A Cautionary Tale: False Efficiencies in the Traveling Salesman Problem*

The Traveling Salesman Problem provides an opportunity to explore whether attempts to optimize an algorithm in fact succeed or fail. Attempted optimizations themselves have time penalties in their execution and those time penalties may be greater than the improvements provided to the algorithm. When approaching the Traveling Salesman Problem not as a graph traversal problem but as a backtracking permutation problem, one may attempt a “bestfirst” optimization in the recursion. This significantly slows the program. One may also attempt forward-bounding functions. Two such functions are examined, of which one slows the program and the other neither slows nor speeds the program.