Which Local Search Operator Works Best for the Open-Loop TSP?

Abstract

The traveling salesman problem (TSP) has been widely studied for the classical closed-loop variant. However, very little attention has been paid to the open-loop variant. Most of the existing studies also focus merely on presenting the overall optimization results (gap) or focus on processing time, but do not reveal much about which operators are more efficient to achieve the result. In this paper, we present two new operators (link swap and 3–permute) and study their efficiency against existing operators, both analytically and experimentally. Results show that while 2-opt and relocate contribute equally in the closed-loop case, the situation changes dramatically in the open-loop case where the new operator, link swap, dominates the search; it contributes by 50% to all improvements, while 2-opt and relocate have a 25% share each. The results are also generalized to tabu search and simulated annealing.

Keywords

• traveling salesman problem
• open-loop TSP
• randomized algorithms
• local search
• NP–hard
• O–Mopsi game