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Intrusive tumor growth inspired optimization algorithm for data clustering

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Abstract

Inspired by the invasive tumor growth mechanism, this paper proposes a new meta-heuristic algorithm. A population of tumor cells can be divided into three subpopulations as proliferative cells, quiescent cells, and dying cells according to the nutrient concentration they get. Different cells have different behaviors and interactions among them for competition. In the tumor growing process, an invasive cell is born around a proliferative cell for the higher nutrient concentration and a necrotic cell occurs around a dying cell for the lower nutrient concentration, which presents the balance between life and death. To evaluate the performance of the intrusive tumor growth optimization algorithm (ITGO), we compared it to the many well-known heuristic algorithms by the Wilcoxon’s signed-rank test with Bonferroni–Holm correction method and the Friedman’s test. At the end, it is applied to solve the data clustering problem, which is a NP-hard problem. The experimental results show that the proposed ITGO algorithm outperforms other traditional heuristic algorithms for several benchmark datasets.

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References

  1. Kang F, Li J, Ma Z (2011) Rosenbrock artificial bee colony algorithm for accurate global optimization of numerical functions. Inf Sci 181:3508–3531

    Article  MATH  MathSciNet  Google Scholar 

  2. Kundu D, Suresh K, Ghosh S, Das S, Panigrahi BK, Das S (2011) Multi-objective optimization with artificial weed colonies. Inf Sci 181:2441–2454

    Article  MathSciNet  Google Scholar 

  3. Akay B, Karaboga D (2012) A modified artificial bee colony algorithm for real-parameter optimization. Inf Sci 192:120–142

    Article  Google Scholar 

  4. Yeh W-C (2012) Novel swarm optimization for mining classification rules on thyroid gland data. Inf Sci 197:65–76

    Article  Google Scholar 

  5. Christmas J, Keedwell E, Frayling TM, Perry JRB (2011) Ant colony optimisation to identify genetic variant association with type 2 diabetes. Inf Sci 181:1609–1622

    Article  Google Scholar 

  6. Zhang Y, Gong D-W, Ding Z (2012) A bare-bones multi-objective particle swarm optimization algorithm for environmental/economic dispatch. Inf Sci 192:213–227

    Article  Google Scholar 

  7. Manoj VJ, Elias E (2012) Artificial bee colony algorithm for the design of multiplier-less nonuniform filter bank transmultiplexer. Inf Sci 192:193–203

    Article  Google Scholar 

  8. Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  10. Dorigo M (1992) Optimization, learning and natural algorithms, Ph.D. Thesis, Politecnico di Milano, Italy

  11. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Piscataway, NJ, pp 1942–1948

  12. Tang D, Cai Y, Zhao J, Xue Y (2014) A quantum-behaved particle swarm optimization with memetic algorithm and memory for continuous non-linear large scale problems. Inf Sci 289:162–189

    Article  Google Scholar 

  13. Rao RV, Savsani VJ, Vakharia DP (2012) Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems. Inf Sci 183:1–15

    Article  MathSciNet  Google Scholar 

  14. Yang XS, Deb S (2009) Cuckoo search via Levy flights. In: Proceedings of World congress on nature & biologically inspired computing. IEEE Publications, USA, pp 210–214

  15. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  17. Gandomi AH, Alavi AH (2012) Krill Herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845

    Article  MATH  MathSciNet  Google Scholar 

  18. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department

  19. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(December):702–713

    Article  Google Scholar 

  20. Civicioglu P (2013) Artificial cooperative search algorithm for numerical optimization problems. Inf Sci 229:58–76

    Article  Google Scholar 

  21. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  22. Mehrabiana AR, Lucas C (2006) A novel numerical optimization algorithm inspired from weed colonization. Ecol Inf 1:1355–1366

    Google Scholar 

  23. Shelokar PS, Jayaraman VK, Kulkarni BD (2004) An ant colony approach for clustering. Anal Chim Acta 509:187–195

    Article  Google Scholar 

  24. Adib AB (2005) NP-hardness of the cluster minimization problem revisited. J Phys A Math Gen 40:8487–8492

    Article  MathSciNet  Google Scholar 

  25. Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. In: Computing surveys. ACM, pp 264–323

  26. Jain AK (2010) Data clustering: 50 years beyond K-means. Pattern Recogn Lett 31:651–666

    Article  Google Scholar 

  27. Das S, Abraham A, Konar A (2009) Automatic hard clustering using improved differential evolution algorithm. In: Studies in computational intelligence, pp 137–174

  28. Hatamlou A, Abdullah S, Nezamabadi-Pour H (2011) Application of gravitational search algorithm on data clustering. In: Rough sets and knowledge technology. Springer, Berlin, pp 337–346

  29. Hatamlou A, Abdullah S, Nezamabadi-Pour H (2012) A combined approach for clustering based on K-means and gravitational search algorithms. Swarm Evol Comput 6:47–52

    Article  Google Scholar 

  30. Izakian H, Abraham A (2011) Fuzzy C-means and fuzzy swarm for fuzzy clustering problem. Expert Syst Appl 38:1835–1838

    Article  Google Scholar 

  31. Senthilnath J, Omkar SN, Mani V (2011) Clustering using firefly algorithm: performance study. Swarm Evol Comput 1:164–171

    Article  Google Scholar 

  32. Ghosh A, Halder A, Kothari M, Ghosh S (2008) Aggregation pheromone density based data clustering. Inf Sci 178:2816–2831

    Article  Google Scholar 

  33. Hatamlou A, Abdullah S, Hatamlou M (2011) Data clustering using big bang–big crunch algorithm. In: Communications in computer and information science, pp 383–388

  34. Fathian M, Amiri B, Maroosi A (2007) Application of honey-bee mating optimization algorithm on clustering. Appl Math Comput 190:1502–1513

    Article  MATH  MathSciNet  Google Scholar 

  35. Satapathy SC, Naik A (2011) Data clustering based on teaching–learning-based optimization. In: Panigrahi BK, Suganthan PN, Das S, Satapathy SC (eds) Swarm, evolutionary, and memetic computing. Lecture notes in computer science, vol 7077. Springer, Berlin, Heidelberg, pp 148–156

    Chapter  Google Scholar 

  36. Unnikrishnan GU, Unnikrishnan VU, Reddy JN et al (2010) Review on the constitutive models of tumor tissue for computational analysis. Appl Mech Rev 63(4):040801

    Article  Google Scholar 

  37. Deisboeck TS, Berens ME, Kansal AR, Torquato S, Rachamimov A et al (2001) Patterns of self-organization in tumor systems: complex growth dynamics in a novel brain tumor spheroid model. Cell Prolif 34:115–134

    Article  Google Scholar 

  38. Mahmood MS, Mahmood S, Dobrota D (2011) Formulation and numerical simulations of a continuum model of avascular tumor growth. Math Biosci 231(2):159–171

    Article  MATH  MathSciNet  Google Scholar 

  39. Jeon J, Quaranta V, Cummings PT (2010) An off-lattice hybrid discrete-continuum model of tumor growth and invasion. Biophys J 98(1):37–47

    Article  Google Scholar 

  40. Jiao Y, Torquato S (2011) Emergent behaviors from a cellular automaton model for invasive tumor growth in heterogeneous microenvironments. PLoS Comput Biol 7(12):e1002314

    Article  Google Scholar 

  41. Roose T, Chapman SJ, Maini PK (2007) Mathematical models of avascular tumor growth. SIAM Rev 49(2):179–208

    Article  MATH  MathSciNet  Google Scholar 

  42. Mantegna RN (1991) Levy walks and enhanced diffusion in Milan stock exchange. Phys A 179:232–242

    Article  Google Scholar 

  43. Mantegna RN (1994) Fast, accurate algorithm for numerical simulation of Levy stable stochastic process. Phys Rev E 5(49):4677–4683

    Article  Google Scholar 

  44. Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical Report, Nanyang Technological University, Singapore and KanGAL Report Number 2005005 (Kanpur Genetic Algorithms Laboratory, IIT Kanpur)

  45. Tang K, Yao X, Suganthan PN, MacNish C, Chen Y-P, Chen C-M, Yang Z (2007) Benchmark functions for the CEC’2008 special session and competition on large scale global optimization, Technical Report. University of Science and Technology of China (USTC), School of Computer Science and Technology, Nature Inspired Computation and Applications Laboratory (NICAL), China

  46. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceeding IEEE international conference neural network, Perth, Western Australia, pp 1942–1948

  47. Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295

    Article  Google Scholar 

  48. Zhang Q (2011) http://dces.essex.ac.uk/staff/qzhang/. Accessed 6 Oct 13

  49. Neri F, Mininno E, Iacca G (2013) Compact particle swarm optimization. Inf Sci 239:96–121

    Article  MathSciNet  Google Scholar 

  50. Mininno E, Cupertino F, Naso D (2008) Real-valued compact genetic algorithms for embedded microcontroller optimization. IEEE Trans Evol Comput 12:203–219

    Article  Google Scholar 

  51. https://sites.google.com/site/tlbocodes

  52. Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1:3–18

    Article  Google Scholar 

  53. Shin YB, Kita E (2014) Search performance improvement of particle swarm optimization by second best particle information. Appl Math Comput 246:346–354

    Article  MathSciNet  Google Scholar 

  54. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE international conference evolutionary computation, pp 69–73

  55. Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans Evol Comput 6:58–73

    Article  Google Scholar 

  56. Parsopoulos KE, Vrahatis MN (2004) UPSO: a unified particle swarm optimization scheme, lecture series on computer and computation science, vol 1. Springer, Berlin, pp 868–873

  57. Merz CJ, Blake CL (1996) UCI repository of machine learning databases. http://www.ics.uci.edu/-mlearn/MLRepository.html

  58. van den Bergh F, Engelbrecht A (2006) A study of particle swarm optimization particle trajectories. Inf Sci 176:937–971

    Article  MATH  Google Scholar 

  59. Mirjalili S, Mirjalili SM, Lewis A (2014) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188–209

    Article  MathSciNet  Google Scholar 

  60. Lim WH, Isa NAM (2014) Bidirectional teaching and peer-learning particle swarm optimization. Inf Sci 280:111–134

    Article  Google Scholar 

  61. Lam AYS, Li VOK, Yu JJQ (2012) Real-coded chemical reaction optimization. IEEE Trans Evol Comput 16:339–353

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation Project (No. 61070092/F020504); the building of strong Guangdong Province for Chinese Medicine Scientific Research (20141165); the Humanities and social science fund project for Guangdong Pharmaceutical University (RWSK201409).

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Correspondence to Shoubin Dong.

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Tang, D., Dong, S., He, L. et al. Intrusive tumor growth inspired optimization algorithm for data clustering. Neural Comput & Applic 27, 349–374 (2016). https://doi.org/10.1007/s00521-015-1849-4

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