Abstract
In this paper, a method based on Nelder and Mead’s simplex search method is developed for solving multi-objective optimization problems. Unlike other multi-objective optimization algorithms based on classical methods, this method does not require any a priori knowledge about the problem. Moreover, it does not need any pre-defined weights or additional constraints as it works without scalarizing the multi-objective problem. The algorithm works with a population of points and is capable of generating a multitude of Pareto optimal solutions. Equipped with the constraint handling strategy adopted in this work, the method is found to be competitive with respect to the existing algorithms.
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Notes
- 1.
To compare two points on the basis of dominance, a front value is assigned to each point depending on the front on which the point lies. All the points on a particular front have the same front value which is equal to the number of points which are dominated by that front.
- 2.
For discussion on R and \(\delta \) in the expression, see Mehta and Dasgupta [13].
- 3.
The authors gratefully acknowledge the availability of the source codes for NSGA-II algorithm on the Web site http://www.iitk.ac.in/kangal/codes.shtml, from where these were downloaded on September 8, 2011.
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Mehta, V.K., Dasgupta, B. (2020). A Multi-objective Optimization Method Based on Nelder–Mead Simplex Search Method. In: Voruganti, H., Kumar, K., Krishna, P., Jin, X. (eds) Advances in Applied Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-1201-8_72
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