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Efficient meta-heuristic approach for the multiobjective green p-hub centre routing problem

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Abstract
The design of responsive and green networks necessarily entails the optimisation of multiple conflicting objectives with strategic, tactical, or operational decisions. This paper addresses a bi-objective green p-hub centre routing problem with hub location-allocation decisions and vehicle routing decisions. In their respective routes, vehicles may only travel using one selected speed between each node pair. The objectives are the minimisation of the worst service time and the environmental costs incurred during the transportation of all necessary demand flows, respectively. Since the studied problem is NP-hard, a meta-heuristic approach based on the non-dominated sorting genetic algorithm-II meta-heuristic is proposed. Additionally, min-max location and sequential allocation-routing method is developed to generate initial solutions. Furthermore, problemspecific crossover and mutation operators are implemented to efficiently explore the search space. Whereas, a novel rankbased speed selection procedure is devised to determine the appropriate travel speeds for generated off-springs based on their relative ranks in current population. Computational experiments are performed on the Australian Post (AP) dataset, and results indicate that our proposed heuristic approach provides good solutions in competitive CPU times. Finally, a discussion on the obtained Pareto frontier approximations is offered, and analysis is conducted on the effects of key decision parameters such as the number of located hub nodes, and the number of vehicles available at open hubs.
Keywords
Multi-objective optimisation, Costs, Routing, Metaheuristics, Statistics, Sociology, Evolutionary computation, Transportation, Genetic algorithm, green routing, hub location, multiobjective optimization (MOO), vehicle routing, EVOLUTIONARY ALGORITHMS, LOCATION-PROBLEMS, MODELS

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Citation

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MLA
Ibnoulouafi, El Mehdi, et al. “Efficient Meta-Heuristic Approach for the Multiobjective Green p-Hub Centre Routing Problem.” IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, vol. 30, no. 2, 2026, pp. 449–63, doi:10.1109/tevc.2024.3410517.
APA
Ibnoulouafi, E. M., Aouam, T., Oudani, M., & Ghogho, M. (2026). Efficient meta-heuristic approach for the multiobjective green p-hub centre routing problem. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, 30(2), 449–463. https://doi.org/10.1109/tevc.2024.3410517
Chicago author-date
Ibnoulouafi, El Mehdi, Tarik Aouam, Mustapha Oudani, and Mounir Ghogho. 2026. “Efficient Meta-Heuristic Approach for the Multiobjective Green p-Hub Centre Routing Problem.” IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 30 (2): 449–63. https://doi.org/10.1109/tevc.2024.3410517.
Chicago author-date (all authors)
Ibnoulouafi, El Mehdi, Tarik Aouam, Mustapha Oudani, and Mounir Ghogho. 2026. “Efficient Meta-Heuristic Approach for the Multiobjective Green p-Hub Centre Routing Problem.” IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 30 (2): 449–463. doi:10.1109/tevc.2024.3410517.
Vancouver
1.
Ibnoulouafi EM, Aouam T, Oudani M, Ghogho M. Efficient meta-heuristic approach for the multiobjective green p-hub centre routing problem. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION. 2026;30(2):449–63.
IEEE
[1]
E. M. Ibnoulouafi, T. Aouam, M. Oudani, and M. Ghogho, “Efficient meta-heuristic approach for the multiobjective green p-hub centre routing problem,” IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, vol. 30, no. 2, pp. 449–463, 2026.
@article{01J01RGGEAH10EHZMTFRC54XHT,
  abstract     = {{The design of responsive and green networks necessarily entails the optimisation of multiple conflicting objectives
with strategic, tactical, or operational decisions. This paper
addresses a bi-objective green p-hub centre routing problem with
hub location-allocation decisions and vehicle routing decisions.
In their respective routes, vehicles may only travel using one
selected speed between each node pair. The objectives are the
minimisation of the worst service time and the environmental
costs incurred during the transportation of all necessary demand
flows, respectively. Since the studied problem is NP-hard, a
meta-heuristic approach based on the non-dominated sorting
genetic algorithm-II meta-heuristic is proposed. Additionally,
min-max location and sequential allocation-routing method is
developed to generate initial solutions. Furthermore, problemspecific crossover and mutation operators are implemented to
efficiently explore the search space. Whereas, a novel rankbased speed selection procedure is devised to determine the
appropriate travel speeds for generated off-springs based on their
relative ranks in current population. Computational experiments
are performed on the Australian Post (AP) dataset, and results
indicate that our proposed heuristic approach provides good
solutions in competitive CPU times. Finally, a discussion on the
obtained Pareto frontier approximations is offered, and analysis
is conducted on the effects of key decision parameters such as
the number of located hub nodes, and the number of vehicles
available at open hubs.}},
  author       = {{Ibnoulouafi, El Mehdi and Aouam, Tarik and Oudani, Mustapha and Ghogho, Mounir}},
  issn         = {{1089-778X}},
  journal      = {{IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION}},
  keywords     = {{Multi-objective optimisation,Costs,Routing,Metaheuristics,Statistics,Sociology,Evolutionary computation,Transportation,Genetic algorithm,green routing,hub location,multiobjective optimization (MOO),vehicle routing,EVOLUTIONARY ALGORITHMS,LOCATION-PROBLEMS,MODELS}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{449--463}},
  title        = {{Efficient meta-heuristic approach for the multiobjective green p-hub centre routing problem}},
  url          = {{http://doi.org/10.1109/tevc.2024.3410517}},
  volume       = {{30}},
  year         = {{2026}},
}

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