TSASC: tree–seed algorithm with sine–cosine enhancement for continuous optimization problems

Abstract

Tree–seed algorithm (TSA) establishes a novel approach to solve continuous optimization problems, which is applied in many fields because of its simplicity and strength in finding optimal solutions. However, due to somewhat imbalance of its ability between exploration and exploitation in different search phases, the exploratory capability of TSA is relatively weak in optimizing multimodal and high-dimensional objective functions. To make some improvements, we propose a hybrid heuristic tree–seed algorithm named TSASC by integrating two features from sine–cosine algorithm. The proposed algorithm is then tested in comparison with TSA and other relevant algorithms through 30 benchmark functions from IEEE CEC 2014 and 3 constrained real engineering optimization problems. The results prove its enhanced balance between exploration and exploitation in both finding better global optimal solutions and effectively avoiding falling into local optimum, which shows that it has promising advantages in solving continuous optimization problems in engineering practices.

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References

  1. Angeline PJ (1994) Genetic programming: on the programming of computers by means of natural selection. Biosystems 33(1):69–73

    Google Scholar 

  2. Babalik A, Cinar AC, Kiran MS (2018) A modification of tree-seed algorithm using Deb’s rules for constrained optimization. Appl Soft Comput 63:289–305

    Google Scholar 

  3. Bai L, Li Y, Gong L (2014) Protein secondary structure optimization using an improved artificial bee colony algorithm based on AB offlattice model. Eng Appl Artif Intell 27(1):70–79

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  5. Cerný V (1985) Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 45(1):41–51

    MathSciNet  MATH  Google Scholar 

  6. Chen W, Cai M, Tan X, Wei B (2019) Parameter identification and state-of-charge estimation for Li-ion batteries using an improved tree seed algorithm. IEICE Trans Inf Syst 8:1489–1497

    Google Scholar 

  7. Chou J, Ghaboussi J (2001) Genetic algorithm in structural damage detection. Comput Struct 79(14):1335–1353

    Google Scholar 

  8. Cinar AC, Kiran MS (2018) Similarity and logic gate-based tree-seed algorithms for binary optimization. Comput Ind Eng 115:631–646

    Google Scholar 

  9. Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127

    Google Scholar 

  10. Dan S (2008) Biogeography based optimization. IEEE Trans Evol Comput 12(6):702–713

    Google Scholar 

  11. Ding Z, Li J, Hao H, Lu Z (2019a) Nonlinear hysteretic parameter identification using an improved tree-seed algorithm. Swarm Evol Comput 46:69–83

    Google Scholar 

  12. Ding Z, Li J, Hao H, Lu Z (2019b) Structural damage identification with uncertain modelling error and measurement noise by clustering based tree seeds algorithm. Eng Struct 185:301–314

    Google Scholar 

  13. Elaziz MA, Oliva D, Xiong S (2017) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500

    Google Scholar 

  14. Formato RA (2009) Central force optimization: a new deterministic gradientlike optimization metaheuristic. Opsearch 46(1):25–51

    MathSciNet  MATH  Google Scholar 

  15. Gupta S, Deep K (2019) A hybrid self-adaptive sine cosine algorithm with opposition based learning. Expert Syst Appl 119:210–230

    Google Scholar 

  16. Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222:175–184

    MathSciNet  Google Scholar 

  17. Issa M, Hassanien AE, Oliva D, Helmi A, Ziedan I, Alzohairy AM (2018) ASCA-PSO: adaptive sine cosine optimization algorithm integrated with particle swarm for pairwise local sequence alignment. Expert Syst Appl 99:56–70

    Google Scholar 

  18. Jiang J, Feng Y, Zhao J, Li K (2017) DataABC: a fast ABC based energy-efficient live VM consolidation policy with data-intensive energy evaluation model. Future Gener Comput Syst 74:132–141

    Google Scholar 

  19. Jiang J, Jiang S, Meng X, Qiu C (2019a) EST-TSA: an effective search tendency based to tree seed algorithm. Phys A Stat Mech Appl 534:122323

    Google Scholar 

  20. Jiang J, Wu D, Chen Y, Li K (2019b) Complex network oriented artificial bee colony algorithm for global bi-objective optimization in three-echelon supply chain. Appl Soft Comput 76:193–204

    Google Scholar 

  21. Jiang J, Xu M, Meng X, Li K (2020) STSA: a sine Tree-Seed Algorithm for complex continuous optimization problems. Phys A Stat Mech Appl 537:122802

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  23. Kiran MS (2015) TSA: tree-seed algorithm for continuous optimization. Expert Syst Appl 42(19):6686–6698

    Google Scholar 

  24. Kiran MS (2016) An implementation of tree-seed algorithm (TSA) for constrained optimization. In: Lavangnananda K, Phon-Amnuaisuk S, Engchuan W, Chan J (eds) Intelligent and evolutionary systems. Springer, Cham

    Google Scholar 

  25. Kiran MS (2017) Withering process for tree-seed algorithm. Proc Comput Sci 111:46–51

    Google Scholar 

  26. Li X, Yin M (2013) A hybrid cuckoo search via lévy flights for the permutation flow shop scheduling problem. Int J Prod Res 51(16):4732–4754

    Google Scholar 

  27. Li S, Fang H, Liu X (2018) Parameter optimization of support vector regression based on sine cosine algorithm. Expert Syst Appl 91:63–77

    Google Scholar 

  28. Liu C, Fan L (2016) A hybrid evolutionary algorithm based on tissue membrane systems and CMA-ES for solving numerical optimization problems. Knowl Based Syst 105:38–47

    Google Scholar 

  29. Mirjalili S (2016a) Dragonfly algorithm: a new metaheuristic optimization technique for solving singleobjective, discrete, and multiobjective problems. Neural Comput Appl 27(4):1053–1073

    Google Scholar 

  30. Mirjalili S (2016b) SCA: a sine cosine algorithm for solving optimization problems. Knowl Based Syst 96(96):120–133

    Google Scholar 

  31. Mirjalili S, Gandomi HA, Mirjalili SZ (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Google Scholar 

  32. Nenavath H, Jatoth RK (2019) Hybrid SCA-TLBO: a novel optimization algorithm for global optimization and visual tracking. Neural Comput Appl 31(9):5497–5526

    Google Scholar 

  33. Pontani M, Conway BA (2010) Particle swarm optimization applied to space trajectories. J Guid Control Dyn 33(5):1429–1441

    Google Scholar 

  34. Rajendran C, Ziegler H (2007) Antcolony algorithms for permutation flowshop scheduling to minimize makespan total flowtime of jobs. Eur J Oper Res 155(2):426–438

    MATH  Google Scholar 

  35. Rashedi E, Nezamabadipour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    MATH  Google Scholar 

  36. Salimi H (2015) Stochastic fractal search: a powerful metaheuristic algorithm. Knowl Based Syst 75(C):1–18

    Google Scholar 

  37. Sindhu R, Ngadiran R, Yacob YM, Zahri NAH, Hariharan M (2017) Sine–cosine algorithm for feature selection with elitism strategy and new updating mechanism. Neural Comput Appl 28(10):2947–2958

    Google Scholar 

  38. Singh N, Singh SB (2017) A novel hybrid GWO-SCA approach for optimization problems. Eng Sci Technol Int J 20(6):1586–1601

    Google Scholar 

  39. Srinivas M, Patnaik LM (1994) Genetic algorithms: a survey. IEEE Comput 27(6):17–26

    Google Scholar 

  40. Tabrizian Z, Afshari E, Amiri GG, Beygi MH, Nejad SMP (2013) A new damage detection method: big bang-big crunch (BB-BC) algorithm. Shock Vib 20(4):633–648

    Google Scholar 

  41. Venter G, Sobieszczanskisobieski J (2003) Particle swarm optimization. AIAA J 41(8):129–132

    Google Scholar 

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Acknowledgements

The authors are grateful to the financial support by the Natural Science Foundation of the Science and Technology Department of Jilin Province, China (No. 20180101044JC), the Foundation of the Education Department of Jilin Province, China (No. JJKH20200141KJ), the Foundation of Social Science of Jilin Province, China (No. 2019B68), the Foundation of Jilin University of Finance and Economics (Nos. 2020ZY14, 2020ZY09) and National Natural Science Foundation of China (No. 61572225).

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Correspondence to Jianhua Jiang.

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Appendix

Appendix

See Table 10.

Table 10 Functions from IEEE CEC 2014

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Jiang, J., Han, R., Meng, X. et al. TSASC: tree–seed algorithm with sine–cosine enhancement for continuous optimization problems. Soft Comput (2020). https://doi.org/10.1007/s00500-020-05099-w

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Keywords

  • Continuous optimization problem
  • Tree–seed algorithm (TSA)
  • Sine–cosine algorithm (SCA)
  • Swarm intelligence