A data structure useful for finding Hamiltonian cycles

Computers & Operations Research

2006

-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.

Section: Implementation Issuesmentioning

confidence: 99%

Section: Implementation Issuesmentioning

confidence: 99%

See 1 more Smart Citation

Implementation analysis of efficient heuristic algorithms for the traveling salesman problem

Gamboa

Computers & Operations Research

2006

“…The 2-level tree (Chrobak et al, 1990) has for many years been considered the preeminent choice for representing the tour, retaining that reputation until the recent emergence of the k-level satellite tree proposed by Osterman and Rego (2003). The 2-level tree divides the tour into approximately 1 2 n segments each containing as many nodes as grouped under a parent node, where a doubly linked list is used to connect both segments and client nodes within the segments.…”

Section: Advances On Data Structures For Large Stspsmentioning

confidence: 99%

Ejection chain and filter-and-fan methods in combinatorial optimization

2009

Ann Oper Res

-The design of effective neighborhood structures is fundamental to the performance of local search and metaheuristic algorithms for combinatorial optimization. Significant efforts have been made in the creation of larger and more powerful neighborhoods that are able to explore the solution space more extensively and effectively while keeping computation complexity within acceptable levels. The most important advances in this domain derive from dynamic and adaptive neighborhood constructions originating in ejection chain methods and a special form of a candidate list design that constitutes the core of the filter-and-fan method. The objective of this paper is to lay out the general framework of the ejection chain and filter-and-fan methods and present applications to a number of important combinatorial optimization problems. The features of the methods that make them effective in these applications is expected to provide insights into solving challenging problems in other settings.

“…The two-level tree data structure (two-level tree) initially proposed by Chrobak et al [1] appears as a solution for an efficient implementation of the 2-optimal and 3-optimal procedures as well as their generalization as the Lin-Kernighan procedure [8]. See Fredman et al [2] for a comparative study on the performance of alternative data structures.…”

Section: The Two-level Tree Representationmentioning

confidence: 99%

Data structures and ejection chains for solving large-scale traveling salesman problems

Gamboa

European Journal of Operational Research

2005

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.