Solving large problems with a small working memory

Abstract

We describe an important elaboration of our multiscale/multiresolution model for solving the Traveling Salesman Problem (TSP). Our previous model emulated the non-uniform distribution of receptors on the human retina and the shifts of visual attention. This model produced nearoptimal solutions of TSP in linear time by performing hierarchical clustering followed by a sequence of coarse-to-fine approximations of the tour. Linear time complexity was related to the minimal amount of search performed by the model, which posed minimal requirements on the size of the working memory. The new model implements the small working memory requirement. The model only stores information about as few as 2-5 clusters at any one time in the solution process. This requirement matches the known capacity of human working memory. We conclude by speculating that this model provides a possible explanation of how the human mind can effectively deal with very large search spaces.