A HYBRID APPROACH TO SOLVING COMPLEX OPTIMIZATION PROBLEMS USING EVOLUTIONARY ALGORITHMS AND MATHEMATICAL MODELING
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.
References
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 DOI: https://doi.org/10.9790/5728-10342333
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 DOI: https://doi.org/10.1088/1742-6596/1529/4/042073
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 DOI: https://doi.org/10.9790/5728-10341622
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 DOI: https://doi.org/10.4314/swj.v18i3.27
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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: https://doi.org/10.9734/arjom/2024/v20i3791
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 DOI: https://doi.org/10.5897/AJMCSR2019.0798
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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: https://doi.org/10.1140/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 DOI: https://doi.org/10.47836/pjst.29.2.16
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. DOI: https://doi.org/10.47836/pjst.30.4.29
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 DOI: 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).
Copyright (c) 2024 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
