Volume 57, Number 5, September-October 2023
|Page(s)||2819 - 2832|
|Published online||31 October 2023|
A fuzzy particle swarm optimization method with application to shape design problem
LaR2a, Department of Mathematics, Faculty of Science, Abdelmalek Essaâdi University, B.P. 2121 M’Hannech II, 93030 Tetouan, Morocco
1 Faculty of Science and Technology, Cady Ayyad University, B.P. 549 Avenue Abdelkrim El Khattabi, 40000 Marrakesh, Morocco
* Corresponding author: email@example.com
Accepted: 26 September 2023
In this study, we focus on a specific class of bilateral free boundaries problems. We approach this problem by formulating it as a shape optimization problem using a defined cost functional. The existence of an optimal solution for the optimization problem is proved. To tackle this problem, we propose an iterative approach that combines the particle swarm optimization and fuzzy logic methods. Additionally, we employ the finite element method as a discretization technique for the state equation. To validate our approaches, we investigate various types of domains. Furthermore, we compare the performance of these approaches in two scenarios: one with exact measurements used for identification and another with noisy measurements.
Mathematics Subject Classification: 49Q10 / 65L60 / 90C59 / 94D05
Key words: Finite element method / fuzzy logic / inverse problem / particle swarm optimization / shape optimization
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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