Solving traveling salesman's problem using functional language

Two different approaches for solving the traveling salesman problem (TSP) using the conventional combinatorial search method and the proposed heuristic search algorithm are presented. In the algorithms presented, the cities are traversed in a breadth first search (BFS) manner, but the heuristic approach has some mathematical intelligence embedded in it to reduce the search polynomially. Both the algorithms, for heuristic as well as combinatorial search (BFS), are implemented using LISP. The recursive nature of the LISP functions has been exploited to manipulate the wildly exploding search trees. The results of the LISP run are presented along with the performance criteria, such as percentage of node visitation in the search tree. These results show that the heuristic method yields an optimal solution in polynomial time proportional to the width of the search space.<>