Bi-objective Orienteering: Towards a Dynamic Multi-objective Evolutionary Algorithm

  • Jakob Bossek
  • Christian GrimmeEmail author
  • Stephan Meisel
  • Günter Rudolph
  • Heike Trautmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11411)


We tackle a bi-objective dynamic orienteering problem where customer requests arise as time passes by. The goal is to minimize the tour length traveled by a single delivery vehicle while simultaneously keeping the number of dismissed dynamic customers to a minimum. We propose a dynamic Evolutionary Multi-Objective Algorithm which is grounded on insights gained from a previous series of work on an a-posteriori version of the problem, where all request times are known in advance. In our experiments, we simulate different decision maker strategies and evaluate the development of the Pareto-front approximations on exemplary problem instances. It turns out, that despite severely reduced computational budget and no oracle-knowledge of request times the dynamic EMOA is capable of producing approximations which partially dominate the results of the a-posteriori EMOA and dynamic integer linear programming strategies.


Multi-objective optimization Metaheuristics Vehicle routing Combinatorial optimization Dynamic optimization 



J. Bossek, C. Grimme, S. Meisel and H. Trautmann acknowledge support by the European Research Center for Information Systems (ERCIS).


  1. 1.
    Azzouz, R., Bechikh, S., Ben Said, L.: Dynamic multi-objective optimization using evolutionary algorithms: a survey. In: Bechikh, S., Datta, R., Gupta, A. (eds.) Recent Advances in Evolutionary Multi-objective Optimization. ALO, vol. 20, pp. 31–70. Springer, Cham (2017). Scholar
  2. 2.
    Berube, J.-F., Gendreau, M., Potvin, J.-Y.: An exact \(\in \)-constraint method for bi-objective combinatorial optimization problems: application to the traveling salesman problem with profits. Eur. J. Oper. Res. 194(1), 39–50 (2009)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bossek, J., Grimme, C., Meisel, S., Rudolph, G., Trautmann, H.: Local search effects in bi-objective orienteering. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2018, pp. 585–592. ACM, New York (2018)Google Scholar
  4. 4.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  5. 5.
    Filippi, C., Stevanato, E.: Approximation schemes for bi-objective combinatorial optimization and their application to the TSP with profits. Comput. Oper. Res. 40(10), 2418–2428 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ghannadpour, S.F., Noori, S., Tavakkoli-Moghaddam, R.: A multi-objective vehicle routing and scheduling problem with uncertainty in customers’ request and priority. J. Comb. Optim. 28, 414–446 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Grimme, C., Meisel, S., Trautmann, H., Rudolph, G., Wölck, M.: Multi-objective analysis of approaches to dynamic routing of a vehicle. In: ECIS 2015 Completed Research Papers. Paper 62. AIS Electronic Library (2015)Google Scholar
  8. 8.
    Jozefowiez, N., Glover, F., Laguna, M.: Multi-objective meta-heuristics for the traveling salesman problem with profits. J. Math. Model. Algorithms 7(2), 177–195 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Meisel, S.: Anticipatory Optimization for Dynamic Decision Making. Operations Research/Computer Science Interfaces Series, vol. 51. Springer, New York (2011). Scholar
  10. 10.
    Meisel, S., Grimme, C., Bossek, J., Wölck, M., Rudolph, G., Trautmann, H.: Evaluation of a multi-objective EA on benchmark instances for dynamic routing of a vehicle. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2015, pp. 425–432. ACM, New York (2015)Google Scholar
  11. 11.
    Meisel, S., Wölck, M.: Evaluating idle time policies for real-time routing of a service vehicle. In: ECIS 2015 Completed Research Papers. Paper 132. AIS Electronic Library (2015)Google Scholar
  12. 12.
    Nagata, Y., Kobayashi, S.: A powerful genetic algorithm using edge assembly crossover for the traveling salesman problem. INFORMS J. Comput. 25(2), 346–363 (2013)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Nahum, O.E., Hadas, Y.: A framework for solving real-time multi-objective VRP. In: Żak, J., Hadas, Y., Rossi, R. (eds.) EWGT/EURO -2016. AISC, vol. 572, pp. 103–120. Springer, Cham (2018). Scholar
  14. 14.
    Pillac, V., Gendreau, M., Guéret, C., Medaglia, A.L.: A review of dynamic vehicle routing problems. Eur. J. Oper. Res. 225(1), 1–11 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Raquel, C., Yao, X.: Dynamic multi-objective optimization: a survey of the state-of-the-art. In: Yang, S., Yao, X. (eds.) Evolutionary Computation for Dynamic Optimization Problems, pp. 85–106. Springer, Heidelberg (2013). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jakob Bossek
    • 1
  • Christian Grimme
    • 1
    Email author
  • Stephan Meisel
    • 1
  • Günter Rudolph
    • 2
  • Heike Trautmann
    • 1
  1. 1.Department of Information SystemsUniversity of MünsterMünsterGermany
  2. 2.Department of Computer ScienceTU Dortmund UniversityDortmundGermany

Personalised recommendations