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Time Governed Multi-Objective Optimization

Year 2021, Volume: 16 , 167 - 181, 31.12.2021
https://doi.org/10.55549/epstem.1068585

Abstract

Multi-objective optimization (MOO) is an optimization involving minimization or maximization of several objective functions more than the conventional one objective optimization, which is useful in many fields. Many of the current methodologies addresses challenges and solutions that attempt to solve simultaneously several Objectives with multiple constraints subjoined to each. Often MOO are generally subjected to linear inequality, equality and or bounded constraint that prevent all objectives from being optimized at once. This paper reviews some recent articles in area of MOO and presents deep analysis of Random and Uniform Entry-Exit time of objectives. It further breaks down process into sub-process and then provide some new concepts for solving problems in MOO, which comes due to periodical objectives that do not stay for the entire duration of process lifetime, unlike permanent objectives which are optimized once for the entire process duration. A methodology based on partial optimization that optimizes each objective iteratively and weight convergence method that optimizes sub-group of objectives are given. Furthermore, another method is introduced which involve objective classification, ranking, estimation and prediction where objectives are classified based on their properties, and ranked using a given criteria and in addition estimated for an optimal weight point (pareto optimal point) if it certifies a coveted optimal weight point. Then finally predicted to find how far it deviates from the estimated optimal weight point. A Sample Mathematical Tri-Objectives and Real-world Optimization was analyzed using partial method, ranking and classification method, the result showed that an objective can be added or removed without affecting previous or existing optimal solutions. Therefore, suitable for handling time governed MOO. Although this paper presents concepts work only, it’s practical application are beyond the scope of this paper, however base on analysis and examples presented, the concept is worthy of igniting further research and application.

References

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  • Blank, J., & Deb, K. (2020). Pymoo: Multi-objective optimization in python. IEEE Access, 8, 89497-89509.
  • Boukas, E. K., Haurie, A., & Michel, P. (1990). An optimal control problem with a random stopping time. Journal of Optimization Theory and Applications, 64(3), 471-480.
  • Farran, M., & Zayed, T. (2015). Fitness-oriented multi-objective optimisation for infrastructures rehabilitations. Structure and Infrastructure Engineering, 11(6), 761-775.
  • Fazlollahi, S., Becker, G., Ashouri, A., & Maréchal, F. (2015). Multi-objective, multi-period optimization of district energy systems: IV–A case study. Energy. 1(84), 365-381.
  • Khalil, I. S., Doyle, J. C., & Glover, K. (1996). Robust and optimal control. Prentice hall.
  • Kumar, D., Sharma, A., & Sharma, S. K. (2012). Developing model for fuel consumption optimization in aviation industry. Innovative Systems Design and Engineering, 3(10), 26-37.
  • Kwakernaak, H., & Sivan, R. (1972). Linear optimal control systems. Wiley-Interscience.
  • Lewis, F. L., Vrabie, D., & Syrmos, V. L. (2012). Optimal control. John Wiley & Sons.
  • Miettinen, K., Ruiz, F., & Wierzbicki, A. P. (2008). Introduction to multiobjective optimization: Interactive approaches. In Multiobjective optimization (pp. 27-57). Springer.
  • Okello, M. (2020). Multi-objective optimization concept based on periodical and permanent objective within a process. Preprints. (doi: 10.20944/preprints202005.0331.v1).
  • Sayin, S. (2003). Nonlinear multiobjective optimization kluwer academic publishers. European Journal of Operational Research. 148(1), 229-230.
  • Shokoohi, M., Tabesh, M., Nazif, S., & Dini, M. (2017). Water quality based multi-objective optimal design of water distribution systems. Water Resources Management, 31(1), 93-108.
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  • Vinter, R. B., & Vinter, R. B. (2010). Optimal control. Birkhäuser.
  • Wang, R., Lai, S., Wu, G., Xing, L., Wang, L., & Ishibuchi, H. (2018). Multi-clustering via evolutionary multi-objective optimization. Information Sciences, 450, 128-140.
  • Wang, Y., Lin, X., Pedram, M., Park, S., & Chang, N. (2013, March). Optimal control of a grid-connected hybrid electrical energy storage system for homes. In 2013 Design, Automation & Test in Europe Conference & Exhibition (DATE) (pp. 881-886). IEEE.
  • Wrzaczek, S., Kuhn, M., & Frankovic, I. (2020). Using age structure for a multi-stage optimal control model with random switching time. Journal of Optimization Theory and Applications, 184(3), 1065-1082.
  • Xiao, C., Xiongqing, Y. & Yu, W. (2018). Multipoint optimization on fuel efficiency in conceptual design of wide-body aircraft. Chinese Journal of Aeronautics, 31(1), 99-106.
  • Yang, X. S. (2012). Flower pollination algorithm for global optimization. In International conference on unconventional computing and natural computation (pp. 240-249). Springer.
  • Zhang, X., Tian, Y., Cheng, R., & Jin, Y. (2016). A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization. IEEE Transactions on Evolutionary Computation, 22(1), 97-112.
Year 2021, Volume: 16 , 167 - 181, 31.12.2021
https://doi.org/10.55549/epstem.1068585

Abstract

References

  • Białaszewski, T., & Kowalczuk, Z. (2016). Solving highly-dimensional multi-objective optimization problems by means of genetic gender. In Advanced and Intelligent Computations in Diagnosis and Control. (pp. 317-329). Springer.
  • Blank, J., & Deb, K. (2020). Pymoo: Multi-objective optimization in python. IEEE Access, 8, 89497-89509.
  • Boukas, E. K., Haurie, A., & Michel, P. (1990). An optimal control problem with a random stopping time. Journal of Optimization Theory and Applications, 64(3), 471-480.
  • Farran, M., & Zayed, T. (2015). Fitness-oriented multi-objective optimisation for infrastructures rehabilitations. Structure and Infrastructure Engineering, 11(6), 761-775.
  • Fazlollahi, S., Becker, G., Ashouri, A., & Maréchal, F. (2015). Multi-objective, multi-period optimization of district energy systems: IV–A case study. Energy. 1(84), 365-381.
  • Khalil, I. S., Doyle, J. C., & Glover, K. (1996). Robust and optimal control. Prentice hall.
  • Kumar, D., Sharma, A., & Sharma, S. K. (2012). Developing model for fuel consumption optimization in aviation industry. Innovative Systems Design and Engineering, 3(10), 26-37.
  • Kwakernaak, H., & Sivan, R. (1972). Linear optimal control systems. Wiley-Interscience.
  • Lewis, F. L., Vrabie, D., & Syrmos, V. L. (2012). Optimal control. John Wiley & Sons.
  • Miettinen, K., Ruiz, F., & Wierzbicki, A. P. (2008). Introduction to multiobjective optimization: Interactive approaches. In Multiobjective optimization (pp. 27-57). Springer.
  • Okello, M. (2020). Multi-objective optimization concept based on periodical and permanent objective within a process. Preprints. (doi: 10.20944/preprints202005.0331.v1).
  • Sayin, S. (2003). Nonlinear multiobjective optimization kluwer academic publishers. European Journal of Operational Research. 148(1), 229-230.
  • Shokoohi, M., Tabesh, M., Nazif, S., & Dini, M. (2017). Water quality based multi-objective optimal design of water distribution systems. Water Resources Management, 31(1), 93-108.
  • Taboada, H. A., Baheranwala, F., Coit, D. W., & Wattanapongsakorn, N. (2007). Practical solutions for multi-objective optimization: An application to system reliability design problems. Reliability Engineering & System Safety, 92(3), 314-322.
  • Vinter, R. B., & Vinter, R. B. (2010). Optimal control. Birkhäuser.
  • Wang, R., Lai, S., Wu, G., Xing, L., Wang, L., & Ishibuchi, H. (2018). Multi-clustering via evolutionary multi-objective optimization. Information Sciences, 450, 128-140.
  • Wang, Y., Lin, X., Pedram, M., Park, S., & Chang, N. (2013, March). Optimal control of a grid-connected hybrid electrical energy storage system for homes. In 2013 Design, Automation & Test in Europe Conference & Exhibition (DATE) (pp. 881-886). IEEE.
  • Wrzaczek, S., Kuhn, M., & Frankovic, I. (2020). Using age structure for a multi-stage optimal control model with random switching time. Journal of Optimization Theory and Applications, 184(3), 1065-1082.
  • Xiao, C., Xiongqing, Y. & Yu, W. (2018). Multipoint optimization on fuel efficiency in conceptual design of wide-body aircraft. Chinese Journal of Aeronautics, 31(1), 99-106.
  • Yang, X. S. (2012). Flower pollination algorithm for global optimization. In International conference on unconventional computing and natural computation (pp. 240-249). Springer.
  • Zhang, X., Tian, Y., Cheng, R., & Jin, Y. (2016). A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization. IEEE Transactions on Evolutionary Computation, 22(1), 97-112.
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Moses Oyaro Okello

Publication Date December 31, 2021
Published in Issue Year 2021Volume: 16

Cite

APA Okello, M. O. (2021). Time Governed Multi-Objective Optimization. The Eurasia Proceedings of Science Technology Engineering and Mathematics, 16, 167-181. https://doi.org/10.55549/epstem.1068585