Topology Optimization (TO) enables unrestricted exploration within a design domain and is typically based on a spatial discretization that is also used as the mesh for simulation. In this article, we propose to use for the simulation a mesh-based equivalent circuit method termed the Reluctance Network Analysis (RNA), with nonlinear magnetic properties of the material. The simulation tool is then used in a topology optimization process solved with generalized optimality criteria (GOC) method. During the optimization, the sensitivity matrix is needed, and we describe here how to derive the matrix in the case of a nonlinear RNA using Adjoint Variable Method (AVM). Finally, we implemented this topology optimization through a case study of an electromagnetic actuator.