Journal of Global Optimization

, Volume 48, Issue 1, pp 41–55 | Cite as

A genetic algorithm for a global optimization problem arising in the detection of gravitational waves

  • Daniela di Serafino
  • Susana Gomez
  • Leopoldo Milano
  • Filippo Riccio
  • Gerardo Toraldo


The detection of gravitational waves is a long-awaited event in modern physics and, to achieve this challenging goal, detectors with high sensitivity are being used or are under development. In order to extract gravitational signals emitted by coalescing binary systems of compact objects (neutron stars and/or black holes), from noisy data obtained by interferometric detectors, the matched filter technique is generally used. Its computational kernel is a box-constrained global optimization problem with many local solutions and a highly nonlinear and expensive objective function, whose derivatives are not available. To tackle this problem, we designed a real-coded genetic algorithm that exploits characteristic features of the problem itself; special attention was devoted to the choice of the initial population and of the recombination operator. Computational experiments showed that our algorithm is able to compute a reasonably accurate solution of the optimization problem, requiring a much smaller number of function evaluations than the grid search, which is generally used to solve this problem. Furthermore, the genetic algorithm largely outperforms other global optimization algorithms on significant instances of the problem.


Global optimization Genetic algorithm Detection of gravitational waves 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Thorne K.S.: Gravitational radiation. In: Hawking, S.W., Israel, W. (eds) 300 Years of Gravitation, pp. 330–458. Cambridge University Press, Cambridge (1987)Google Scholar
  2. 2.
    Babak S., Balasubramanian R., Churches D., Cokelaer T., Sathyaprakash B.S.: A template bank to search for gravitational waves from inspiralling compact binaries I: physical models. Class. Quantum Grav. 23, 5477–5504 (2006)CrossRefGoogle Scholar
  3. 3.
    Mohanty S.D.: Hierarchical search strategy for the detection of gravitational waves from coalescing binaries: extension to post-newtonian waveforms. Phys. Rev. D 57(2), 630–658 (1998)CrossRefGoogle Scholar
  4. 4.
    Sengupta, A.S., Dhurandhar, S., Lazzarini, A.: Faster implementation of the hierarchical search algorithm for detection of gravitational waves from inspiraling compact binaries. Phys. Rev. D 67(8), 082,004 (2003)CrossRefGoogle Scholar
  5. 5.
    Milano L., Barone F., Milano M.: Time domain amplitude and frequency detection of gravitational waves from coalescing binaries. Phys. Rev. D 55(8), 4537–4554 (1997)CrossRefGoogle Scholar
  6. 6.
    Barrón C., Gómez S., Romero D., Saavedra A.: A genetic algorithm for Lennard–Jones atomic clusters. Appl. Math. Lett. 12(7), 85–90 (1999)CrossRefGoogle Scholar
  7. 7.
    Papoulis A.: Probability, Random Variables, and Stochastic Processes. 3rd edn. McGraw-Hill, New York (1991)Google Scholar
  8. 8.
    Sathyaprakash B.S., Dhurandhar S.V.: Choice of filters for the detection of gravitational waves from coalescing binaries. Phys. Rev. D 44(12), 3819–3834 (1991)CrossRefGoogle Scholar
  9. 9.
    Dhurandhar S.V., Sathyaprakash B.S.: Choice of filters for the detection of gravitational waves from coalescing binaries. II. Detection in colored noise. Phys. Rev. D 49(4), 1707–1722 (1994)CrossRefGoogle Scholar
  10. 10.
    Allen, B., et al.: LAL Software Documentation. Revision 1.44 (2005). Available at
  11. 11.
    Mohanty S.D., Dhurandhar S.V.: Hierarchical search strategy for the detection of gravitational waves from coalescing binaries. Phys. Rev. D 54(12), 7108–7128 (1996)CrossRefGoogle Scholar
  12. 12.
    Blanchet L., Rlyer B., Wiseman A.G.: Gravitational waveforms from inspiralling compact binaries to second-post-Newtonian order. Class. Quantum Grav. 13, 575–584 (1996)CrossRefGoogle Scholar
  13. 13.
    Holland J.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  14. 14.
    Michalewicz Z.: Genetic Algorithms + Data Structures = Evolution Programs. 3rd edn. Springer, New York (1998)Google Scholar
  15. 15.
    Herrera F., Lozano M., Verdegay J.L.: Tackling real-coded genetic algorithms: operators and tools for behavioural analysis. Artif. Intell. Rev. 12(4), 265–319 (1998)CrossRefGoogle Scholar
  16. 16.
    Maaranen H., Miettinen K., Penttinen A.: On initial populations of a genetic algorithm for continuous optimization problems. J. Glob. Optim. 37(3), 405–436 (2007)CrossRefGoogle Scholar
  17. 17.
    Bäck, T., Fogel, D.B., Michalewicz, Z. (eds): Evolutionary Computation 1: Basic Algorithms and Operators. IOP Publishing, Bristol (2000)Google Scholar
  18. 18.
    De Jong K.A.: Evolutionary Computation: A Unified Approach. MIT press, Cambridge (2006)Google Scholar
  19. 19.
    Herrera F., Lozano M., Sánchez A.M.: A taxonomy for the crossover operator for real-coded genetic algorithms: an experimental study. Int. J. Intell. Syst. 18(3), 309–338 (2003)CrossRefGoogle Scholar
  20. 20.
    Rasio A.R., Shapiro S.L.: Coalescing binary neutron stars. Class. Quantum Grav. 16(6), R1–R29 (1999)CrossRefGoogle Scholar
  21. 21.
    Matsumoto M., Nishimura T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comp. Sim. 8(1), 3–30 (1998)CrossRefGoogle Scholar
  22. 22.
    Mitra S., Dhurandhar S.V., Finn L.S.: Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation. Phys. Rev. D 72, 102,001 (2005)CrossRefGoogle Scholar
  23. 23.
    Back T.: Mutation parameters. In: Back, T., Fogel, D.B., Michalewicz, Z. (eds) Evolutionary Computation 2: Advanced Algorithms and Operators, pp. 142–151. IOP Publishing, Bristol (2000)Google Scholar
  24. 24.
    Vajda, P., Eiben, A., Hordijk, W.: Parameter control methods for selection operators in genetic algorithms. In: Parallel problem solving from nature—PPSN X, Lecture Notes in Computer Science, pp. 620–630. Springer, Berlin/Heidelberg (2008)Google Scholar
  25. 25.
    Price W.: A controlled random search procedure for global optimisation. Comput. J. 20, 367–370 (1977)CrossRefGoogle Scholar
  26. 26.
    Vaz A.I.F., Vicente L.N.: A particle swarm pattern search method for bound constrained global optimization. J. Glob. Optim. 39(2), 197–219 (2007)CrossRefGoogle Scholar
  27. 27.
    Jones D.R., Perttunen C.D., Stuckman B.E.: Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79(1), 157–181 (1993)CrossRefGoogle Scholar
  28. 28.
    Liuzzi, G., Lucidi, S., Piccialli, V.: A direct-based approach exploiting local minimizations for the solution of large-scale global optimization problems. Comput. Optim. Appl. (2008)Google Scholar
  29. 29.
    Strongin R.G.: Algorithms for multi-extremal mathematical programming problems employing the set of joint space-filling curves. J. Glob. Optim. 2(4), 357–378 (1992)CrossRefGoogle Scholar
  30. 30.
    Strongin R.G., Sergeyev Y.D.: Global Optimization with Non-Convex Constraints Sequential and Parallel Algorithms, Nonconvex Optimization and its Applications vol. 45. Kluwer, Dordrecht (2000)Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  • Daniela di Serafino
    • 1
  • Susana Gomez
    • 2
  • Leopoldo Milano
    • 3
  • Filippo Riccio
    • 1
  • Gerardo Toraldo
    • 4
  1. 1.Department of MathematicsSecond University of NaplesCasertaItaly
  2. 2.Institute of Applied MathematicsNational University of MexicoMexico CityMexico
  3. 3.Department of Physical SciencesUniversity of Naples Federico IINaplesItaly
  4. 4.DIAATUniversity of Naples Federico IIPorticiItaly

Personalised recommendations