A Goal-Robust-Optimization Approach for Solving Open Vehicle Routing Problems with Demand Uncertainty



We investigate a goal-robust-optimization approach for solving open vehicle routing problem with demand uncertainty. The approach obtains an optimal solution that minimizes the weighted sum of undesirable deviations from a predetermined time window; for any realizations of the demand-uncertainty set, the solution enables the cumulative travel time for each route to finish within a predetermined time window as closely as possible. To improve the probability of finding exact solution for the robust-optimization model using a heuristic algorithm, we also propose a particle swarm optimization based on genetic algorithms (HPSO-GA) within the framework of hyper-heuristic to solve the goal-robust-optimization model. The computational results demonstrate that the optimal solution obtained by our goal-robust-optimization approach substantially reduced the penalty cost incurred by deviations from a predetermined time window.


Robust optimization Hyper-heuristics Genetic algorithm Particle swarm optimization 


  1. 1.
    Bertsimas, D. J. (1992). A vehicle routing problem with stochastic demand. Operational Research, 40, 574–585.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Cao, E., & Lai, M. (2010). The open vehicle routing problem with fuzzy demands. Expert Systems with Applications, 37(3), 2405–2411.CrossRefGoogle Scholar
  3. 3.
    Han, J., Lee, C., & Park, S. (2013). A robust scenario approach for the vehicle routing problem with uncertain travel times. Transportation Science, 48(3), 373–390.CrossRefGoogle Scholar
  4. 4.
    Adulyasak, Y., & Jaillet, P. (2015). Models and algorithms for stochastic and robust vehicle routing with deadlines. Transportation Science, 50(2), 608–626.CrossRefGoogle Scholar
  5. 5.
    Sungur, I., Ordóñez, F., & Dessouky, M. (2008). A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty. IIE Transactions, 40(5), 509–523.CrossRefGoogle Scholar
  6. 6.
    Gounaris, C. E., Wiesemann, W., & Floudas, C. A. (2013). The robust capacitated vehicle routing problem under demand uncertainty. Operational Research, 61(3), 677–693.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Lee, C., Lee, K., & Park, S. (2011). Robust vehicle routing problem with deadlines and travel time/demand uncertainty. Journal of the Operational Research Society, 63(9), 1294–1306.CrossRefGoogle Scholar
  8. 8.
    Agra, A., Christiansen, M., Figueiredo, R., et al. (2013). The robust vehicle routing problem with time windows. Computers & Operations Research, 40(3), 856–866.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Cao, E., Lai, M., & Yang, H. (2014). Open vehicle routing problem with demand uncertainty and its robust strategies. Expert Systems with Applications, 41(7), 3569–3575.CrossRefGoogle Scholar
  10. 10.
    Lei, W., Mhand, H., & Hiba, B. (2017). A new robust criterion for the vehicle routing problem with uncertain travel time. Computers & Industrial Engineering, 112, 607–615.CrossRefGoogle Scholar
  11. 11.
    Gounaris, C. E., Repoussis, P. P., Tarantilis, C. D., et al. (2014). An adaptive memory programming framework for the robust capacitated vehicle routing problem. Transportation Science, 50(4), 1239–1260.CrossRefGoogle Scholar
  12. 12.
    Solano, C. E., Prins, C., & Santos, A. C. (2015). Local search based meta-heuristics for the robust vehicle routing problem with discrete scenarios. Applied Soft Computing, 32, 518–531.CrossRefGoogle Scholar
  13. 13.
    Braaten, S., Gjønnes, O., Hvattum, L. M., et al. (2017). Heuristics for the robust vehicle routing problem with time windows. Expert Systems with Applications, 77, 136–147.CrossRefGoogle Scholar
  14. 14.
    Fischetti, M., & Monaci, M. (2009). Light robustness. In R. K. Ahuja, R. H. Möhring, & C. D. Zaroliagis (Eds.), Robust and online large-scale optimization (pp. 61–84). Berlin: Springer.CrossRefGoogle Scholar
  15. 15.
    Bertsimas, D., & Sim, M. (2009). Robust discrete optimization and network flows. Mathematical Programming, 98, 49–71.MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Fisher, M. (1994). Optimal solution of vehicle routing problems using minimum k-trees. Operational Research, 42, 626–642.MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Li, F., Golden, B., & Wasil, E. (2004). The open vehicle routing problem: Algorithms, large-scale test problems, and computational results. Computers & Operations Research, 34(10), 2918–2930.CrossRefMATHGoogle Scholar
  18. 18.
    Christofides, N., Mingozzi, A., & Toth, P. (1979). The vehicle routing problem. Combinatorial optimization (pp. 315–338). Chichester: Wiley.MATHGoogle Scholar
  19. 19.
    Solomon, M. M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35(2), 254–265.MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Reading: Addison Weekly.MATHGoogle Scholar
  21. 21.
    Davis, L. (1991). Handbook of genetic algorithm. New york: Van nostrand reinhold.Google Scholar

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Authors and Affiliations

  1. 1.School of Mechanical and AutomationShanghai UniversityShanghaiChina
  2. 2.School of Transportation and Vehicle EngineeringShandong University of TechnologyZiboChina

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