Nonlinear Optimization Problems with Bipolar Fuzzy Relation Equations using Neural Networks

In this paper, we present a novel application of neural networks for solving nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set for these problems is generally non-convex, which makes conventional nonlinear optimization methods less suitable for solving them. To address this challenge, we propose the use of neural networks {and some rules for simplification of the problem}. To find an input vector \( x \in [۰,۱]^n \) that satisfies the constraints and minimizes (or maximizes) the objective function, \( n \) neural networks are trained simultaneously. Each neural network identifies the corresponding variable of the vector \( x \in [۰,۱]^n \). The loss function integrates both the constraints and the objective function. Our experiments demonstrate that the proposed method can solve these problems with high accuracy and reasonable computational time. The proposed method is compared to the existing methods.

کلیدواژه ها:

Neural Networks ، Nonlinear Optimization Problems ، Bipolar Fuzzy Relation Equations ، Novel Architecture ، Max-Min composition