Performance evaluation of distance metrics on Firefly Algorithm for VRP with time windows

  • Divya AggarwalEmail author
  • Vijay Kumar
Original Research


In this paper, a modification in randomness factor is proposed for enhancing the exploitation capability of firefly algorithm. The proposed approach is applied on Vehicle Routing Problem with Time Windows (VRPTW). There is no single distance measure that fits for all type of VRPTW. An attempt has been made to evaluate on three different distance measures on the proposed approach. The performance of proposed approach on different distance measures has been evaluated on two well-known instances of Solomon’s benchmark test. The experimental results show that the performance of Brute–Curtis distance measure outperforms the other measures.


Vehicle Routing Problem with Time Windows Firefly algorithm Optimization Intensity 


  1. 1.
    Golden BL, Assad A (1988) Vehicle routing: methods and studies. Elsevier Science Publishers, UKzbMATHGoogle Scholar
  2. 2.
    Hassanzadeh T, Faez K, Seyfi G (2012) A speech recognition system based on structure equivalent fuzzy neural network trained by firefly algorithm. In: Proceedings of IEEE international conference on biomedical engineering, pp 63–67Google Scholar
  3. 3.
    Glover F (1989) Tabu search. Part 1, ORSA. J Comput 1(3):190–206MathSciNetzbMATHGoogle Scholar
  4. 4.
    Pirlot M (1996) General local search methods. Eur J Oper 92:493–511CrossRefGoogle Scholar
  5. 5.
    X.S. Nature-inspired metaheuristic algorithms. Luniver Press, Bristol, 2008Google Scholar
  6. 6.
    Kumar V, Kumar D (2014) Performance evaluation of distance metrics in the clustering algorithms. INFOCOMP J Comput Sci 13(1):38–52Google Scholar
  7. 7.
    Sayadi M, Ramezanian R, Ghaffari-Nasab N (2010) A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems. Int J Ind Eng Comput 1(1):1–10Google Scholar
  8. 8.
    Pullen H, Webb M (1967) A computer application to a transport scheduling problem. Comput J 10:10–13CrossRefGoogle Scholar
  9. 9.
    Madsen OBG (1976) Optimal scheduling of trucks—a routing problem with tight due times for delivery. In: Strobel H, Genser R, Etschmaier M (eds) Optimization applied to transportation systems. IIASA, International Institute for Applied System Analysis, Laxenburgh, pp 126–136Google Scholar
  10. 10.
    Knight K, Hofer J (1968) Vehicle scheduling with timed and connected calls: a case study. Oper Res Q 19:299–310CrossRefGoogle Scholar
  11. 11.
    Golden BL, Assad AA (1986) Perspectives on vehicle routing: exciting new developments. Oper Res 34:803–809CrossRefGoogle Scholar
  12. 12.
    Desrochers M, Lenstra JK, Savelsbergh MWP, Soumis F (1988) Vehicle routing with time windows: optimization and approximation. In: Golden B, Assad A (eds) Vehicle routing: methods and studies. Elsevier Science Publishers, UK, pp 65–84Google Scholar
  13. 13.
    Chiang W, Russell R (1996) Simulated annealing metaheuristics for the vehicle routing problem with time windows. Ann Oper Res 63:3–27CrossRefGoogle Scholar
  14. 14.
    Osman I (1993) Metastrategy simulated annealing and tabu search heuristic algorithms for the vehicle routing problem. Ann Oper Res 41:421–434CrossRefGoogle Scholar
  15. 15.
    Cordeau J-F, Desaulniers G, Desrosiers J, Solomon MM, Soumis F (2000) The VRP with Time Windows. Les Cahiers du GERADGoogle Scholar
  16. 16.
    Yang XS (2011) Metaheuristic optimization: algorithm analysis and open problems. Experimental algorithms. Springer, Berlin, pp 21–32CrossRefGoogle Scholar
  17. 17.
    Yang XS (2012) Efficiency analysis of swarm intelligence and randomization techniques. J Comput Theoret Nanosci 9(2):189–198CrossRefGoogle Scholar
  18. 18.
    Das S, Maity S, Qu BY, Suganthan PN (2011) Real-parameter evolutionary multimodal optimization survey of the state-of-the-art. Swarm Evol Comput 1(2):71–88CrossRefGoogle Scholar
  19. 19.
    Yang XS (2009) Firefly algorithms for multimodal optimization. Stochastic algorithms: foundations and applications. Springer, UK, pp 169–178CrossRefGoogle Scholar
  20. 20.
    Abedinia O, Amjady N, Naderi MS (2012) Multi-objective environmental/economic dispatch using firefly technique. In: Proceedings of IEEE international conference on environment and electrical engineering, pp 461–466Google Scholar
  21. 21.
    Durkota K (2011) Implementation of a discrete firefly algorithm for the qap problem within the sage framework. BSc thesis, Czech Technical UniversityGoogle Scholar
  22. 22.
    Marichelvam MK, Prabaharan T, Yang XS (2014) A discrete firefly algorithm for the multiobjective hybrid flowshop scheduling problems. EEE Trans Evol Comput 18(2):301–305CrossRefGoogle Scholar
  23. 23.
    Osaba E, Carballedo R, Yang XS, Diaz F (2016) An evolutionary discrete firefly algorithm with novel operators for solving the vehicle routing problem with time windows. In: Nature-inspired computation in engineering, pp 21–41CrossRefGoogle Scholar
  24. 24.
    Tilahun SL, Ong HC (2012) Modified firefly algorithm. J Appl Math. MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Gandomi A, Yang XS, Talatahari S, Alavi A (2013) Firefly algorithm with chaos. Commun Nonlinear Sci Numer Simul 18(1):89–98MathSciNetCrossRefGoogle Scholar
  26. 26.
    Coelho LDS, de Andrade Bernert DL, Mariani VC (2011) A chaotic firefly algorithm applied to reliability-redundancy optimization. In: Proceedings of IEEE congress on evolutionary computation, pp 517–521Google Scholar
  27. 27.
    Ma L, Cao P (2016) Comparative study of several improved firefly algorithms. In: IEEE International Conference on Information and Automation (ICIA), IEEE, NingboGoogle Scholar
  28. 28.
    Goel R, Maini R (2018) A hybrid of ant colony and firefly algorithms (HAFA) for solving vehicle routing problems. J Comput Sci 25:28–37MathSciNetCrossRefGoogle Scholar
  29. 29.
    Yelghi A, Kose C (2018) A modified firefly algorithm for global minimum optimization. Appl Soft Comput 62:29–44CrossRefGoogle Scholar
  30. 30.
    Tighzert L, Fonlupt C, Mendil B (2018) A set of new compact firefly algorithms. Swarm Evol Comput 40:92–115CrossRefGoogle Scholar
  31. 31.
    Yang XS (2010) Firefly algorithm, stochastic test functions and design optimisation. Bio-Inspired Comput 2(2):78–84CrossRefGoogle Scholar
  32. 32.
    Yang XS, Deb S (2010) Eagle strategy using lévy walk and firefly algorithms for stochastic optimization. Stud Comput Intell 284:101–111zbMATHGoogle Scholar
  33. 33.
    Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper Res 35:254–265MathSciNetCrossRefGoogle Scholar

Copyright information

© Bharati Vidyapeeth's Institute of Computer Applications and Management 2019

Authors and Affiliations

  1. 1.Computer Science and Engineering DepartmentThapar Institute of Engineering and TechnologyPatialaIndia
  2. 2.Computer Science and Engineering DepartmentNational Institute of TechnologyHamirpurIndia

Personalised recommendations