The selective travelling salesman problem
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
An efficient four-phase heuristic for the generalized orienteering problem
Computers and Operations Research
A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
On the nucleolus of the basic vehicle routing game
Mathematical Programming: Series A and B
Computers and Operations Research
Mathematics of Operations Research
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
Discrete Mathematics
Solving the Orienteering Problem Through Branch-And-Cut
INFORMS Journal on Computing
Time-Indexed Formulations for Machine Scheduling Problems: Column Generation
INFORMS Journal on Computing
Traveling Salesman Problems with Profits
Transportation Science
A note on relatives to the Held and Karp 1-tree problem
Operations Research Letters
An exact algorithm for IP column generation
Operations Research Letters
Chebyshev center based column generation
Discrete Applied Mathematics
A note on relatives to the Held and Karp 1-tree problem
Operations Research Letters
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Given an undirected graph with edge costs and both revenues and weights on the vertices, the traveling salesman subtour problem is to find a subtour that includes a depot vertex, satisfies a knapsack constraint on the vertex weights, and that minimizes edge costs minus vertex revenues along the subtour.We propose a decomposition scheme for this problem. It is inspired by the classic side-constrained 1-tree formulation of the traveling salesman problem, and uses stabilized column generation for the solution of the linear programming relaxation. Further, this decomposition procedure is combined with the addition of variable upper bound (VUB) constraints, which improves the linear programming bound. Furthermore, we present a heuristic procedure for finding feasible subtours from solutions to the column generation problems. An extensive experimental analysis of the behavior of the computational scheme is presented.