An Analysis of Several Heuristics for the Traveling Salesman Problem

@article{Rosenkrantz1977AnAO,
  title={An Analysis of Several Heuristics for the Traveling Salesman Problem},
  author={Daniel J. Rosenkrantz and Richard Edwin Stearns and Philip M. Lewis},
  journal={SIAM J. Comput.},
  year={1977},
  volume={6},
  pages={563-581}
}
Several polynomial time algorithms finding “good,” but not necessarily optimal, tours for the traveling salesman problem are considered. We measure the closeness of a tour by the ratio of the obtained tour length to the minimal tour length. For the nearest neighbor method, we show the ratio is bounded above by a logarithmic function of the number of nodes. We also provide a logarithmic lower bound on the worst case. A class of approximation methods we call insertion methods are studied, and… 
approximation results for the Traveling Salesman and related Problems
In this paper, we revisit the famous heuristic called nearest neighbor (NN) for the traveling salesman problem under maximization and minimization goal. We deal with variants where the edge costs
Approximation Algorithms for the Geometric Covering Salesman Problem
TLDR
This work presents simple heuristic procedures for constructing tours, for a variety of neighborhood types, whose length is guaranteed to be within a constant factor of the length of an optimal tour.
Reoptimization of minimum and maximum traveling salesman's tours
TLDR
In this paper, reoptimization versions of the traveling salesman problem (TSP) are addressed and it is shown that, dealing with metric MaxTSP, a simple heuristic is asymptotically optimum when a constant number of nodes are inserted.
Reoptimization of Minimum and Maximum Traveling Salesman's Tours
TLDR
In this paper, reoptimization versions of the traveling salesman problem (TSP) are addressed and it is shown that, dealing with metric MaxTSP, a simple heuristic is asymptotically optimum when a constant number of nodes are inserted.
Approximating Capacitated Routing and Delivery Problems
TLDR
It is shown that maximum latency TSP is implicit in the dynamic problems, and that the natural "farthest neighbor" heuristic produces a good approximation for several notions of latency.
Worst Case and Probabilistic Analysis of the 2-Opt Algorithm for the TSP
TLDR
A more advanced model of probabilistic instances in which the points can be placed independently according to general distributions on [0,1]d, for an arbitrary d≥2 is considered, and an upper bound on the expected length of any 2-Opt improvement path of $\tilde{O}(n+1/3-1/d}\cdot\phi^{8/3}) is shown.
Min-weight double-tree shortcutting for Metric TSP: Bounding the approximation ratio
TLDR
This paper addresses the related question of the worst-case approximation ratio for the minimum-weight double-tree shortcutting method, and gives lower bounds on the approximation ratio in some specific metric spaces: the ratio of 2 in the discrete shortest path metric, 1.622 in the planar Euclidean metric, and 1.666 in thePlanar Minkowski metric.
Density-Based Clustering Heuristics for the Traveling Salesman Problem
TLDR
The results show that heuristic methods utilizing DBSCAN can facilitate a significant reduction in computation time while improving the quality of solutions obtained when compared with classic construction heuristics.
Complexity and Algorithms for the Traveling Salesman Problem and the Assignment Problem of Second Order ∗
We introduce two new combinatorial optimization problems, which are generalizations of the Traveling Salesman Problem (TSP) and the Assignment Problem (AP) and which we call Traveling Salesman
Algorithms and Experimental Study for the Traveling Salesman Problem of Second Order
TLDR
This work introduces a new combinatorial optimization problem, which is a generalization of the Traveling Salesman Problem (TSP) and which it is motivated by an application in bioinformatics, especially the Permuted Variable Length Markov model.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 20 REFERENCES
Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem
Abstract : An O(n sup 3) heuristic algorithm is described for solving n-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as
On the Relation Between the Traveling-Salesman and the Longest-Path Problems
The main result of this paper is that the traveling-salesman problem is a special case of the longest-path problem. Two formulations of the traveling-salesman problem are considered, the version in
An Effective Heuristic Algorithm for the Traveling-Salesman Problem
This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem. The procedure is based on a general
An Engineering Approach to the Traveling Salesman Problem
An engineering approach to the traveling salesman problem is a method which is intuitively “reasonable” to the non-mathematician. It consists of a sequence of operations which 1 develops good
A Method for Solving Traveling-Salesman Problems
The traveling-salesman problem is a generalized form of the simple problem to find the smallest closed loop that connects a number of points in a plane. Efforts in the past to find an efficient
A Heuristic Approach to Solving Travelling Salesman Problems
A code for solving travelling salesman problem employing heuristic ideas is described. Acyclic permutations of the cities are constructed by first choosing two cities at random for a permutation of
The Traveling Salesman Problem: A Survey
TLDR
A survey and synthesis of research on the traveling salesman problem is given and a general classification of the solution techniques and a detailed description of some of the proven methods are given.
Three Heuristic Rules for Sequencing Jobs to a Single Production Facility
TLDR
The study consists of examining the performance of the three heuristic rules in terms of the optimal downtime obtained by the branch and bound algorithm and the downtime which results from a random sequencing of jobs through the facility.
Algorithm 97: Shortest path
TLDR
The procedure was originally programmed in FORTRAN for the Control Data 160 desk-size computer and was limited to te t ra t ion because subroutine recursiveness in CONTROL Data 160 FORTRan has been held down to four levels in the interests of economy.
On the shortest spanning subtree of a graph and the traveling salesman problem
7. A. Kurosh, Ringtheoretische Probleme die mit dem Burnsideschen Problem uber periodische Gruppen in Zussammenhang stehen, Bull. Acad. Sei. URSS, Ser. Math. vol. 5 (1941) pp. 233-240. 8. J.
...
1
2
...