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On a model-free meta-heuristic approach for unconstrained optimization

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Abstract

The efficacy of meta-heuristic algorithms has been demonstrated in solving unconstrained optimization problems. Inspired by the food foraging behavior of beetles, we propose herein a model-free meta-heuristic optimization algorithm, referred to as the Beetle Antennae Search-Bellwether Swarm, which incorporates the schemes of adaptive antenna fiber length and direction vector. A joint annealing-heating scheme along with the re-initialization mechanism is proposed such that each antenna fiber length could simultaneously gradually decrease or increase in different circumstances. We also propose to adapt each individual antenna fiber length based on the best smell perception direction (bellwether). The proposed schemes of adaptive antenna fiber length yield the algorithm almost insusceptible to different initial antenna fiber lengths for a relatively large range of initial antenna fiber lengths. The softmax combiner is leveraged to obtain the direction vector such that the beetle would be steered to step toward the new randomly combined direction and arrive at a candidate position. The beetle position is further updated by evaluating whether the candidate position is conducive to minimizing the objective function. The illustrative simulations demonstrate the fast initial convergence, cost-effectiveness and feasibility of the proposed algorithm.

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References

  1. Krivulin N (2017) Tropical optimization problems in time-constrained project scheduling. Optimization 66(2):205–224

    Article  MathSciNet  Google Scholar 

  2. Agrawal A, Barratt S, Boyd S (2021) Learning convex optimization models. IEEE/CAA J Autom Sin 8(8):1355–1364

    Article  MathSciNet  Google Scholar 

  3. Chen X, Gao S, Zhang S, Zhao Y (2022) On topology optimization for event-triggered consensus with triggered events reducing and convergence rate improving. IEEE Trans Circuits Syst II Exp Briefs 69(3):1223–1227

    Google Scholar 

  4. Alinaghian M, Jamshidian M, Tirkolaee EB (2022) The time-dependent multi-depot fleet size and mix green vehicle routing problem: improved adaptive large neighbourhood search. Optimization 71(11):3165–3193

    Article  MathSciNet  Google Scholar 

  5. Gajpal Y, Abdulkader MMS, Zhang S, Appadoo SS (2017) Optimizing garbage collection vehicle routing problem with alternative fuel-powered vehicles. Optimization 66(11):1851–1862

    Article  MathSciNet  Google Scholar 

  6. Luenberger DG, Ye Y (2021) Linear and nonlinear programming. Springer, Cham

    Book  Google Scholar 

  7. Yang B, Wang J, Zhang X, Yu T, Yao W, Shu H, Zeng F, Sun L (2020) Comprehensive overview of meta-heuristic algorithm applications on PV cell parameter identification. Energy Convers Manage 208:112595

    Article  Google Scholar 

  8. Tang J, Liu G, Pan Q (2021) A review on representative swarm intelligence algorithms for solving optimization problems: applications and trends. IEEE/CAA J Autom Sin 8(10):1627–1643

    Article  MathSciNet  Google Scholar 

  9. Hashim FA, Hussien AG (2022) Snake optimizer: a novel meta-heuristic optimization algorithm. Knowl-Based Syst 242:108320

    Article  Google Scholar 

  10. Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73

    Article  Google Scholar 

  11. Beyer H-G, Schwefel H-P (2002) Evolution strategies—a comprehensive introduction. Nat Comput 1:3–52

    Article  MathSciNet  Google Scholar 

  12. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359

    Article  MathSciNet  Google Scholar 

  13. Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 12(6):702–713

    Article  Google Scholar 

  14. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the ICNN’95—International Conference on Neural Networks, Perth, WA, Australia, pp 1942–1948

  15. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471

    Article  MathSciNet  Google Scholar 

  16. Dorigo M, Blum C (2005) Ant colony optimization theory: a survey. Theor Comput Sci 344(2):243–278

    Article  MathSciNet  Google Scholar 

  17. Zhao S, Zhang T, Ma S, Chen M (2022) Dandelion optimizer: a nature-inspired metaheuristic algorithm for engineering applications. Eng Appl Artif Intel 114:105075

    Article  Google Scholar 

  18. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    Article  MathSciNet  Google Scholar 

  19. Lam AY, Li VO (2009) Chemical-reaction-inspired metaheuristic for optimization. IEEE Trans Evolut Comput 14(3):381–399

    Article  Google Scholar 

  20. Zhao W, Wang L, Zhang Z (2019) Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl-Based Syst 163:283–304

    Article  Google Scholar 

  21. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inform Sci 179(13):2232–2248

    Article  Google Scholar 

  22. Mittal H, Tripathi A, Pandey AC, Pal R (2021) Gravitational search algorithm: a comprehensive analysis of recent variants. Multimed Tools Appl 80(5):7581–7608

    Article  Google Scholar 

  23. Wahab MNA, Nefti-Meziani S, Atyabi A (2015) A comprehensive review of swarm optimization algorithms. PLoS ONE 10(5):0122827

    Article  Google Scholar 

  24. Rajwar K, Deep K, Das S (2023) An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges. Artif Intell Rev 56(11):13187–13257

    Article  Google Scholar 

  25. Kingma DP, Ba J (2017) Adam: a method for stochastic optimization. arXiv:1412.6980

  26. Jiang X, Li S (2018) BAS: beetle antennae search algorithm for optimization problems. Int J Robot Control 1(1):1–5

    Article  Google Scholar 

  27. Li C, Zhu S, Sun Z, Rogers J (2021) BAS optimized ELM for KUKA iiwa robot learning. IEEE Trans Circuits Syst II Exp Briefs 68(6):1987–1991

    Google Scholar 

  28. Khan AT, Li S, Zhou X (2021) Trajectory optimization of 5-link biped robot using beetle antennae search. IEEE Trans Circuits Syst II Exp Briefs 68(10):3276–3280

    Google Scholar 

  29. Yin X, Ma Y (2018) Aggregation service function chain mapping plan based on beetle antennae search algorithm. In: Proceedings of the 2nd International Conference on Telecommunications and Communication Engineering, New York, USA, pp 225–230

  30. Zhu Z, Zhang Z, Man W, Tong X, Qiu J, Li F (2018) A new beetle antennae search algorithm for multi-objective energy management in microgrid. In: 13th IEEE Conference on Industrial Electronics and Applications(ICIEA), Wuhan, China, pp 1599–1603

  31. Sun Y, Zhang J, Li G, Wang Y, Sun J, Jiang C (2019) Optimized neural network using beetle antennae search for predicting the unconfined compressive strength of jet grouting coalcretes. Int J Numer Anal Methods Geomech 43(4):801–813

    Article  Google Scholar 

  32. Fan Y, Shao J, Sun G (2019) Optimized PID controller based on beetle antennae search algorithm for electro-hydraulic position servo control system. Sensors 19(12):2727

    Article  Google Scholar 

  33. Göpfert MC, Briegel H, Robert D (1999) Mosquito hearing: sound-induced antennal vibrations in male and female Aedes aegypti. J Exp Biol 202(20):2727–2738

    Article  Google Scholar 

  34. Khan AH, Cao X, Xu B, Li S (2022) A model-free approach for online optimization of nonlinear systems. IEEE Trans Circuits Syst II Exp Briefs 69(1):109–113

    Google Scholar 

  35. Hazarika N, Taylor JG (2001) A temperature-dependent SOFTMAX combiner. In: IJCNN’01. International Joint Conference on Neural Networks. Proc., Washington, DC, USA, pp 1847–1851

  36. Zhang Y, Cao W, Wu M, Xia K (2016) A hybrid modeling method for continuous annealing line heating process. In: 35th Chinese Control Conf. (CCC), Chengdu, China, pp 2263–2267

  37. Zhang Y, Jin Y, Cao W, Li Z, Yuan Y (2018) A dynamic data-driven model for predicting strip temperature in continuous annealing line heating process. In: 37th Chinese Control Conf. (CCC), Wuhan, China, pp 1887–1891

  38. Edmonds J (1971) Matroids and the greedy algorithm. Math. Program. 1(1):127–136

    Article  MathSciNet  Google Scholar 

  39. Korte B, Lovász L (1981) Mathematical structures underlying greedy algorithms. Springer, Berlin, pp 205–209

    Google Scholar 

  40. Girlich E, Höding M, Zaporozhets A, Chubanov S (2003) A greedy algorithm for capacitated lot-sizing problems. Optimization 52(2):241–249

    Article  MathSciNet  Google Scholar 

  41. Engelbrecht AP (2014) Fitness function evaluations: a fair stopping condition? In: IEEE symposium on swarm intelligence, Orlando, FL, USA, pp 1–8

  42. Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evol Comput 44:148–175

    Article  Google Scholar 

  43. Eberhart, Shi Y (2001) Particle swarm optimization: Developments, applications and resources. In: Proceedings of the congress on evolutionary computation, Seoul, Korea (South), pp 81–86

  44. Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugen 7(2):179–188

    Article  Google Scholar 

  45. Charytanowicz M et al (2010) Complete gradient clustering algorithm for features analysis of X-ray images. Springer, Berlin, pp 15–24

    Google Scholar 

  46. Han J, Moraga C (1995) The influence of the sigmoid function parameters on the speed of backpropagation learning. In: From natural to artificial neural computation, pp 195–201. Springer, Berlin

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61871104.

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Author notes

  1. The authors Wei Xia and Deming He contributed equally to this work.

Authors and Affiliations

  1. School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Wei Xia & Deming He

  2. School of Computer Science and Technology (School of Cyberspace Security), Xinjiang University, Ürümqi, 830046, China

    Wei Xia

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  1. Wei Xia
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  2. Deming He
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Correspondence to Wei Xia.

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Xia, W., He, D. On a model-free meta-heuristic approach for unconstrained optimization. J Supercomput 80, 22548–22562 (2024). https://doi.org/10.1007/s11227-024-06279-3

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