A fuzzy particle swarm optimization method with application to shape design problem. (English) Zbl 1531.49041
Summary: 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.
MSC:
| 49Q10 | Optimization of shapes other than minimal surfaces |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 90C59 | Approximation methods and heuristics in mathematical programming |
| 94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |
Keywords:
finite element method; fuzzy logic; inverse problem; particle swarm optimization; shape optimizationReferences:
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