Multi-Objective Multi-Dimensional Transportation: A Case Study to the Flow of the Commodities of the Main Roads to Main Nodes in the North Western Coastal Strip of Egypt
The distribution of merchandises and commodities from source towns to final destinations is a vital issue. The job of transporter’s decisions can be optimized by reformulating the transportation problem as generalization of the classical transportation problems. Multiobjective multi-dimensional transportation network is considered the extension of conventional two-dimensional transportation network and is convenient for dealing with transportation systems with multiple supply nodes, multiple demand nodes, as well as diverse modes of transportation demands or delivering multiple kinds of merchandises. In this study, we implement an improved Biogeography based optimization IBBO to the flow of the commodities of the main roads to main nodes in the North Western Coastal Strip of Egypt, where there are four main roads and three nodes. The proposed algorithm incorporates the dominance criteria to handle multiple objective functions which enable the decision maker to cover all the Pareto frontier of the problem which have a large-scale size. Numerical results were reported in order to establish the real computational burden of the proposed algorithm and to assess its convergence performances for solving real geographical problem.
References
[1]
Mousa, A.A. (2010) Using Genetic Algorithm and TOPSIS Technique for Multi-objective Transportation Problem: A Hybrid Approach. International Journal of Computer Mathematics, 87, 3017-3029.
https://doi.org/10.1080/00207160902875262
[2]
Rodrigue, J.-P. and Ducruet, C. (2017) The Geography of Transportation Networks. Routledge, New York, 440 p.
[3]
Abokila, T. (2017) The Role of Roads in Developing the North Western Coastal Strip of Egypt: An Analytical Study Employing GIS. PhD Thesis, Banha University, Banha.
[4]
El-Shorbagy, M.A., Mousa, A.A.A., ALoraby, H. and Abo-Kila, T. (2020) Evolutionary Algorithm for Multi-Objective Multi-Index Transportation Problem under Fuzziness. Journal of Applied Research on Industrial Engineering, 7, 36-56.
[5]
Skitsko, V. and Voinikov, M. (2020) Solving Four-Index Transportation Problem with the Use of a Genetic Algorithm. LogForum, 16, Article No. 6.
https://doi.org/10.17270/J.LOG.2020.493
[6]
An, O., Chen, X., Li, Y., Han, Y., Zhang, J. and Shi, H. (2021) An Improved Non-Dominated Sorting Biogeography-Based Optimization Algorithm for the (Hybrid) Multi-Objective Flexible Job-Shop Scheduling Problem. Applied Soft Computing, 99, Article ID: 106869. https://doi.org/10.1016/j.asoc.2020.106869
[7]
Tu, J., Chen, H., Liu, J., Asghar Heidari, A., Zhang, X., Wang, M., Ruby, R. and Pham Q.-V. (2021) Evolutionary Biogeography-Based Whale Optimization Methods with Communication Structure: Towards Measuring the Balance. Knowledge-Based Systems, 212, Article ID: 106642.
https://doi.org/10.1016/j.knosys.2020.106642
[8]
Mirjalili, S. (2019) Biogeography-Based Optimisation. In: Mirjalili, S., Ed., Evolutionary Algorithms and Neural Networks, Vol. 780, Springer, Cham, 57-72.
https://doi.org/10.1007/978-3-319-93025-1_5
[9]
Ma, H. and Simon, D. (2011) Blended Biogeography-Based Optimization for Constrained Optimization. Engineering Applications of Artificial Intelligence, 24, 517-525. https://doi.org/10.1016/j.engappai.2010.08.005
[10]
Arlinghaus, S.L., Arlinghaus, W.C. and Harary, F. (2001) Graph Theory and Geography: An Interactive View. John Wiley, New York.
[11]
Hamdy, T. (2016) Operations Research: An Introduction. 10th Edition, Pearson Publisher, London.
[12]
Osman M.S., Abo-Sinna, M.A. and Mousa, A.A. (2006) IT-CEMOP: An Iterative Co-Evolutionary Algorithm for Multiobjective Optimization Problem with Nonlinear Constraints. Journal of Applied Mathematics & Computation, 183, 373-389.
https://doi.org/10.1016/j.amc.2006.05.095
[13]
Kasana, H.S. and Kumar, K.D. (2003) Introductory Operations Research, Theory and Applications. Springer-Verlag, Berlin.
Abd Elazeem, A.E.M., Mousa, A.A.A., El-Shorbagy, M.A., Elagan, S.K. and Abo-Elnaga, Y. (2021) Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems. Sustainability, 13, Article No. 1372.
https://doi.org/10.3390/su13031372
[16]
Simon, D. (2008) Biogeography-Based Optimization. IEEE Transactions on Evolutionary Computation, 12, 702-713. https://doi.org/10.1109/TEVC.2008.919004
[17]
Ma, H. (2010) An Analysis of the Equilibrium of Migration Models for Biogeography-Based Optimization. Information Sciences, 180, 3444-3464.
https://doi.org/10.1016/j.ins.2010.05.035
[18]
Farrokh Ghatte, H. (2021) A Hybrid of Firefly and Biogeography-Based Optimization Algorithms for Optimal Design of Steel Frames. Arabian Journal for Science and Engineering, 46, 4703-4717. https://doi.org/10.1007/s13369-020-05118-w
[19]
Farag, M.A., El-Shorbagy, M.A. Mousa, A.A. and El-Desoky, I.M. (2020) A New Hybrid Metaheuristic Algorithm for Multiobjective Optimization Problems. International Journal of Computational Intelligence Systems, 13, 920-940.
https://doi.org/10.2991/ijcis.d.200618.001
[20]
Osman, M.S., Abo-Sinna, M.A. and Mousa, A.A. (2009) A Epsilon-Dominance Based Multiobjective Genetic Algorithm for Economic Emission Load Dispatch Optimization Problem. Electric Power Systems Research, 79, 1561-1567.
https://doi.org/10.1016/j.epsr.2009.06.003
[21]
Mousa, A.A. and Elattar, E.E. (2014) Best Compromise Alternative to EELD Problem Using Hybrid Multiobjective Quantum Genetic Algorithm. Applied Mathematics & Information Sciences, 8, 2889-2902. https://doi.org/10.12785/amis/080626
