An Adaptive Multi-Crossover Population Algorithm for Solving Routing Problems

  • E. Osaba
  • E. Onieva
  • R. Carballedo
  • F. Diaz
  • A. Perallos
Part of the Studies in Computational Intelligence book series (SCI, volume 512)


Throughout the history, Genetic Algorithms (GA) have been widely applied to a broad range of combinatorial optimization problems. Its easy applicability to areas such as transport or industry has been one of the reasons for its great success. In this paper, we propose a new Adaptive Multi-Crossover Population Algorithm (AMCPA). This new technique changes the philosophy of the basic genetic algorithms, giving priority to the mutation phase and providing dynamism to the crossover probability. To prevent the premature convergence, in the proposed AMCPA, the crossover probability begins with a low value, and varies depending on two factors: the algorithm performance on recent generations and the current generation number. Apart from this, as another mechanism to avoid premature convergence, our AMCPA has different crossover functions, which are used alternatively. We test the quality of our new technique applying it to three routing problems: the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP) and the Vehicle Routing Problem with Backhauls (VRPB). We compare the results with the ones obtained by a basic GA to conclude that our new proposal outperforms it.


Adaptive Population Algorithm Genetic Algorithm Routing Problems Combinatorial Optimization Intelligent Transport Systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Affenzeller, M., Wagner, S., Winkler, S.: Genetic algorithms and genetic programming: modern concepts and practical applications, vol. 6. Chapman & Hall/CRC (2009)Google Scholar
  2. 2.
    Albayrak, M., Allahverdi, N.: Development a new mutation operator to solve the traveling salesman problem by aid of genetic algorithms. Expert Systems with Applications 38(3), 1313–1320 (2011)CrossRefGoogle Scholar
  3. 3.
    Anbuudayasankar, S., Ganesh, K., Lenny Koh, S., Ducq, Y.: Modified savings heuristics and genetic algorithm for bi-objective vehicle routing problem with forced backhauls. Expert Systems with Applications 39(3), 2296–2305 (2012)CrossRefGoogle Scholar
  4. 4.
    Bae, J., Rathinam, S.: Approximation algorithms for multiple terminal, hamiltonian path problems. Optimization Letters 6(1), 69–85 (2012)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Bianchessi, N., Righini, G.: Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery. Computers & Operations Research 34(2), 578–594 (2007)MATHCrossRefGoogle Scholar
  6. 6.
    Davis, L.: Applying adaptive algorithms to epistatic domains. In: Proceedings of the International Joint Conference on Artificial Intelligence, vol. 1, pp. 161–163 (1985)Google Scholar
  7. 7.
    Davis, L.: Adapting operator probabilities in genetic algorithms. In: Proceeding of the Third International Conference on Genetic Algorithms, pp. 61–69 (1989)Google Scholar
  8. 8.
    De Jong, K.: Analysis of the behavior of a class of genetic adaptive systems. PhD thesis, University of Michigan, Michigan, USA (1975)Google Scholar
  9. 9.
    Fernandez-Prieto, J., Gadeo-Martos, M., Velasco, J.R., et al.: Optimisation of control parameters for genetic algorithms to test computer networks under realistic traffic loads. Applied Soft Computing 11(4), 3744–3752 (2011)CrossRefGoogle Scholar
  10. 10.
    Gajpal, Y., Abad, P.: Multi-ant colony system (macs) for a vehicle routing problem with backhauls. European Journal of Operational Research 196(1), 102–117 (2009)MATHCrossRefGoogle Scholar
  11. 11.
    Gao, J., Gen, M., Sun, L., Zhao, X.: A hybrid of genetic algorithm and bottleneck shifting for multiobjective flexible job shop scheduling problems. Computers & Industrial Engineering 53(1), 149–162 (2007)MATHCrossRefGoogle Scholar
  12. 12.
    Goldberg, D.: Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Professional (1989)Google Scholar
  13. 13.
    Golden, B., Baker, E., Alfaro, J., Schaffer, J.: The vehicle routing problem with backhauling: two approaches. In: Proceedings of the Twenty-first Annual Meeting of SE TIMS, South Carolina, USA, pp. 90–92 (1985)Google Scholar
  14. 14.
    Grefenstette, J.J.: Optimization of control parameters for genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics 16(1), 122–128 (1986)CrossRefGoogle Scholar
  15. 15.
    Harvey, I.: The microbial genetic algorithm. In: Kampis, G., Karsai, I., Szathmáry, E. (eds.) ECAL 2009, Part II. LNCS, vol. 5778, pp. 126–133. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    Holland, J.H.: Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT Press (1975)Google Scholar
  17. 17.
    Laporte, G.: The vehicle routing problem: An overview of exact and approximate algorithms. European Journal of Operational Research 59(3), 345–358 (1992)MATHCrossRefGoogle Scholar
  18. 18.
    Lawler, E., Lenstra, J., Kan, A., Shmoys, D.: The traveling salesman problem: a guided tour of combinatorial optimization, vol. 3. Wiley, New York (1985)MATHGoogle Scholar
  19. 19.
    Li, W., Shi, Y.: On the maximum tsp with γ-parameterized triangle inequality. Optimization Letters 6(3), 415–420 (2012)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Liefooghe, A., Humeau, J., Mesmoudi, S., Jourdan, L., Talbi, E.: On dominance-based multiobjective local search: design, implementation and experimental analysis on scheduling and traveling salesman problems. Journal of Heuristics 18(2), 317–352 (2012)CrossRefGoogle Scholar
  21. 21.
    Lin, S.: Computer solutions of the traveling salesman problem. Bell System Technical Journal 44(10), 2245–2269 (1965)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Martínez-Torres, M.: A genetic search of patterns of behaviour in oss communities. Expert Systems with Applications 39(18), 13,182–13,192 (2012)Google Scholar
  23. 23.
    Mattos Ribeiro, G., Laporte, G.: An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem. Computers & Operations Research 39(3), 728–735 (2012)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Moon, I., Lee, J.H., Seong, J.: Vehicle routing problem with time windows considering overtime and outsourcing vehicles. Expert Systems with Applications 39(18), 13,202–13,213 (2012)Google Scholar
  25. 25.
    Mukherjee, S., Ganguly, S., Das, S.: A strategy adaptive genetic algorithm for solving the travelling salesman problem. In: Panigrahi, B.K., Das, S., Suganthan, P.N., Nanda, P.K. (eds.) SEMCCO 2012. LNCS, vol. 7677, pp. 778–784. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  26. 26.
    Ngueveu, S., Prins, C., Wolfler Calvo, R.: An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Computers & Operations Research 37(11), 1877–1885 (2010)MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    Nikolić, M., Teodorović, D.: Empirical study of the bee colony optimization (bco) algorithm. Expert Systems with Applications 40(1), 4609–4620 (2013)CrossRefGoogle Scholar
  28. 28.
    Osaba, E., Carballedo, R., Diaz, F., Perallos, A.: Analysis of the suitability of using blind crossover operators in genetic algorithms for solving routing problems. In: Proceedings of the 8th International Symposium on Applied Computational Intelligence and Informatics, pp. 17–23. IEEE (2013)Google Scholar
  29. 29.
    Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Computers & Operations Research 31(12), 1985–2002 (2004)MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Ray, S., Bandyopadhyay, S., Pal, S.: New operators of genetic algorithms for traveling salesman problem. In: Proceedings of the 17th International Conference on Pattern Recognition, vol. 2, pp. 497–500. IEEE (2004)Google Scholar
  31. 31.
    Reinelt, G.: Tsplib: A traveling salesman problem library. ORSA Journal on Computing 3(4), 376–384 (1991)MATHCrossRefGoogle Scholar
  32. 32.
    Rocha, M., Sousa, P., Cortez, P., Rio, M.: Quality of service constrained routing optimization using evolutionary computation. Applied Soft Computing 11(1), 356–364 (2011)CrossRefGoogle Scholar
  33. 33.
    Sarin, S.C., Sherali, H.D., Yao, L.: New formulation for the high multiplicity asymmetric traveling salesman problem with application to the chesapeake problem. Optimization Letters 5(2), 259–272 (2011)MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Schaffer, J.D., Morishima, A.: An adaptive crossover distribution mechanism for genetic algorithms. In: Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and Their Application, pp. 36–40. L. Erlbaum Associates Inc. (1987)Google Scholar
  35. 35.
    Sharma, S., Gupta, K.: Solving the traveling salesmen problem through genetic algorithm with new variation order crossover. In: International Conference on Emerging Trends in Networks and Computer Communications, pp. 274–276. IEEE (2011)Google Scholar
  36. 36.
    Spears, W.M.: Adapting crossover in evolutionary algorithms. In: Proceedings of the Conference on Evolutionary Programming, pp. 367–384 (1995)Google Scholar
  37. 37.
    Srinivas, M., Patnaik, L.M.: Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics 24(4), 656–667 (1994)CrossRefGoogle Scholar
  38. 38.
    Syswerda, G.: Schedule optimization using genetic algorithms. In: Handbook of Genetic Algorithms, pp. 332–349 (1991)Google Scholar
  39. 39.
    Tarantilis, C., Kiranoudis, C.: A flexible adaptive memory-based algorithm for real-life transportation operations: Two case studies from dairy and construction sector. European Journal of Operational Research 179(3), 806–822 (2007)MATHCrossRefGoogle Scholar
  40. 40.
    Vafaee, F., Nelson, P.C.: A genetic algorithm that incorporates an adaptive mutation based on an evolutionary model. In: Proceedings of the International Conference on Machine Learning and Applications, pp. 101–107. IEEE (2009)Google Scholar
  41. 41.
    Wang, C., Zhang, J., Yang, J., Hu, C., Liu, J.: A modified particle swarm optimization algorithm and its application for solving traveling salesman problem. In: Proceedings of the International Conference on Neural Networks and Brain, vol. 2, pp. 689–694. IEEE (2005)Google Scholar
  42. 42.
    Wang, L., Tang, D.: An improved adaptive genetic algorithm based on hormone modulation mechanism for job-shop scheduling problem. Expert Systems with Applications 38(6), 7243–7250 (2011)CrossRefGoogle Scholar
  43. 43.
    Xu, P., Zheng, J., Chen, H., Liu, P.: Optimal design of high pressure hydrogen storage vessel using an adaptive genetic algorithm. International Journal of Hydrogen Energy 35(7), 2840–2846 (2010)CrossRefGoogle Scholar
  44. 44.
    Ye, Z., Li, Z., Xie, M.: Some improvements on adaptive genetic algorithms for reliability-related applications. Reliability Engineering & System Safety 95(2), 120–126 (2010)CrossRefGoogle Scholar
  45. 45.
    Zhang, J., Chung, H.S., Zhong, J.: Adaptive crossover and mutation in genetic algorithms based on clustering technique. In: Proceedings of the Conference on Genetic and Evolutionary Computation, pp. 1577–1578. ACM (2005)Google Scholar
  46. 46.
    Zhang, J., Chung, H.S., Lo, W.L.: Clustering-based adaptive crossover and mutation probabilities for genetic algorithms. IEEE Transactions on Evolutionary Computation 11(3), 326–335 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • E. Osaba
    • 1
  • E. Onieva
    • 1
  • R. Carballedo
    • 1
  • F. Diaz
    • 1
  • A. Perallos
    • 1
  1. 1.Deusto Institute of Technology (DeustoTech)University of DeustoBilbaoSpain

Personalised recommendations