An efficient cost scaling algorithm for the assignment problem
Mathematical Programming: Series A and B
Algorithms and codes for dense assignment problems: the state of the art
Discrete Applied Mathematics
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Tabu Search
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
Cut-and-solve: An iterative search strategy for combinatorial optimization problems
Artificial Intelligence
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Tolerance based contract-or-patch heuristic for the asymmetric TSP
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
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We introduce a new combinatorial optimization problem, which is a generalization of the Traveling Salesman Problem (TSP) and which we call Traveling Salesman Problem of Second Order (2-TSP). It is motivated by an application in bioinformatics, especially the Permuted Variable Length Markov model. We propose seven elementary heuristics and two exact algorithms for the 2-TSP, some of which are generalizations of similar algorithms for the Asymmetric Traveling Salesman Problem (ATSP), some of which are new ideas. Finally we experimentally compare the algorithms for random instances and real instances from bioinformatics. Our experiments show that for the real instances most heuristics lead to optimum or almost-optimum solutions, and for the random instances the exact algorithms need less time than for the real instances.