863 research outputs found
Cost distributions in a symmetric Euclidean traveling salesman problems : asupplement to TSPLIB
We present analytically and experimentally determined cost distributions for all euclidean two-dimensional symmetric instances of the Traveling Salesman Problem in the TSPLIB library. Results obtained show characteristic cost distributions in all cases with and a high stability against degeneration
Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem
We propose a new genetic algorithm with optimal recombination for the
asymmetric instances of travelling salesman problem. The algorithm incorporates
several new features that contribute to its effectiveness: (i) Optimal
recombination problem is solved within crossover operator. (ii) A new mutation
operator performs a random jump within 3-opt or 4-opt neighborhood. (iii)
Greedy constructive heuristic of W.Zhang and 3-opt local search heuristic are
used to generate the initial population. A computational experiment on TSPLIB
instances shows that the proposed algorithm yields competitive results to other
well-known memetic algorithms for asymmetric travelling salesman problem.Comment: Proc. of The 11th International Conference on Large-Scale Scientific
Computations (LSSC-17), June 5 - 9, 2017, Sozopol, Bulgari
Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems
We consider geometric instances of the Maximum Weighted Matching Problem
(MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000
vertices. Making use of a geometric duality relationship between MWMP, MTSP,
and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields
in near-linear time solutions as well as upper bounds. Using various
computational tools, we get solutions within considerably less than 1% of the
optimum.
An interesting feature of our approach is that, even though an FWP is hard to
compute in theory and Edmonds' algorithm for maximum weighted matching yields a
polynomial solution for the MWMP, the practical behavior is just the opposite,
and we can solve the FWP with high accuracy in order to find a good heuristic
solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental
Algorithms, 200
k-RNN: Extending NN-heuristics for the TSP
In this paper we present an extension of existing Nearest-Neighbor heuristics
to an algorithm called k-Repetitive-Nearest-Neighbor. The idea is to start with
a tour of k nodes and then perform a Nearest-Neighbor search from there on.
After doing this for all permutations of k nodes the result gets selected as
the shortest tour found. Experimental results show that for 2-RNN the solutions
quality remains relatively stable between about 10% to 40% above the optimum
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