10.3390/pr9101774
|
| [46] |
S. Wang, Q. X. Liu, Y. X. Liu, H. M. Jia, L. Abualigah, R. Zheng, et al., A Hybrid SSA and SMA with mutation opposition-based learning for constrained engineering problems, Comput. Intel. Neurosc., 2021 (2021), 6379469. doi: 10.1155/2021/6379469. doi: 10.1155/2021/6379469
|
| [47] |
S. Mirjalili, How effective is the grey wolf optimizer in training multi-layer perceptrons, Appl. Intell., 43 (2015), 150–161. doi: 10.1007/s10489-014-0645-7. doi: 10.1007/s10489-014-0645-7
|
| [48] |
T. Ray, P. Saini, Engineering design optimization using a swarm with an intelligent information sharing among individuals, Eng. Optim., 33 (2001), 735–748. doi: 10.1080/03052150108940941. doi: 10.1080/03052150108940941
|
| [49] |
A. H. Gandomi, X. S. Yang, A. H. Alavi, Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems, Eng. Comput., 29 (2013), 17–35. doi: 10.1007/s00366-011-0241-y. doi: 10.1007/s00366-011-0241-y
|
| [50] |
A. Sadollah, A. Bahreininejad, H. Eskandar, M. Hamdi, Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems, Appl. Soft. Comput., 13 (2013), 2592–612. doi: 10.1016/j.asoc.2012.11.026. doi: 10.1016/j.asoc.2012.11.026
|
| [51] |
S. Saremi, S. Mirjalili, A. Lewis, Grasshopper Optimization Algorithm: Theory and application, Adv. Eng. Softw., 105 (2017), 30–47. doi: 10.1016/j.advengsoft.2017.01.004. doi: 10.1016/j.advengsoft.2017.01.004
|
| [52] |
H. Liu, Z. Cai, Y. Wang, Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization, Appl. Soft. Comput., 10 (2010), 629–640. doi: 10.1016/j.asoc.2009.08.031. doi: 10.1016/j.asoc.2009.08.031
|
| [53] |
N. Singh, J. Kaur, Hybridizing sine-cosine algorithm with harmony search strategy for optimization design problems, Soft. Comput., 25 (2021), 11053–11075. doi: 10.1007/s00500-021-05841-y. doi: 10.1007/s00500-021-05841-y
|
| [54] |
B. K. Kannan, S. N. Kramer, An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design, J. Mech. Des., 116 (1994), 405–411. doi: 10.1115/1.2919393. doi: 10.1115/1.2919393
|
| [55] |
R. M. Rizk-Allah, Hybridizing sine cosine algorithm with multi-orthogonal search strategy for engineering design problems, J. Comput. Des. Eng., 5 (2018), 249–273. doi: 10.1016/j.jcde.2017.08.002. doi: 10.1016/j.jcde.2017.08.002
|
| [56] |
Y. Ling, Y. Q. Zhou, Q. F. Luo, Lévy flight trajectory-based whale optimization algorithm for global optimization, IEEE Acess, 5 (2017), 6168–6186. doi: 10.1109/ACCESS.2017.2695498. doi: 10.1109/ACCESS.2017.2695498
|
| [57] |
D. Pelusi, R. Mascella, L. Tallini, J. Nayak, B. Naik, Y. Deng, An improved moth-flame optimization algorithm with hybrid search phase, Knowl. Based Syst., 191 (2020), 105277. doi: 10.1016/j.knosys.2019.105277. doi: 10.1016/j.knosys.2019.105277
|
| [58] |
A. Baykasoğlu, S. Akpinar, Weighted superposition attraction (WSA): A swarm intelligence algorithm for optimization problems-part2: Constrained optimization, Appl. Soft. Comput., 37 (2015), 396–415. doi: 10.1016/j.asoc.2015.08.052. doi: 10.1016/j.asoc.2015.08.052
|
Figures(15) / Tables(19)
Rong Zheng, Heming Jia, Laith Abualigah, Qingxin Liu, Shuang Wang. An improved arithmetic optimization algorithm with forced switching mechanism for global optimization problems[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 473-512. doi: 10.3934/mbe.2022023
DownLoad: