A Bi-Level Optimization Framework for Solar Concentrator Installation and Prism Layout Design Using Genetic Algorithms
DOI:
https://doi.org/10.4108/eetsmre.12581Keywords:
Solar concentrator, Genetic Algorithms, bi-level optimizationAbstract
As clean energy systems expand, the efficient installation of solar concentrators is increasingly constrained by the interaction between site layout and internal optical design. This study proposes an integrated bi-level optimization model that jointly determines concentrator installation on a floor plan and the internal prism design of each unit. The framework explicitly considers Blocklight obstructions, standardized concentrator types, internal exits, Total Light Efficiency (TLE), and economic profit. The upper level optimizes concentrator selection, placement, and orientation, while the lower level refines internal prism layouts and exit positions. A nested Genetic Algorithm framework is developed to solve the resulting bi-level optimization problem. Experimental results demonstrate that the framework can produce feasible and economically attractive solutions for solar concentrator deployment in constrained installation.
Downloads
References
[1] OMICS International. 2016. The role and impact of fossil fuels in our world. OMICS International. Available at: https://www.omicsonline.org. [Accessed Jan. 2026].
[2] Energy Institute. 2024. World Energy Statistical Review 2024. Energy Institute. Available at: https://www.energyinst.org/statistical-review. [Accessed Jan. 2026].
[3] Statista. 2023. Fossil fuel share in energy consumption 1965–2023. Statista. Available at: https://www.statista.com/statistics/222300/fossil-fuel-consumption-share-worldwide/. [Accessed Jan. 2026].
[4] Wolf, S., Bullard, R., Buonocore, J. J., Donley, N., Farrelly, T., Fleming, J., González, D. J. X., Oreskes, N., Ripple, W., Saha, R., and Willis, M. D. 2025. Scientists’ warning on fossil fuels. Oxford Open Climate Change, 5(1), kgaf011.
[5] ClientEarth. 2024. Fossil fuels and climate change: The facts. ClientEarth. Available at: https://www.clientearth.org/latest/news/fossil-fuels-and-climate-change-the-facts/. [Accessed Jan. 2026].
[6] Nijsse, F. J. M. M., Mercure, J. F., Sharpe, S., and Ives, M. C. 2023. The momentum of the solar energy transition. Nature Communications, 14(1), 1–15.
[7] Maka, A. O. M. and Alabid, J. M. 2022. Solar energy technology and its roles in sustainable development. Clean Energy, 6(3), 476–483.
[8] Li, X., Wang, Y., and Zhang, Z. 2025. Renewable energy capacity and technological innovations. Environmental Progress, 44(2), 100–112.
[9] Wang, K.-J., Makond, B., and Liu, S.-Y. 2011. Location and allocation decisions in a two-echelon supply chain with stochastic demand—A genetic-algorithm-based solution. Expert Systems with Applications, 38(5), 6125–6131.
[10] Wang, K.-J. and Dao, L. D. 2020. Multiple-objective optimization for solar concentrator layout. Journal of Solar Energy Engineering, 142(1), 011009.
[11] Wang, K.-J., Dung, N. D. T., and Whang, A. J.-W. 2014. Prism-based sunlight concentrator layout: A genetic algorithm solution. Journal of Solar Energy Engineering, 136(2), 021016.
[12] Wang, K. J. and Yang, J. W. 2014. Sunlight concentrator design using a revised genetic algorithm. Renewable Energy, 72, 322–335.
[13] Wikipedia contributors. 2026. Snell’s law. Wikipedia, The Free Encyclopedia. Available at: https://en.wikipedia.org/wiki/Snell%27s_law. [Accessed Jan. 2026].
[14] Kim, G. and Moon, I. 2021. Integrated planning for product selection, shelf-space allocation, and replenishment decision with elasticity and positioning effects. Journal of Retailing and Consumer Services, 58, 102274.
[15] Regateiro, F., Bento, J., and Dias, J. 2012. Floor plan design using block algebra and constraint satisfaction. Advanced Engineering Informatics, 26(2), 361–382.
[16] Oduguwa, V. and Roy, R. 2002. Bi-level optimisation using genetic algorithm. In Proceedings of the 2002 IEEE International Conference on Artificial Intelligence Systems (ICAIS), pp. 322–327.
[17] Gusain, C. et al. 2023. Study of meta-heuristic optimization methodologies for solving optimization problems. SoftwareX, 22, 101346.
[18] Benaissa, B. and Kobayashi, M. 2024. Metaheuristic optimization algorithms: An overview. Journal of Sciences - ACS, 14(1), 166–179.
[19] Santoso, T., Ahmed, S., and Shapiro, A. 2019. A Python package for multi-stage stochastic programming. Optimization-Online, Technical Report. Available at: http://www.optimization-online.org. [Accessed Jan. 2026].
[20] Santoso, T., Ahmed, S., Goetschalckx, M., and Shapiro, A. 2005. A stochastic programming approach for supply chain network design under uncertainty. European Journal of Operational Research, 167(1), 96–115.
[21] Numba Development Team. 2025. Numba: A high-performance Python compiler. Available at: https://numba.readthedocs.io/en/stable/. [Accessed Jan. 2026].
[22] De Rainville, F.-M., Fortin, F.-A., Parizeau, M., and Gagné, C. 2012. DEAP: A Python framework for evolutionary algorithms. In Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation (GECCO), New York, NY, USA, pp. 85–92.
[23] DEAP Development Team. 2025. DEAP: Distributed evolutionary algorithms in Python, version 1.4.3. Available at: https://deap.readthedocs.io/en/master/. [Accessed Jan. 2026].
[24] Fortin, F.-A., De Rainville, F.-M., Gardner, M.-A., Parizeau, M., and Gagné, C. 2012. DEAP: Evolutionary algorithms made easy. Journal of Machine Learning Research, 13, 2171–2175.
[25] Holland, J. H. 1975. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. Ann Arbor, MI: University of Michigan Press.
[26] Zomaya, A. Y. and Kazman, R. 2010. Simulated annealing techniques. In Tucker, A. B. (Ed.), Computer Science and Engineering Handbook, 2nd ed. Boca Raton, FL: CRC Press, pp. 33-1–33-16.
[27] Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. 1983. Optimization by simulated annealing. Science, 220(4598), 671–680.
[28] Kennedy, J. and Eberhart, R. 1995. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks (ICNN’95), vol. 4, Perth, WA, Australia, pp. 1942–1948.
[29] Leung, Y., Gao, Y., and Xu, Z. 1997. Degree of population diversity—A perspective on premature convergence in genetic algorithms and its Markov chain analysis. IEEE Transactions on Neural Networks, 8(5), 1165–1176.
[30] Hassanat, A. B., Prasath, V. B. S., Al-Msaid, H., and Abu-Qdari, S. A. 2013. Reducing premature convergence problem in genetic algorithm: Application on travel salesman problem. Computer and Information Science, 6(1), 47–55.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Le Duc Dao, Nguyen Thanh Loi
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
This is an open access article distributed under the terms of the CC BY-NC-SA 4.0, which permits copying, redistributing, remixing, transformation, and building upon the material in any medium so long as the original work is properly cited.
