A HYBRID APPROACH TO SOLVING COMPLEX OPTIMIZATION PROBLEMS USING EVOLUTIONARY ALGORITHMS AND MATHEMATICAL MODELING

Authors

Keywords:

Hybrid approach, Optimization problems, Evolutionary algorithms, Mathematical modelling

Abstract

It can be difficult to optimize complex issues, and doing so frequently calls for the application of cutting-edge methods like mathematical modelling and evolutionary algorithms. Our proposal in this work is to address complex optimization issues using a hybrid strategy that integrates both approaches. The suggested method builds a surrogate model of the issue by mathematical modelling, which is subsequently optimized through the application of evolutionary algorithms. The hybrid methodology is tested against other optimization methods, such as particle swarm optimization and genetic algorithms, on a series of benchmark tasks. The experimental findings demonstrate that in terms of both computing time and solution quality, the suggested hybrid strategy performs better than various alternative methods. The suggested methodology exhibits great potential as a means of resolving intricate optimization issues across diverse fields, such as engineering, finance, and healthcare.

Dimensions

Aderibigbe, F.M. and Apanapudor, J.S.(2014a): Computing Techniques for the Conjugate Search Directions of the Extended Conjugate Gradient Method Algorithm for Optimal Control Problems, IOSR Journal of Mathematics, Vol. 10(3) version IV pp.23 - 33

Apanapudor, J.S. and Aderibigbe, F.M(2015): On the Justification of the ECGM algorithm for Optimal Control Problems, Quest Journal of Research in applied Mathematics, Vol.2, Issue 5, pp.7 - 13

Apanapudor, J.S., Aderibigbe, F.M.and Okwonu, F.Z.(2020): An Optimal Penalty Constant for Discrete Optimal Control Regulator Problems, Journal of Physics: Conference Series 1529 042073

Aderibigbe, F.M. and Apanapudor,J.S.(2014b): On the Extended Conjugate Gradient Methods (ECGM) algorithm for Discrete Optimal Control Problems and some of its features, IOSR Journal of Mathematics (IOSR-JM) Vol.10(3) (version IV) pp.16 - 22

Apanapudor, J.S. Umukoro, J.,Okwonu, F.Z. and Okposo, N.(2023): Optimal Solution Techniques for Control Problem of Evolution Equations, Science World Journal, Vol.18(3),Published by Faculty of Science , Kaduna State University, https://dx.doi.org/10.4314/swj.v1813.27

Apanapudor, J.S. Akporido, D.K.,and Okwonu, F.Z. (2023): On the Generalized minimum cost flow problem: An Application in Natural Gas Distribution Networks, FUW Trends in Science and Technology Journal ,Vol. 8(3) pp. 176 – 181

Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (2013). Linear programming and network flow. John Wiley & Sons.

Coello Coello, C. A., Pulido, G. T., & Lechuga, M. S. (2004). Handling multiple objectives with particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8(3), 256–279. https://doi.org/10.1109/TEVC.2004.826067

Dantzig, G. B., & Thapa, M. N. (2003). Linear programming: 1. Introduction. Springer Science & Business Media.

Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. John Wiley & Sons.

Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. https://doi.org/10.1109/4235.996017

Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. https://doi.org/10.1109/4235.996017

Dorigo, M., & Stützle, T. (2004). Ant Colony Optimization. MIT Press. https://doi.org/10.7551/mitpress/1290.001.0001

Fonseca, C. M., & Fleming, P. J. (1995). Multiobjective genetic algorithms and the Pareto set. International Journal of Systems Science, 26(6), 527–534.

Gendreau, M., & Potvin, J. Y. (2010). Handbook of metaheuristics. Springer Science & Business Media. https://doi.org/10.1007/978-1-4419-1665-5

Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Addison-Wesley.

Holland, J. H. (2005). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. The University of Michigan Press.

Hooke, R., & Jeeves, T. A. (2001). Direct search solution for numerical and statistical problems. [JACM]. Journal of the Association for Computing Machinery, 8(2), 212–229. https://doi.org/10.1145/321062.321069

Iweobodo,D.C., Njoseh, I.N. and Apanapudor, J.S.(2024):An Overview of Iweobodo-Mamadu-Njoseh Wavelet and its Steps in Solving Time Fractional Advection -Diffusion Problems, Asian Research Journal of Mathematics, Vol. 20(3), pp.59 - 67

Izevbizua O. and Apanapudor JS (2019) Total revenue function for non-regular fixed lifetime inventory system. African Journal of Mathematics and Computer Science Research 12 (2), 24-30 https://scholar.google.com/citations?view_op=view_citation&hl=en&user=m5qJ9AoAAAAJ&citation_for_view=m5qJ9AoAAAAJ:roLk4NBRz8UC

Izevbizua, O. and Apanapudor, J.S.(2019)Implementing fries model for the fixed lifetime Inventory system, OPSEARCH, https://doi.org/10.1007/s12597-019-00403-1

Kalyanmoy, D. (2006). Multi-objective optimization using evolutionary algorithms: An introduction. John Wiley & Sons.

Laumanns, M., Thiele, L., Deb, K., & Zitzler, E. (2002). Combining convergence and diversity in evolutionary multiobjective optimization. Evolutionary Computation, 10(3), 263–282. https://doi.org/10.1162/106365602760234108

Lawler, E. L. (2001). Combinatorial optimization: networks and matroids. Courier Corporation.

Michalewicz, Z. (2006). Genetic algorithms + data structures = evolution programs. Springer Science & Business Media. https://doi.org/10.1007/978-3-662-03315-9

Nemhauser, G. L., & Wolsey, L. A. (2008). Integer and combinatorial optimization. John Wiley & Sons. https://doi.org/10.1002/9781118627372

Nocedal, J., & Wright, S. J. (2006). Numerical optimization. Springer Science & Business Media.

Okposo, N.I., Addai, E., Apanapudor, J.S., and Gomez-Aguilar, J.F.(2023): A Study of Monkey-pox transmission model within the scope of fractal-fractional derivative with power-law kernel, The European Physical Journal Plus, https://doi.org/epjp/s13360-023-04334-1

Okwonu,F.Z.,Ahad, N.A.,Apanapudor,J.S.,and Arunaye, F.I.(2021):Robust Multivariate Correlation Techniques: A Confirmation Analysis using COVID-19 Data Set, Pertanika Journal of Science and Technology, Vol. 29(2), pp.999 – 1015

Okwonu, F.Z. Ahad, N.A., Okoloko,I. E., Apanapudor, J.S.,and Arunaye, F.I. (2022): Robust Hybrid Classification Methods and Applications, Pertanika Journal of Science and Technology,Vol. 10(4), pp. 2831 - 2850.

Okwonu, F. Z. Ahad, N.A., Apanapudor, J.S. and Arunaye, F.I.(2023): Chi-square and Adjusted Standardised Residual Analysis,ASM Sc.Journal Vol. 18, https://doi.org/10.32802/asmscj.2023.985

Ravindran, A., Phillips, D. T., & Solberg, J. J. (2013). Operations research: principles and practice. John Wiley & Sons.

Sivanandam, S., Sumathi, S., & Deepa, T. (2008). Introduction to Genetic Algorithms. Springer.

Shi, Y., & Eberhart, R. C. (2008). A modified particle swarm optimizer. In Proceedings of the IEEE International Conference on Evolution

Voss, S. (2010). Evolutionary algorithms: The key to solving complex optimization problems. Applied Soft Computing, 10(2), 1–10.

Wang, G. G. (2013). A hybrid evolutionary algorithm for complex engineering optimization problems. Engineering Optimization, 45(3), 291–309.

Zhang, Y., Liu, X., & Ma, L. (2021). Blockchain in supply chain management: A literature review and future research directions. Journal of Business Logistics, 42(1), 14–26

Zhou, Z., Li, X., & Jiang, J. (2021). The role of blockchain technology in the fight against COVID-19: A review. International Journal of Information Management, 44, 74–79.

Zitzler, E., Laumanns, M., & Thiele, L. (2011). SPEA2: Improving the strength Pareto evolutionary algorithm. TIK-Report, (103).

Published

30-06-2024

How to Cite

A HYBRID APPROACH TO SOLVING COMPLEX OPTIMIZATION PROBLEMS USING EVOLUTIONARY ALGORITHMS AND MATHEMATICAL MODELING. (2024). FUDMA JOURNAL OF SCIENCES, 8(3), 443-449. https://doi.org/10.33003/fjs-2024-0803-2576

Issue

Vol. 8 No. 3 (2024): FUDMA Journal of Sciences - Vol. 8 No. 3 (Special Issue)

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

A HYBRID APPROACH TO SOLVING COMPLEX OPTIMIZATION PROBLEMS USING EVOLUTIONARY ALGORITHMS AND MATHEMATICAL MODELING. (2024). FUDMA JOURNAL OF SCIENCES, 8(3), 443-449. https://doi.org/10.33003/fjs-2024-0803-2576

Most read articles by the same author(s)