Neural network models in combinatorial optimization

Abstract

This chapter reviews the theory and application of artificial neural network (ANN) models with the intention of solving combinatorial optimization problems (COPs). Brief introductions to the theory of ANNs and to the classical models of ANNs applied to COPs are presented at the beginning of this chapter. Since the classical ANN models follow gradient-based search, they usually converge to a local optimal solution. To overcome this, several methods that extend the capability of ANNs to avoid the local minima have been reviewed in this chapter. Apart from that, not all the ANNs converge to a local minimum; thus, stability and/or convergence criteria of various ANNs have been addressed. The thin wafer that divides continuous and discrete optimization problems while applying ANNs to solve the COPs is highlighted. Applications of ANNs to solve the general optimization problems and to solve the discrete optimization problems have been surveyed. To conclude, issues regarding the performance behavior of the ANNs are discussed at the end of this chapter.