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Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem
Theoretical Computer Science
Approximate local search in combinatorial optimization
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP: extended abstract
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Theoretical properties of two ACO approaches for the traveling salesman problem
ANTS'10 Proceedings of the 7th international conference on Swarm intelligence
A survey of approximation results for local search algorithms
Efficient Approximation and Online Algorithms
Average-case approximation ratio of the 2-opt algorithm for the TSP
Operations Research Letters
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
Multi-robot repeated area coverage
Autonomous Robots
Annals of Mathematics and Artificial Intelligence
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Local search with k-change neighborhoods is perhaps the oldest and most widely used heuristic method for the traveling salesman problem, yet almost no theoretical performance guarantees for it were previously known. This paper develops several results, some worst-case and some probabilistic, on the performance of 2- and k-opt local search for the traveling salesman problem, with respect to both the quality of the solution and the speed with which it is obtained.