Given a graph G, we intend to partition its nodes into two sets of equal size so as to minimize the sum of the cost of arcs having end-points in different sets. This problem, called the uniform Graph Partitioning Problem (GPP), is known to be NP-Complete. In this paper we propose the first reported learning-automaton based solution to the problem. We compare this new solution to various reported schemes such as the Kernighan-Lin's algorithm, and two excellent recent heuristic methods proposed by Rolland et. al. — an extended local search algorithm and a genetic algorithm. The current automaton-based algorithm outperforms all the other schemes. We believe that it is the fastest algorithm reported to date. Additionally, our solution can also be adapted for the GPP in which the edge costs are not constant but random variables whose distribution are unknown.