Generalized Hopfield network based structural optimization using sequential unconstrained minimization technique with additional penalty strategy

This paper presents and examines a neuron-like framework of the generalized Hopfield network (GHN) that is capable to solve nonlinear engineering optimization problems with mixed discrete, integer and real continuous variables. The sequential unconstrained minimization technique (SUMT) was applied to construct the GHN for dealing with the design constraints. An additional penalty function for dealing with the discrete and integer variables was then imposed on the formulation of SUMT to construct an energy function of GHN for formulating the neuron-like dynamical system. The numerical solution process for such a dynamic system is simply solving a set of simultaneous first-order ordinary differential equations (ODE) that is the main feature of this optimization method. The experimental examples showed the presenting strategy is reliable. The suitable values or the adaptation technique for some parameters in computation was discussed in the paper. The presenting strategy indeed provides an alternative way of handling the engineering optimization dynamically and expands the usage of ODE. An asymmetrical three-bar truss design, a reinforced concrete beam design and a 10-bar structural design are contributed to illustrate the presenting neuron-like network method.