Evolutionary algorithm for multi-objective multi-index transportation problem under fuzziness

Document Type: Research Paper


1 Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom, Egypt.

2 Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia.

3 Department of Mathematics and Statistics, Faculty of Sciences, Taif University, Taif, Saudi Arabia.

4 Department of Geography, Faculty of Arts, Banha University, Egypt.


An Improved Genetic Algorithm (I-GA) for solving multi-objective Fuzzy Multi–Index Multi-objective Transportation Problem (FM-MOTP) is presented. Firstly, we introduce a new structure for the individual to be able to represent all possible feasible solutions. In addition, in order to keep the feasibility of the chromosome, a criterion of the feasibility was designed. Based on this criterion, the crossover and mutation were modified and implemented to generate feasible chromosomes. Secondly, an external archive of Pareto optimal solutions is used, which best conform a Pareto front. For avoiding an overwhelming number of solutions, the algorithm has a finite-sized archive of non-dominated solutions, which is updated iteratively at the presence of new solutions. Finally, the computational studies using two numerical problems, taken from the literature, demonstrate the effectiveness of the proposed algorithm to solve FM-MOTP Problem under fuzziness.


Main Subjects

[1]    Gupta, P. K., & Mohan, M. (2006). Problems in operations research. Sultan Chand & Sons, New Delhi.

[2]    Kapoor, V. K. (2006). Operations research: techniques for management. Sultan Chand.

[3]    Haley, K. B. (1962). New methods in mathematical programming—the solid transportation problem. Operations research10(4), 448-463.

[4]    Junginger, W. (1993). On representatives of multi-index transportation problems. European journal of operational research66(3), 353-371.

[5]    Rautman, C. A., Reid, R. A., & Ryder, E. E. (1993). Scheduling the disposal of nuclear waste material in a geologic repository using the transportation model. Operations research, 459-469.

[6]    Ahuja, A., & Arora, S. R. (2001). Multi index fixed charge bicriterion transportation problem. Indian journal of pure and applied mathematics32(5), 739-746.

[7]    Sakawa, M. (2013). Fuzzy sets and interactive multi-objective optimization. Springer science & business media.

[8]    Edalatpanah, S. A. (2019). A nonlinear approach for neutrosophic linear programming. J. Appl. Res. Ind. Eng. 6(4), 367-373.

[9]    Mousa, A. A. (2010). Using genetic algorithm and TOPSIS technique for multi-objective transportation problem: a hybrid approach. International journal of computer mathematics87(13), 3017-3029.

[10] Mousa, A. A., Geneedy, H. M., & Elmekawy, A. Y. (2010, May). Efficient evolutionary algorithm for solving multiobjective transportation problem. The international conference on mathematics and engineering physics (ICMEP-5) (pp. 1-11). Military Technical College Kobry Elkobbah, Cairo, Egypt.

[11] Zaki, S. A., Mousa, A. A. A., Geneedi, H. M., & Elmekawy, A. Y. (2012). Efficient multi-objective genetic algorithm for solving transportation, assignment, and transshipment problems. Applied mathematics, 3, 92-99.

[12] Jafari, H., & Hajikhani, A. (2016). Multi objective decision making for impregnability of needle mat using design of experiment technique and respond surface methodology. Journal of applied research on industrial engineering3(1 (4)), 30-38.

[13] Kasana, H. S., & Kumar, K. D. (2013). Introductory operations research: theory and applications. Springer science & business media.

[14] Haley, K. B. (1963). The multi-index problem. Operations research11(3), 368-379.

[15] Badrloo, S., & Kashan, A. H. (2019). Combinatorial optimization of permutation-based quadratic assignment problem using optics inspired optimization. J. Appl. Res. Ind. Eng. 6(4), 314-332.

[16] El-Wahed, W. F. A. (2001). A multi-objective transportation problem under fuzziness. Fuzzy sets and systems117(1), 27-33.

[17] Zimmerman, H. J. (1983). Using fuzzy sets in operational research. European journal of operational research13(3), 201-216.

[18] Deb, K. (1999). An introduction to genetic algorithms. Sadhana24(4-5), 293-315.

[19] Gen, M., & Cheng, R. (2000). Genetic algorithms and engineering optimization. John wiley & sons. Inc.

[20] Michalewicz, Z. (1996). Binary or float? In Genetic algorithms+ data structures= evolution programs (pp. 97-106). Berlin, Heidelberg: Springer.

[21] El-Shorbagy, M. A., Ayoub, A. Y., Mousa, A. A., & El-Desoky, I. M. (2019). An enhanced genetic algorithm with new mutation for cluster analysis. Computational statistics34(3), 1355-1392.

[22] El-Shorbagy, M. A., Mousa, A. A., & Farag, M. A. (2019). An intelligent computing technique based on a dynamic-size subpopulations for unit commitment problem. OPSEARCH56(3), 911-944.

[23] Abdelsalam, A. M., & El-Shorbagy, M. A. (2018). Optimization of wind turbines siting in a wind farm using genetic algorithm based local search. Renewable energy123, 748-755.

[24] Osman, M. S., Abo-Sinna, M. A., & Mousa, A. A. (2006). IT-CEMOP: An iterative co-evolutionary algorithm for multi-objective optimization problem with nonlinear constraints. Applied mathematics and computation183(1), 373-389.

[25] El-Shorbagy, M. A., Mousa, A. A., & Farag, M. (2017). Solving nonlinear single-unit commitment problem by genetic algorithm based clustering technique. Review of computer engineering research4(1), 11-29.