An approximation algorithm for a symmetric Generalized Multiple Depot, Multiple Travelling Salesman Problem (original) (raw)

2007, Operations Research Letters

In this paper, we present an algorithm with an approximation factor of 2 for a Generalized, Multiple Depot, Multiple Travelling Salesman Problem (GMTSP) when the costs are symmetric and satisfy the triangle inequality. The algorithm requires finding a degree constrained minimum spanning tree which we compute using a Lagrangian relaxation. c ij = c ji and satisfy the triangle inequality, namely, c ij + c jk c ik for all i, j, k ∈ V . A tour of salesman V i is an ordered set, TOUR i , of at least r + 2, r 1 elements of the form {V i , V i 1 , . . . , V i r , V i }, where V i l , l = 1, . . . , r i corresponds to r i distinct destinations being visited in that sequence by the ith salesman.