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Constrained optimization with stochastic feasibility regions applied to vehicle path planning

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Abstract

In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the sensors have measurement errors, the stochasticity of the data has to be incorporated into the models. In this paper, we consider using a genetic algorithm for the constrained optimization problem of finding the trajectory with minimum length between two locations, avoiding the obstacles on the way. To incorporate the variability of the sensor readings, we propose a modified genetic algorithm, addressing the stochasticity of the feasible regions. In this way, the probability that a possible solution in the search space, say x, is feasible can be derived from the random observations of obstacles and pathways, creating a real-time data learning algorithm. By building a confidence region from the observed data such that its border intersects with the solution point x, the level of the confidence region defines the probability that x is feasible. We propose using a smooth penalty function based on the Gaussian distribution, facilitating the borders of the feasible regions to be reached by the algorithm.

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References

  1. Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1978)

    Google Scholar 

  2. Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Professional, Reading (1989)

    MATH  Google Scholar 

  3. Homaifar, A., Qi, C.X., Lai, S.H.: Constrained optimization via genetic algorithms. Simulation 62, 242–253 (1994)

    Article  Google Scholar 

  4. Coello, C.A.C.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191, 1245–1287 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Davis, L.: Genetic Algorithms and Simulated Annealing. Pitman, London (1987)

    MATH  Google Scholar 

  6. Riche, R.L., Haftka, R.: Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm. AIAA J. 31(5), 951–970 (1993)

    Article  MATH  Google Scholar 

  7. Smith, A., Tate, D.: Genetic optimization using a penalty function. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 499–503. University of Illinois at Urbana-Champaign, Morgan Kaufmann, San Mateo, CA (1993)

  8. Nearchou, A.C.: Adaptive navigation of autonomous vehicles using evolutionary algorithms. Artif. Intell. Eng. 13, 159–173 (1999)

    Article  Google Scholar 

  9. Zheng, C., Ding, M., Zhou, C.: Real-time route planning for unmanned air vehicle with an evolutionary algorithm. Int. J. Pattern Recognit. Artif. Intell. 17(1), 63–81 (2003)

    Article  Google Scholar 

  10. Zheng, C., Ding, M., Zhou, C., Li, L.: Coevolving and cooperating path planner for multiple unmanned air vehicles. Eng. Appl. Artif. Intell. 17(8), 887–896 (2004)

    Article  Google Scholar 

  11. Zheng, C., Li, L., Xu, F., Sun, F., Ding, M.: Evolutionary route planner for unmanned air vehicles. IEEE Trans. Robot. 21(4), 609–620 (2005)

    Article  Google Scholar 

  12. Nikolos, I., Valavanis, K., Tsourveloudis, N., Kostaras, A.: Evolutionary algorithm based offline/online path planner for UAV navigation. IEEE Trans. Syst. Man Cybern. B Cybern. 33(6), 898–912 (2003)

    Article  Google Scholar 

  13. Nikolos, I., Zografos, E., Brintaki, A.: UAV path planning using evolutionary algorithm. In: Javaan, S.C., Lakhmi, C.J., Akiko, M., Mika, S.-I. (eds.) Innovations in Intelligent Machines, pp. 77–111. Springer, Berlin (2007)

    Chapter  Google Scholar 

  14. Hu, Y., Yang, S.X.: A knowledge based genetic algorithm for path planning of a mobile robot. In: Proceedings of the 2004 IEEE International Conference on Robotics and Automation, vol. 5, pp. 4350–4355 (2004)

  15. Jia, D., Vagners, J.: Parallel evolutionary algorithms for UAV path planning. In: Proceedings of the AIAA 1st Intelligent Systems Technical Conference (2004)

  16. Macharet, D.G., Neto, A.A., Campos, M.F.M.: Feasible UAV path planning using genetic algorithms and Bezier curves. In: Proceedings of SBIA Advances in Artificial Intelligence, pp. 223–232 (2010)

  17. Volkan, P.Y.: A new vibrational genetic algorithm enhanced with a Voronoi diagram for path planning of autonomous UAV. Aerosp. Sci. Technol. 16(1), 47–55 (2012)

    Article  Google Scholar 

  18. Fu, Y., Ding, M., Zhou, C.: Phase angle-encoded and quantum-behaved particle swarm optimization applied to three-dimensional route planning for UAV. IEEE Trans. Syst. Man Cybern. 42(2), 511–526 (2012)

    Article  Google Scholar 

  19. Roberge, V., Tarbouchi, M., Labont, G.: Comparison of parallel genetic algorithm and particle swarm optimization for real-time UAV path planning. IEEE Trans. Ind. Inf. 9(1), 132–141 (2013)

    Article  Google Scholar 

  20. Zhang, D., Zhao, J., Lei, G., Wang, S., Zheng, X.: Hurry path planning based on adaptive genetic algorithm. Appl. Mech. Mater. 446–447, 1292–1297 (2014)

    Article  Google Scholar 

  21. Sugihara, K., Yuh, J.: GA-based motion planning for underwater robotic vehicles. In: Proceedings of 10th International Symposium on Unmanned Untethered Submersible Technology, pp. 406–415. Autonomous Undersea Systems Institute (1996)

  22. Smierzchalski, R.: Evolutionary trajectory planning of ships in navigation traffic areas. J. Mar. Sci. Technol. 4, 1–6 (1999)

    Article  Google Scholar 

  23. Schouwenaars, T., How, J., Feron, E.: Decentralized cooperative trajectory planning of multiple aircraft with hard safety guarantees. In: Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA-2004-5141 (2004)

  24. Tsitsiklis, J.N.: Efficient algorithms for globally optimal trajectories. IEEE Trans. Autom. Control 40(9), 1528–1538 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  25. Nikolos, I.K., Brintaki, A.: Coordinated UAV path planning using differential evolution. In: Proceedings of the 13th Mediterranean Conference on Control and Automation, IEEE, pp. 549–556 (2005)

  26. Shimaa, T., Rasmussena, S.J., Sparksa, A.G., Passinob, K.M.: Multiple task assignments for cooperating uninhabited aerial vehicles using genetic algorithms. Comput. Oper. Res. 33, 3252–3269 (2006)

    Article  Google Scholar 

  27. Edison, E., Shima, T.: Integrated task assignment and path optimization for cooperating uninhabited aerial vehicles using genetic algorithms. Comput. Oper. Res. 38, 340–356 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Sedighi, K.H., Ashenayi, K., Manikas, T.W., Wainwright, R.L., Tai, H.-M.: Autonomous local path planning for a mobile robot using a genetic algorithm. In: Congress on Evolutionary Computation, CEC2004, vol. 2, pp. 1338–1345 (2004)

  29. Lin, H., Xiao, J., Michalewicz, Z.: Evolutionary algorithm for path planning in mobile robot environment. In: Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, vol. 1, pp. 211–216 (1994)

  30. Tu, J., Yang, S.X.: Genetic algorithm based path planning for a mobile robot. In: Proceedings of the 2003 lEEE lnlernatioarl Conference on Robotics and Automation, vol. 1, pp. 1221–1226 (2003)

  31. Altaharwa, I., Sheta, A.F., Alweshah, M.: A mobile robot path planning using genetic algorithm in static environment. J. Comput. Sci. 4, 341–344 (2008)

    Article  Google Scholar 

  32. Hermanu, A., Manikas, T., Ashenayi, K., Wainwright, R.: Autonomous robot navigation using a genetic algorithm with an efficient genotype structure. In: Dagli, C.H., et al. (eds.) Intelligent Engineering Systems Through Artificial Neural Networks: Smart Engineering Systems Design: Neural Networks, Fuzzy Logic, Evolutionary Programming, Complex Systems and Artificial Life, pp. 319–324. ASME Press, New York (2004)

    Google Scholar 

  33. Candido, S.: Autonomous robot path planning using a genetic algorithm (n.d.). http://pdf.aminer.org/000/265/208/autonomous_path_planning_in_a_variety_of_environments

  34. Castillo, O., Trujillo, L.: Multiple objective genetic algorithms for path-planning optimization in autonomous mobile robots. In: Soft Computing—A Fusion of Foundations, Methodologies and Applications—Fuzzy-Neural Computation and Robotics, vol. 11, no. 3, pp. 269–279 (2006)

  35. Ryerson, A., Zhang, Q.: Vehicle path planning for complete field coverage using genetic algorithms. CIGR, Commission Internationale du Genie Rural—E-Journal, vol. 9 (2007)

  36. Liu, X.-F., Peng, Z.-R., Chang, Y.-T., Zhang, L.-Y.: Multi-objective evolutionary approach for UAV cruise route planning to collect traffic information. J. Cent. South Univ. 19(12), 3614–3621 (2012)

    Article  Google Scholar 

  37. Kok, J., Gonzalez, L.F., Kelson, N.: FPGA implementation of an evolutionary algorithm for autonomous unmanned aerial vehicle on-board path planning. IEEE Trans. Evol. Comput. 17, 272–281 (2013)

    Article  Google Scholar 

  38. Michalewicz, Z., Nazhiyath, G.: A co-evolutionary algorithm for numerical optimization problems with nonlinear constraints. In: Proceedings of the Second IEEE International Conference on Evolutionary Computation, pp. 647–651. IEEE Press (1995)

  39. Chootinan, P., Chen, A.: Constraint handling in genetic algorithms using a gradient-based repair method. Comput. Oper. Res. 33, 2263–2281 (2006)

    Article  MATH  Google Scholar 

  40. Michalewicz, Z., Janikow, C.Z.: Handling constraints in genetic algorithms. In: Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 151–157. Morgan Kaufmann (1993)

  41. Koziel, S., Michalewicz, Z.: Evolutionary algorithms, homomorphous mapping and constrained parameter optimization. Evol. Comput. 7, 19–44 (1999)

    Article  Google Scholar 

  42. Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 4, 284–294 (2000)

    Article  Google Scholar 

  43. Lin, C.-Y., Wu, W.-H.: Self-organizing adaptive penalty strategy in constrained genetic search. Struct. Multidiscip. Optim. 26, 417–428 (2004)

    Article  Google Scholar 

  44. Wang, Y., Cai, Z., Zhou, Y., Fan, Z.: Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint handling technique. Struct. Multidiscip. Optim. 37(4), 395–413 (2009)

    Article  Google Scholar 

  45. Montemurro, M., Vincenti, A., Vannucci, P.: The automatic dynamic penalisation method (ADP) for handling constraints with genetic algorithms. Comput. Methods Appl. Mech. Eng. 256, 70–87 (2013)

    Article  MathSciNet  Google Scholar 

  46. Liu, X.: On compact formulation of constraints induced by disjoint prohibited-zones. IEEE Trans. Power Syst. 25(4), 2004–2005 (2010)

    Article  Google Scholar 

  47. Jabr, R.A.: Solution to economic dispatching with disjoint feasible regions via semidefinite programming. IEEE Trans. Power Syst. 27, 572–573 (2012)

    Article  Google Scholar 

  48. Dupacová, J., Gaivoronski, A., Kos, Z., Szántai, T.: Stochastic programming in water management: a case study and a comparison of solution techniques. Eur. J. Oper. Res. 52, 28–44 (1991)

    Article  MATH  Google Scholar 

  49. Henrion, R., Li, P., Moller, A., Steinbach, S., Wendt, M., Wozny, G.: Stochastic optimization for operating chemical processes under uncertainty. In: Grotschel, M., Krunke, S., Rambau, J. (eds.) Online Optimization of Large Scale Systems, pp. 457–478. Springer, Berlin Heidelberg (2001)

    Chapter  Google Scholar 

  50. Henrion, R., Moller, A.: Optimization of a continuous distillation process under random inflow rate. Comput. Math. Appl. 45, 247262 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  51. Charnes, A., Cooper, W.W.: Chance-constrained programming. Manag. Sci. 6, 73–79 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  52. Miller, B.L., Wagner, H.M.: Chance constrained programming with joint constraints. Oper. Res. 13, 930–945 (1995)

    Article  MATH  Google Scholar 

  53. Cooper, W.W., Huang, Z., Lelas, V., Li, S.X., Olesen, O.B.: Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. J. Product. Anal. 9, 53–79 (1998)

    Article  Google Scholar 

  54. Rachev, S., Romisch, W.: Quantitative stability in stochastic programming: the method of probability metrics. Math. Oper. Res. 27(4), 792–818 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  55. Calafiore, G.C., El Ghaoui, L.: On distributionally robust chance-constrained linear programs. J. Optim. Theory Appl. 130(1), 1–23 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  56. Chen, W., Sim, M., Sun, J., et al.: From CVaR to uncertainty set: implications in joint chance-constrained optimization. Oper. Res. 58, 470–485 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  57. Kuecuekyavuz, S.: On mixing sets arising in chance-constrained programming. Math. Program. 132, 31–56 (2012)

    Article  MathSciNet  Google Scholar 

  58. Dias, R., Garcia, N., Zambom, A.Z.: A penalized nonparametric method for nonlinear constrained optimization based on noisy data. Comput. Optim. Appl. 45, 521–541 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This paper was partially supported by FAEPEX Grant 519.292 (573/13), CNPq 302182/2010-1, Fapesp: 2013/07375-0, Fapesp: 2013/00506-1 and CAPES.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Loyola University Chicago, 1032 W. Sheridan Road, Chicago, IL, 60660, USA

    Adriano Zanin Zambom

  2. Department of Statistics, State University of Campinas - UNICAMP, Rua Sergio Buarque de Holanda, 651 - Barao Geraldo, Campinas, SP, 13083-859, Brazil

    Julian A. A. Collazos

  3. Department of Mathematics and Statistics, Universidad del Tolima, Barrio Santa Helena Parte Alta - Ibague, Tolima, Colombia

    Ronaldo Dias

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  1. Adriano Zanin Zambom
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  2. Julian A. A. Collazos
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Correspondence to Adriano Zanin Zambom.

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Zambom, A.Z., Collazos, J.A.A. & Dias, R. Constrained optimization with stochastic feasibility regions applied to vehicle path planning. J Glob Optim 64, 803–823 (2016). https://doi.org/10.1007/s10898-015-0353-9

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  • DOI: https://doi.org/10.1007/s10898-015-0353-9

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