Upper bounds on ATSP neighborhood size
Discrete Applied Mathematics
Further Extension of the TSP Assign Neighborhood
Journal of Heuristics
Four point conditions and exponential neighborhoods for symmetric TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Job shop scheduling with setup times, deadlines and precedence constraints
Journal of Scheduling
An Iterated Local Search Approach for Finding Provably Good Solutions for Very Large TSP Instances
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Combinatorial dominance guarantees for problems with infeasible solutions
ACM Transactions on Algorithms (TALG)
Beam-ACO for the travelling salesman problem with time windows
Computers and Operations Research
Improving the efficiency of Helsgaun's Lin-Kernighan Heuristic for the symmetric TSP
CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Dominance guarantees for above-average solutions
Discrete Optimization
New State-Space Relaxations for Solving the Traveling Salesman Problem with Time Windows
INFORMS Journal on Computing
A backbone based TSP heuristic for large instances
Journal of Heuristics
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Consider the following restricted (symmetric or asymmetric) traveling-salesman problem (TSP): given an initial ordering of then cities and an integerk 0, find a minimum-cost feasible tour, where a feasible tour is one in which cityi precedes cityj wheneverj =i +k in the initial ordering. Balas (1996) has proposed a dynamic-programming algorithm that solves this problem in time linear inn, though exponential ink. Some important real-world problems are amenable to this model or some of its close relatives.The algorithm of Balas (1996) constructs a layered network with a layer of nodes for each position in the tour, such that source-sink paths in this network are in one-to-one correspondence with tours that satisfy the postulated precedence constraints. In this paper we discuss an implementation of the dynamic-programming algorithm for the general case when the integerk is replaced with city-specific integersk( j),j = 1, . . .,n.We discuss applications to, and computational experience with, TSPs with time windows, a model frequently used in vehicle routing as well as in scheduling with setup, release and delivery times. We also introduce a new model, the TSP with target times, applicable to Just-in-Time scheduling problems. Finally for TSPs that have no precedence restrictions, we use the algorithm as a heuristic that finds in linear time a local optimum over an exponential-size neighborhood. For this case, we implement an iterated version of our procedure, based on contracting some arcs of the tour produced by a first application of the algorithm, then reapplying the algorithm to the shrunken graph with the samek.