An approximation algorithm for a symmetric Generalized Multiple Depot, Multiple Travelling Salesman Problem

3-Approximation algorithm for a two depot, heterogeneous traveling salesman problem

“…There are 2-approximation algorithms for variants of the homogenous, multiple TSP and HPP in [13][14][15]. Also, Rathinam et al in [16] have developed 1.5-approximation algorithm for two variants of a 2 depot, HPP.…”

“…Therefore, given a destination vertex i ∈ T, x e ∀e ∈ E 1 and φ i , one can use the max-flow algorithm to decide whether the given solution is feasible for the constraints in Eq. (13) or find a cut that violates these constraints in polynomial time. By repeating this argument for each of the destination vertices, we can conclude that a polynomial time separation algorithm is available to handle the constraints defined in Eq.…”

Approximation algorithms for multiple terminal, Hamiltonian path problems

“…Essentially, if there are two directed edges e 1 = (i, j) and e 2 = ( j, i) in B, then we get two undirected edges also labeled e 1 and e 2 between i and j in B ud . Let I 2 be a collection of subsets of E such that E ⊇ B ∈ I 2 if and only if graph (V , B ud ) is free of cycles and free of paths connecting any pair of terminals in P. It is known that M 2 = (E , I 2 ) is a matroid [20,21].…”

Discrete Teaching-learning-based optimization Algorithm for Traveling Salesman Problems

“…Thus, exact algorithms [3][4] are not capable of solving problems with large dimensions. On the other hand, heuristics [5][6] are thought to be more preferable and efficient for a complex TSP problem and have become very popular with researchers.…”