8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization (CTW) 2009, Paris, France, June 2-4 2009 (original) (raw)
AI-generated Abstract
The paper discusses an approach to solving the Traveling Salesman Problem (TSP) by leveraging the concept of pseudo backbone edges within the context of Euclidean TSP. It details a methodology that involves contracting these edges to create a smaller TSP instance, which facilitates solving the original problem more efficiently. The proposed method demonstrates effectiveness through experimental results, showcasing improvements over existing known tours for several VLSI instances, emphasizing the importance of selecting good starting tours in the process.
Sign up for access to the world's latest research.
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Related papers
Good Tours for Huge Euclidean TSP Instances by Iterative Backbone Contraction : First Results
2009
This paper presents an iterative approach to find good tours for very large instances of the wellknown Euclidean Traveling Salesman Problem (TSP). The basic idea of the approach consists of iteratively transforming the TSP instance to another one with smaller size by contracting pseudo backbone edges. The iteration is stopped, if the new TSP instance is small enough for directly applying an exact algorithm or an efficient TSP heuristic. The pseudo backbone edges of each iteration are computed by a window based technique in which the TSP instance is tiled in non-disjoint sub-instances. For each of these sub-instances a good tour is computed, independently of the other sub-instances. An edge which is contained in the computed tour of every sub-instance (of the current iteration) containing this edge is denoted to be a pseudo backbone edge. Paths of pseudo-backbone edges are contracted to single edges which are fixed during the subsequent process.
A backbone based TSP heuristic for large instances
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. Keywords Traveling salesman problem · Lin-Kernighan Heuristic · Helsgaun Heuristic (LKH) · Pseudo-Backbones
Effective Heuristics for Large Euclidean TSP Instances Based on Pseudo Backbones
We present two approaches for the Euclidean TSP which compute high quality tours for large instances. Both approaches are based on pseudo backbones consisting of all common edges of good tours. The first approach starts with some precomputed good tours. Using this approach we found record tours for seven VLSI instances. The second approach is window based and constructs from scratch very good tours of huge TSP instances, e. g., the World TSP.
The Path-TSP: Two Solvable Cases
2020
In the Path-TSP, the travelling salesman is looking for the shortest (s, t)-TSP-path, i.e. a path through all cities of a given set of cities starting at a given city s and ending at another given city t, s 6= t, after visiting every city exactly once. In this paper we identify two new polynomially solvable cases of the Path-TSP where the distance matrix of the cities is a Demidenko matrix or a Van der Veen matrix, respectively. In each case we characterize the combinatorial structure of optimal (s, t)-TSP-paths and use the obtained results to generate dynamic programming algorithms for these problems. Given the number n of the cities our algorithms have a time complexity of O(|t − s|n5) in the case of a Demidenko distance matrix and O(n3) in the case of a Van der Veen distance matrix.
Computers & Operations Research, 1999
Scope and Purpose { One of the main characteristics of a neighbourhood structure imposed on the solution set of a combinatorial optimization problem is the diameter of the corresponding neighbourhood graph. The diameter re ects the 'closeness' of one solution to another. We study the diameter of the neighbourhood graph of some exponential size neighbourhood structure for the TSP and show that the diameter of the graph is surprisingly small: at most four. This demonstrates a high potential of some exponential size neighbourhoods. Abstract { A neighbourhood N (T) of a tour T (in the TSP with n cities) is polynomially searchable if the best among tours in N (T) can be found in time polynomial in n. Using Punnen's neighbourhoods introduced in 1996, we construct polynomially searchable neighbourhoods of exponential size satisfying the following property: for any pair of tours T 1 and T 5 , there exist tours T 2 ; T 3 and T 4 such that T i is in the neighbourhood of T i?1 for all i = 2; 3; 4; 5: In contrast, for pyramidal neighbourhoods considered by J. Carlier and P. , one needs up to (log n) intermediate tours to 'move' from a tour to another one.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.