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.

Solving the Large-Scale TSP Problem in 1 h: Santa Claus Challenge 2020

“…Originally, we did not plan to submit our own method because we were the organizers of the event. However, since the number of submissions remained small, we decided to contribute ourselves by using our simple baseline solver from Sengupta et al (2019) with the clustering-based divide-and-conquer approach that we had implemented earlier to serve as a reference solution. We did not expect it to perform well in this competition.…”

“…It defines how the current solution is modified to generate new candidate solutions. The following operators were used: • Relocate ( Gendreau et al, 1992 ), • Link swap ( Sengupta et al, 2019 ), • 2-opt ( Croes, 1958 ), • k -opt ( Shen and Kernighan, 1973 ). …”

“…A Link swap relocates any link by connecting it to one or both end points of the current path. Link swap works only for the open-loop case but has been found to contribute most to the search; approximately 50% of the improvements were due to Link swap as shown by Sengupta et al (2019) . Relocate removes a node from its current position in the path and reallocates it elsewhere by creating a new detour via this node.…”

“…A more sophisticated approach is to create a pseudonode that has a constant distance to all other nodes ( Sengupta et al, 2019 ). Because of the equal distances, it does not matter which nodes it will be connected to.…”

Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour

“…Some authors have investigated which operations contribute most to the optimization success. The operations discussed in Sengupta et al (2019), for example, are contained in the above table as special variants.…”