Soft Computing

, Volume 17, Issue 7, pp 1283–1299 | Cite as

Multi-objective optimal path planning using elitist non-dominated sorting genetic algorithms

  • Faez Ahmed
  • Kalyanmoy Deb
Methodologies and Application


A multi-objective vehicle path planning method has been proposed to optimize path length, path safety, and path smoothness using the elitist non-dominated sorting genetic algorithm—a well-known soft computing approach. Four different path representation schemes that begin their coding from the start point and move one grid at a time towards the destination point are proposed. Minimization of traveled distance and maximization of path safety are considered as objectives of this study while path smoothness is considered as a secondary objective. This study makes an extensive analysis of a number of issues related to the optimization of path planning task-handling of constraints associated with the problem, identifying an efficient path representation scheme, handling single versus multiple objectives, and evaluating the proposed algorithm on large-sized grids and having a dense set of obstacles. The study also compares the performance of the proposed algorithm with an existing GA-based approach. The evaluation of the proposed procedure against extreme conditions having a dense (as high as 91 %) placement of obstacles indicates its robustness and efficiency in solving complex path planning problems. The paper demonstrates the flexibility of evolutionary computing approaches in dealing with large-scale and multi-objective optimization problems.


Multi-objective path planning Potential field Path length Path safety Path smoothness NSGA-II Genetic algorithms 



The study is supported by JC Bose National Fellowship to Prof. K. Deb and Department of Science and Technology, Government of India, under SERC-Engineering Sciences scheme (No. SR/S3/MERC/091/2009). Funding from Academy of Finland under grant 133387 for executing a part of this research is also appreciated.


  1. Ahmed F, Deb K (2011) Multi-objective path planning using spline representation. In: Proceedings of the IEEE international conference on robotics and biomimetics (IEEE-ROBIO 2011), PiscatwayGoogle Scholar
  2. Ahuja N, Chuang J (1997) Shape representation using a generalized potential field model. Pattern Analysis and Machine Intelligence. IEEE Transactions on 19(2):169–176CrossRefGoogle Scholar
  3. Al-Sultan KS, Aliyu MDS (2010) A new potential field-based algorithm for path planning. Journal of Intelligent & Robotic Systems 17(3):265–282CrossRefGoogle Scholar
  4. Bisse E, Bentounes M, Boukas EK (1995) Optimal path generation for a simulated autonomous mobile robot. Autonomous Robots 2(1):11–27CrossRefGoogle Scholar
  5. Burchardt H, Saloman R (2006) Implementation of path planning using genetic algorithms on mobile robots. In: Proceedings of the World Congress on evolutionary computation (WCCI-2006), pp 1831–1836Google Scholar
  6. Castillo O, Trujillo L (2005) Multiple objective optimization genetic algorithms for path planning in autonomous mobile robots. International Journal of Computers, Systems and Signals 6(1):48–63Google Scholar
  7. Castillo O, Trujillo L, Melin P (2007) Multiple objective genetic algorithms for path-planning optimization in autonomous mobile robots. Soft Computing-A Fusion of Foundations, Methodologies and Applications 11(3):269–279Google Scholar
  8. Choset H (1996) Sensor based motion planning: the hierarchical generalized Voronoi graph. PhD thesis, CiteseerGoogle Scholar
  9. Connolly C, Burns J, Weiss R (1990) Path planning using laplace’s equation. In: Proceedings of IEEE international conference on robotics and automation. IEEE, pp 2102–2106Google Scholar
  10. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338zbMATHCrossRefGoogle Scholar
  11. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, ChichesterGoogle Scholar
  12. Deb K, Agrawal RB (1995) Simulated binary crossover for continuous search space. Complex Systems 9(2):115–148MathSciNetzbMATHGoogle Scholar
  13. Deb K, Goyal M (1998) A robust optimization procedure for mechanical component design based on genetic adaptive search. Transactions of the ASME: Journal of Mechanical Design 120(2):162–164CrossRefGoogle Scholar
  14. Deb K, Gupta S (2011) Understanding knee points in bicriteria problems and their implications as preferred solution principles. Engineering Optimization 43(11):1175–1204MathSciNetCrossRefGoogle Scholar
  15. Deb K, Agrawal S, Pratap A, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  16. Elshamli A, Abdullah HA, Areibi S (2004) Genetic algorithms for dynamic path planning. In: Proceedings of IEEE Canadian conference on electrical and computer engineering (CCECE-04), pp 677–680Google Scholar
  17. Ge SS, Cui YJ (2002) Dynamic motion planning for mobile robots using potential field method. Autonomous Robots 13(3):207–222zbMATHCrossRefGoogle Scholar
  18. Gerke M (1999) Genetic path planning for mobile robots. In: Proceedings of the American control conference, vol 4. IEEE, pp 2424–2429Google Scholar
  19. Glasius R, Komoda A, Gielen S (1995) Neural network dynamics for path planning and obstacle avoidance. Neural Networks 8(1):125–133CrossRefGoogle Scholar
  20. Hwang Y, Ahuja N (1992) Gross motion planninga survey. ACM Computing Surveys (CSUR) 24(3):219–291CrossRefGoogle Scholar
  21. Kanayama Y, Hartman B (1997) Smooth local-path planning for autonomous vehicles. Int J Robot Res 16(3):263CrossRefGoogle Scholar
  22. Khatib O (1986) Real-time obstacle avoidance for manipulators and mobile robots. Int J Robot Res 5(1):90MathSciNetCrossRefGoogle Scholar
  23. LaValle S (2006) Planning algorithms. Cambridge University Press, CambridgeGoogle Scholar
  24. Lozano-Pérez T, Wesley M (1979) An algorithm for planning collision-free paths among polyhedral obstacles. Commun ACM 22(10):560–570CrossRefGoogle Scholar
  25. Murrieta-Cid R, Tovar B, Hutchinson S (2005) A sampling-based motion planning approach to maintain visibility of unpredictable targets. Autonomus Robots 19(3):285–300CrossRefGoogle Scholar
  26. Oriolo G, Ulivi G, Vendittelli M (1997) Fuzzy maps: a new tool for mobile robot perception and planning. Journal of Robotic Systems 14(3):179–197CrossRefGoogle Scholar
  27. Pratihar D, Deb K, Ghosh A (1999) Fuzzy-genetic algorithms and time-optimal obstacle-free path generation for mobile robots. Engineering Optimization 32:117–142CrossRefGoogle Scholar
  28. Sauter J, Matthews R, van Dyke Parunak H, Brueckner S (2002) Evolving adaptive pheromone path planning mechanisms. In: Proceedings of the first international joint conference on autonomous agents and multiagent systems, part 1. ACM, pp 434–440Google Scholar
  29. Sugihara K, Smith J (1999) Genetic algorithms for adaptive planning of path and trajectory of a mobile robot in 2D terrains. IEEE Transactions on Information and Systems 82(1):309–317Google Scholar
  30. Xiao M, Michalewicz Z (2000) An evolutionary computation approach to robot planning and navigation. Soft Computing in Mechatronics, pp 117–128Google Scholar
  31. Xue Q, Sheu PCY, Maciejewski AA, Chien SYP (2010) Planning of collision-free paths for a reconfigurable dual manipulator equipped mobile robot. Journal of Intelligent & Robotic Systems 17(3):223–242CrossRefGoogle Scholar
  32. Yang SX, Meng M (2000) Real-time collision-free path planning of robot manipulators using neural network approaches. Autonomous Robots 9(1):27–39CrossRefGoogle Scholar
  33. Zhang Q, Li H (2007) MOEA/D: A multiobjective evolutionary algorithm based on decomposition. Evolutionary Computation, IEEE Transactions on 11(6):712–731CrossRefGoogle Scholar
  34. Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou KC, Tsahalis DT, Périaux J, Papailiou KD, Fogarty T (eds) Evolutionary methods for design optimization and control with applications to industrial problems. International Center for Numerical Methods in Engineering (CIMNE), Athens, Greece, pp 95–100Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Technology KanpurKanpurIndia
  2. 2.Department of Information and Service EconomyAalto University School of EconomicsHelsinkiFinland

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