Tolerance-based greedy algorithms for the traveling salesman problem

In this paper we introduce three greedy algorithms for the traveling salesman problem. These algorithms are unique in that they use arc tolerances, rather than arc weights, to decide whether or not to include an arc in a solution. We report extensive computational experiments on benchmark instances that clearly demonstrate that our tolerance-based algorithms outperform their weight-based counterpart. This paper as well as research on the Assignment Problem indicate high potential of tolerance-based algorithms for various optimization problems and motivates further investigation of the approach.