Intelligence and Cooperative Search by Coupled Local Minimizers

We show how coupling of local optimization processes can lead to better solutions than multi-start local optimization consisting of independent runs. This is achieved by minimizing the average energy cost of the ensemble, subject to synchronization constraints between the state vectors of the individual local minimizers. From an augmented Lagrangian which incorporates the synchronization constraints both as soft and hard constraints, a network is derived wherein the local minimizers interact and exchange information through the synchronization constraints. From the viewpoint of neural networks, the array can be considered as a Lagrange programming network for continuous optimization and as a cellular neural network (CNN). The penalty weights associated with the soft state synchronization constraints follow from the solution to a linear program. This expresses that the energy cost of the ensemble should maximally decrease. In this way successful local minimizers can implicitly impose their state to the others through a mechanism of master-slave dynamics resulting into a cooperative search mechanism. Improved information spreading within the ensemble is obtained by applying the concept of small-world networks. We illustrate the new optimization method on two dierent problems: supervised learning of multilayer perceptrons and optimization of Lennard-Jones clusters. The initial distribution of the local minimizers plays an important role. For the training of multilayer perceptrons this is related to the choice of the prior on the interconnection weights in Bayesian learning methods. Depending on the choice of this initial distribution, coupled local minimizers (CLM) can avoid over tting and produce good generalization, i.e. reach a state of intelligen..