Parameter estimation of a tumor growth model using the real-valued genetic algorithm

  • Authors

    • Tanuja Agrawal ALIGARH MUSLIM UNIVERSITY, ALIGARH
    • Vinti Agrawal JNU, New Delhi
    2014-05-13
    https://doi.org/10.14419/gjma.v2i2.2404

  • This paper presents the use of real-valued Genetic Algorithm (GA) to evolve set of unknown parameters and initial conditions for tumor growth model using data extracted from El-Gohary [1]. The main focus of this work is to reach beyond the possibilities of traditional optimization methods in obtaining the far situated global optimum solutions with the help of arithmetic crossover and uniform mutation operators. Experimental results show the effectiveness of our approach by comparing the results obtained against the one mentioned in El-Gohary [1].

    Keywords: Real-Valued Genetic Algorithms; Tumor Growth Model; Parameter Estimation.

  • References

    1. El-Gohary A, Chaos and optimal control of cancer self-remission and tumor system steady states. Chaos, Solitons & Fractals, 37(5); 1305-16, (2008).
    2. Abbasi B, Jahromi AHE, Arkat J, Hosseinkouchack M, Estimating the parameters of Weibull distribution using simulated annealing algorithm. Applied Mathematics and Computation, 183(1): 85–93, (2006).
    3. Bayram M., Yildiz B, Parameter estimation of an enzyme kinetic system using computer algebra techniques. Applied Mathematics and Computation, 183; 93–98, (1999).
    4. Yildirim N, Akcay F, Okur H, Yildirim D, Parameter estimation of nonlinear models in biochemistry: A comparative study on optimization methods. Applied Mathematics and Computation, 140(1): 29–36, (2003).
    5. Coley DA, Introduction to genetic algorithms for scientists and engineers. London: World Scientific Publishing, (2003).
    6. Gen M, Cheng R, Genetic algorithms and engineering optimization. New York: John Wiley & Sons, (2000).
    7. Goldberg DE, Genetic algorithms in search, optimization and machine learning. Reading: Addison-Wesley, (2003).
    8. Tutkun N, Parameter estimation in mathematical models using the real coded genetic algorithms. Expert Systems with Applications 36: 3342–3345, (2009).
    9. Jost C, Arditi R, from pattern to process: Identifying predatorprey models from time-series data, Population Ecology, Vol. 43: 229-243, (2001).
    10. Mitchell M, Genetic Algorithms: An Overview, Complexity, 1(1): 31-39, (1995).
    11. Jeffries C, Mathematical modeling in Ecology. Boston: Birkhäuser, (1989).
    12. Katz C, A Nonequilibrium Marine Predator-Prey Interaction, Ecology, 66(5): 1426-1438, (1985).
    13. Bharadwaj KK and Al-Shamri MYH, Fuzzy-Genetic Approach to Recommender Systems Based on a Novel Hybrid User Model, Expert Systems with Applications, Elsevier, 35: 1386-1399, (2007).
    14. Mitchell M, An introduction to genetic algorithms, Cambridge, MA: MIT Press, (1998).
    15. Corcoran AL and Sen S, Using Real-valued Genetic Algorithm to Evolve Rule Sets for Classification, In: IEEE-CEC for Complex Social Networks, (1994).
    16. Michalewicz Z, Genetic Algorithms + Data Structures = Evolution Programs, AI Series, New York, Springer-Verlag, (1992).

  • Downloads

  • How to Cite

    Agrawal, T., & Agrawal, V. (2014). Parameter estimation of a tumor growth model using the real-valued genetic algorithm. Global Journal of Mathematical Analysis, 2(2), 58-64. https://doi.org/10.14419/gjma.v2i2.2404