Landscape reshaping algorithm for additive neural networks with application to graph mapping problems

A neural network based algorithm for problems in nonconvex optimisation is described. The algorithm restricts the search by exploiting the properties of the parameter space. It keeps the initial point fixed and reshapes the energy function so that, in the neighbourhood of an arbitrary initial condition, basins of attraction are formed corresponding to valid solutions first and then these basins are made deeper to improve the quality. This algorithm was applied to both the travelling salesman problem (TSP) and the graph mapping problem (GMP) and good results were obtained.