Neural network based penalty function strategy for integer and discrete engineering optimization

This paper presents and examines a neuron-like framework named the generalized Hopfield network (GHN), that is able to solve a parallel model of nonlinear optimization problems with mixed discrete, integer and real continuous variables. The augmented lagrange multiplier (ALM) method was applied to transform a constrained problem to an unconstrained formulation. A penalty function approach was then imposed on the ALM formulation to construct an energy function for formulating the neuron-like dynamical system. The numerical solution process for such a dynamic system is nothing but solving simultaneously first-order ordinary differential equations. The experimental examples showed the presenting strategy is efficient and reliable. The suitable values or the adaptation technique for some parameters in computation was discussed in the paper. The presenting strategy extends the practical limits in numerical optimization method and engineering design.