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-The state-of-the-art of local search heuristics for the traveling salesman problem (TSP) is chiefly based on algorithms using the classical Lin-Kernighan (L-K) procedure and the Stem-and-Cycle (S&C) ejection chain method. Critical aspects of implementing these algorithms efficiently and effectively rely on taking advantage of special data structures and on maintaining appropriate candidate lists to store and update potentially available moves. We report the outcomes of an extensive series of tests on problems ranging from 1,000 to 1,000,000 nodes, showing that by intelligently exploiting elements of data structures and candidate lists routinely included in state-of-the-art TSP solution software, the S&C algorithm clearly outperforms all implementations of the Lin-Kernighan procedure. Moreover, these outcomes are achieved without the use of special tuning and implementation tricks that are incorporated into the leading versions of the L-K procedure to enhance their computational efficiency.

Data structures play a crucial role in the efficient implementation of local search algorithms for problems that require circuit optimization in graphs. The traveling salesman problem (TSP) is the benchmark problem used in this study where two implementations of the stem-and-cycle (S&C) ejection chain algorithm are compared. The first implementation uses an Array data structure organized as a doubly linked list to represent TSP tours as well as the S&C reference structure. The second implementation considers a two-level tree structure. The motivation for this study comes from the fact that the S&C neighborhood structure usually requires subpaths to be reversed in order to preserve a feasible orientation for the resulting tour. The traditional Array structure proves to be inefficient for large-scale problems since to accomplish a path reversal it is necessary to update the predecessor and the successor of each node on the path to be reversed. Computational results performed on a set of benchmark problems up to 316,228 nodes clearly demonstrate the relative efficiency of the two-level tree data structure.