Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study
INFORMS Journal on Computing
A Multilevel Approach to the Travelling Salesman Problem
Operations Research
Searching for backbones and fat: a limit-crossing approach with applications
Eighteenth national conference on Artificial intelligence
Chained Lin-Kernighan for Large Traveling Salesman Problems
INFORMS Journal on Computing
Tour Merging via Branch-Decomposition
INFORMS Journal on Computing
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
Backbones in optimization and approximation
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
The backbone of the travelling salesperson
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
A novel local search algorithm for the traveling salesman problem that exploits backbones
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Implementation analysis of efficient heuristic algorithms for the traveling salesman problem
Computers and Operations Research
Reducing the size of traveling salesman problem instances by fixing edges
EvoCOP'07 Proceedings of the 7th European conference on Evolutionary computation in combinatorial optimization
Improving the efficiency of Helsgaun's Lin-Kernighan Heuristic for the symmetric TSP
CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
Finding good tours for huge Euclidean TSP instances by iterative backbone contraction
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Lower tolerance-based Branch and Bound algorithms for the ATSP
Computers and Operations Research
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part IV
Certification of an optimal TSP tour through 85,900 cities
Operations Research Letters
Large-step markov chains for the TSP incorporating local search heuristics
Operations Research Letters
Hi-index | 0.00 |
We introduce a reduction technique for large instances of the traveling salesman problem (TSP). This approach is based on the observation that tours with good quality are likely to share many edges. We exploit this observation by neglecting the less important tour space defined by the shared edges, and searching the important tour subspace in more depth. More precisely, by using a basic TSP heuristic, we obtain a set of starting tours. We call the set of edges which are contained in each of these starting tours as pseudo-backbone edges. Then we compute the maximal paths consisting only of pseudo-backbone edges, and transform the TSP instance to another one with smaller size by contracting each such path to a single edge. This reduced TSP instance can be investigated more intensively, and each tour of the reduced instance can be expanded to a tour of the original instance. Combining our reduction technique with the currently leading TSP heuristic of Helsgaun, we experimentally investigate 32 difficult VLSI instances from the well-known TSP homepage. In our experimental results we set world records for seven VLSI instances, i.e., find better tours than the best tours known so far (two of these world records have since been improved upon by Keld Helsgaun and Yuichi Nagata, respectively). For the remaining instances we find tours that are equally good or only slightly worse than the world record tours.