K-d trees for semidynamic point sets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Data structures for traveling salesmen
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Experiments on traveling salesman heuristics
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Fitness landscapes and memetic algorithm design
New ideas in optimization
Parallel Genetic Algorithms Population Genetics and Combinatorial Optimization
Proceedings of the 3rd International Conference on Genetic Algorithms
Local Optimization and the Traveling Salesman Problem
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
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
Finding Cuts in the TSP (A preliminary report)
Finding Cuts in the TSP (A preliminary report)
Chained Lin-Kernighan for Large Traveling Salesman Problems
INFORMS Journal on Computing
A New Three-Level Tree Data Structure for Representing TSP Tours in the Lin-Kernighan Heuristic
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
New EAX crossover for large TSP instances
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Implementation of an Effective Hybrid GA for Large-Scale Traveling Salesman Problems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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Meta-heuristics usually lack any kind of performance guarantee and therefore one cannot be certain whether the resulting solutions are (near) optimum solutions or not without relying on additional algorithms for providing lower bounds (in case of minimization).In this paper, we present a highly effective hybrid evolutionary local search algorithm based on the iterated Lin-Kernighan heuristic combined with a lower bound heuristic utilizing 1-trees. Since both upper and lower bounds are improved over time, the gap between the two bounds is minimized by means of effective heuristics. In experiments, we show that the proposed approach is capable of finding short tours with a gap of 0.8% or less for TSP instances up to 10 million cities. Hence, to the best of our knowledge, we present the first evolutionary algorithm and meta-heuristic in general that delivers provably good solutions and is highly scalable with the problem size. We show that our approach outperforms all existing heuristics for very large TSP instances.