New approaches to solving constraint satisfaction problems using iterative improvement techniques have been found to be successful on certain, very large problems such as the million queens. However, on highly constrained problems it is possible for these methods to get caught in local minima. In this paper we present GENET, a connectionist architecture for solving binary and general constraint satisfaction problems by iterative improvement. GENET incorporates a learning strategy to escape from local minima. Although GENET has been designed to be implemented on VLSI hardware, we present empirical evidence to show that even when simulated on a single processor GENET can outperfomr existing iterative improvement techniques on hard instances of certain constraint satisfaction problems.