A Simple and Efficient Method for Solving Multi-Objective Programming Problems and Multi-Objective Optimal Controls
محورهای موضوعی : فصلنامه ریاضی
1 - Department of Mathematics, Jahrom University, P. O. Box: 74135-111, Jahrom, Iran
کلید واژه: Pareto solution, Multi-objective optimal control problem, Programming problem, Nondominated solution,
چکیده مقاله :
In this paper, a new approach based on weighted sum algorithm is applied to solve multi-objective optimal programming problems (MOOPP) and multi-objective optimal control problems (MOOCP). In this approach, first, we change the problem into a new one whose optimal solution is obtained by solving some single-objective problems simply. Then, we prove that the optimal solutions of the two problems are equal. Numerical examples are presented to show the efficiency of the given approach.
In this paper, a new approach based on weighted sum algorithm is applied to solve multi-objective optimal programming problems (MOOPP) and multi-objective optimal control problems (MOOCP). In this approach, first, we change the problem into a new one whose optimal solution is obtained by solving some single-objective problems simply. Then, we prove that the optimal solutions of the two problems are equal. Numerical examples are presented to show the efficiency of the given approach.
[1] H. Alimorad, A new approach for determining multi-objective optimal control of semilinear parabolic
problems, Computational and Applied Mathematics, 38 (2019) 1–11.
[2] H. Bonnel and C. YalcnKaya, Optimization over the efficient set of multi-objective convex optimal
control problems, Journal of Optimization: Theory and Applications, 147 (2010) 93–112.
[3] M. M. El-Kady, M. S. Salim and A. M. El-Sagheer, Numerical treatment of multi-objective optimal
control problems, Automatica, 39 (2003) 47–55.
[4] A. Gambier and E. Bareddin, Multi-objective optimal control: An overview, IEEE Conference on
Control Applications, Singapore, (2007) 170–175.
[5] A. Gambier and M. Jipp, Multi-objective optimal control: An introduction, Proceedings of the 8th
Asian Control Conference (ASCC11), Kaohsiung, Taiwan, (2011) 15–18.
[6] Y. Hu, Effectiveness Theory of Multi-Objective Programming, Shanghai Science and Technology
Press, Shanghai, (1994).
[7] U. Ledzewicz, H. Maurer and H. Sch Attler, Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy, Mathematical Bioscieneces
and Engineering, 8 (2011) 307–323.
[8] G. P. Liu, J. B. Yang and J. F. Whidborne, Multi-Objective Optimization and Control, Research
Studies Press Ltd., Exeter, (2003).
[9] F. Logist, B. Houska, M. Diehl and J. Van Impe, Fast Pareto set generation for nonlinear optimal
control problems with multiple objectives, Structural and Multidisciplinary Optimization, 42 (2010)
591–603.
[10] k. Maity and M. Maiti, Numerical approach of multi-objective optimal control problem in imprecise
environment, Fuzzy Optimization and Decision Making, 4 (2005) 313–330.
[11] J. Matejas and T. Peric, A new iterative method for solving multi-objective linear programming problem, Applied Mathematics and Computation, 243 (2014) 746–754
