Underwater Glider Path Planning and Population Size Reduction in Differential Evolution

  • Aleš Zamuda
  • José Daniel Hernández-Sosa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9520)


This paper presents an approach to underwater glider path planning (UGPP), where the population size reduction mechanism is introduced into the differential evolution (DE) meta-heuristic and two types of DE strategies (DE/best and DE/rand) are applied interchangeably. The newly proposed DE instance algorithms using population size reduction on the best and rand DE strategies are assessed and compared on 12 test scenarios using the proposed approach. A Bonferroni-Dunns statistical hypothesis testing is conducted to confirm out-performance of the favoured DE/best strategy over the DE/rand strategy for the 12 UGGP scenarios utilized. The analysis suggests that the approach can benefit from gradually reducing the population size and also tuning the DE parameters. Thereby, this contributes to extend the operational capabilities of the glider vehicle and to improve its value as a marine sensor, facilitating the implementation of flexible sampling schemes.


Differential evolution Population size reduction Glider path planning Underwater robotics Autonomous underwater vehicle 



This work was partially funded by the Slovenian Research Agency under project P2-0041 and the Canary Island government and FEDER funds under project 2010/62. The codes in Matlab for extending the optimization algorithms utilized are provided by Qingfu Zhang at


  1. 1.
    Alvarez, A., Caiti, A., Onken, R.: Evolutionary path planning for autonomous underwater vehicles in a variable ocean. IEEE J. Oceanic Eng. 29(2), 418–429 (2004)CrossRefGoogle Scholar
  2. 2.
    Bošković, B., Brest, J., Zamuda, A., Greiner, S., Žumer, V.: History mechanism supported differential evolution for chess evaluation function tuning. Soft Comput. Fusion Found. Method. Appl. 15(4), 667–682 (2011)Google Scholar
  3. 3.
    Brest, J., Greiner, S., Bošković, B., Mernik, M., Žumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(6), 646–657 (2006)CrossRefGoogle Scholar
  4. 4.
    Brest, J., Korošec, P., Šilc, J., Zamuda, A., Bošković, B., Maučec, M.S.: Differential evolution and differential ant-stigmergy on dynamic optimisation problems. Int. J. Syst. Sci. 44(4), 663–679 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Brest, J., Maučec, M.S.: Population size reduction for the differential evolution algorithm. Appl. Intell. 29(3), 228–247 (2008)CrossRefGoogle Scholar
  6. 6.
    Cabrera-Gámez, J., Isern-González, J., Hernández-Sosa, D., Domínguez-Brito, A.C., Fernández-Perdomo, E.: Optimization-Based Weather Routing for Sailboats. In: Sauze, C., Finnis, J. (eds.) Robotic Sailing 2012, pp. 23–34. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  7. 7.
    Darwin, C.: On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life. John Murray, London (1859)CrossRefGoogle Scholar
  8. 8.
    Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)CrossRefGoogle Scholar
  9. 9.
    Davis, R.E., Leonard, N.E., Fratantoni, D.M.: Routing strategies for underwater gliders. Deep Sea Res. Part II 56(3), 173–187 (2009)CrossRefGoogle Scholar
  10. 10.
    Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Natural Computing Series. Springer, Heidelberg (2003) CrossRefzbMATHGoogle Scholar
  11. 11.
    Garau, B., Alvarez, A., Oliver, G.: Path planning of autonomous underwater vehicles in current fields with complex spatial variability: an A* approach. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, ICRA 2005, pp. 194–198. IEEE (2005)Google Scholar
  12. 12.
    Hátún, H., Eriksen, C.C., Rhines, P.B.: Buoyant eddies entering the Labrador Sea observed with gliders and altimetry. J. Phys. Oceanogr. 37(12), 2838–2854 (2007)CrossRefGoogle Scholar
  13. 13.
    Hernández Sosa, D.J., Smith, R., Fernández-Perdomo, E., Isern-González, J., Cabrera, J., Domínguez-Brito, A.C., Prieto-Marañón, V.: Glider path-planning for optimal sampling of mesoscale eddies. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2013, Part II. LNCS, vol. 8112, pp. 321–325. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  14. 14.
    Inanc, T., Shadden, S.C., Marsden, J.E.: Optimal trajectory generation in ocean flows. In: Proceedings of the American Control Conference, Portland, OR, USA, pp. 674–679 (2004)Google Scholar
  15. 15.
    Joshi, R., Sanderson, A.: Minimal representation multisensor fusion using differential evolution. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 29(1), 1083–4427 (1999)CrossRefGoogle Scholar
  16. 16.
    Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM J. Optim. 9(1), 112–147 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Leonard, N.E., Paley, D.A., Davis, R.E., Fratantoni, D.M., Lekien, F., Zhang, F.: Coordinated control of an underwater glider fleet in an adaptive ocean sampling field experiment in Monterey Bay. J. Field Rob. 27(6), 718–740 (2010)CrossRefGoogle Scholar
  18. 18.
    Moura, A., Rijo, R., Silva, P., Crespo, S.: A multi-objective genetic algorithm applied to autonomous underwater vehicles for sewage outfall plume dispersion observations. Appl. Soft Comput. 10(4), 1119–1126 (2010)CrossRefGoogle Scholar
  19. 19.
    Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Natural Computing Series. Springer, Heidelberg (2005) zbMATHGoogle Scholar
  20. 20.
    Rudnick, D.L., Davis, R.E., Eriksen, C.C., Fratantoni, D.M., Perry, M.J.: Underwater gliders for ocean research. Marine Tech. Soc. J. 38(2), 73–84 (2004)CrossRefGoogle Scholar
  21. 21.
    Smith, R.N., Chao, Y., Li, P.P., Caron, D.A., Jones, B.H., Sukhatme, G.S.: Planning and implementing trajectories for autonomous underwater vehicles to track evolving ocean processes based on predictions from a regional ocean model. Int. J. Rob. Res. 29(12), 1475–1497 (2010)CrossRefGoogle Scholar
  22. 22.
    Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Zaharie, D.: Influence of crossover on the behavior of differential evolution algorithms. Appl. Soft Comput. 9(3), 1126–1138 (2009)CrossRefGoogle Scholar
  24. 24.
    Zamuda, A., Brest, J., Mezura-Montes, E.: Structured population size reduction differential evolution with multiple mutation strategies on CEC 2013 real parameter optimization. In: 2013 IEEE Conference on Evolutionary Computation, vol. 1, pp. 1925–1931, 20–23 June 2013Google Scholar
  25. 25.
    Zamuda, A., Sosa, J.D.H.: Underwater glider path planning and population reduction in differential evolution. In: Fifteenth International Conference on Computer Aided Systems Theory, Museo Elder de la Ciencia y la Tecnologa, Las Palmas de Gran Canaria, Canary Islands, Spain, 8–13 February 2015, pp. 274–275 (2015)Google Scholar
  26. 26.
    Zamuda, A., Sosa, J.D.H.: Differential evolution and underwater glider path planning applied to the short-term opportunistic sampling of dynamic mesoscale ocean structures. Appl. Soft Comput. 24, 95–108 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering and Computer ScienceUniversity of MariborMariborSlovenia
  2. 2.Institute of Intelligent Systems and Numerical Applications in EngineeringUniversity of Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain

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