On the Capacity of Hopfield Neural Networks as EDAs for Solving Combinatorial Optimisation Problems

Citation

Swingler K (2012) On the Capacity of Hopfield Neural Networks as EDAs for Solving Combinatorial Optimisation Problems. In: Rosa A, Correia A, Madani K, Filipe J & Kacprzyk J (eds.) IJCCI 2012 - Proceedings of the 4th International Joint Conference on Computational Intelligence. 4th International Conference on Evolutionary Computation Theory and Applications, ECTA 2012, and the 4th International Joint Conference on Computational Intelligence, IJCCI 2012, Barcelona, Spain, 05.10.2012-07.10.2012. SciTePress, pp. 152-157.

Abstract
Multi-modal optimisation problems are characterised by the presence of either local sub-optimal points or a number of equally optimal points. These local optima can be considered as point attractors for hill climbing search algorithms. It is desirable to be able to model them either to avoid mistaking a local optimum for a global one or to allow the discovery of multiple equally optimal solutions. Hopfield neural networks are capable of modelling a number of patterns as point attractors which are learned from known patterns. This paper shows how a Hopfield network can model a number of point attractors based on non-optimal samples from an objective function. The resulting network is shown to be able to model and generate a number of local optimal solutions up to a certain capacity. This capacity, and a method for extending it is studied.

Keywords
Optimisation; Hopfield Neural Networks; Estimation of Distribution Algorithms