Improving the Efficiency of Helsgaun's Lin-Kernighan Heuristic for the Symmetric TSP

Helsgaun has introduced and implemented the lower tolerances (α-values) for an approximation of Held-Karp’s 1-tree with the purpose to improve the Lin-Kernighan’s Heuristic (LKH) for the Symmetric TSP (STSP). The LKH appears to exceed the performance of all STSP heuristic algorithms proposed to date. In this paper we improve the Helsgaun’s LKH based on an approximation of Zhang and Looks’ backbones by tolerances and an extension of double bridges further combined with implementation details by all of which we guide the search process instead of Helsgaun’s α-values. Our computational results are competitive and lead to improved solutions for some of the VLSI instances announced at the TSP homepage.