We consider a variation of the well-known traveling salesman problem in which there are multiple agents who all have to tour whole set nodes same graph, while obeying node- and edge-capacity constraints require that must not crash. simplest model input is an undirected graph with capacities equal one. A solution synchronized called agency. Our puts similar relation as so-called evacuation probl...

Definition The traveling salesman problem (TSP) is the following optimization problem. Given a complete graph G with edge costs, find a Hamiltonian cycle of minimum cost in G. Definition The metric traveling salesman problem (∆-TSP) is the TSP restricted to instances satisfying the triangle inequality Definition The traveling salesman problem (TSP) is the following optimization problem. Given a...

Let G = (V, E) be a graph and w: E -» R+ be a length function. Given S C V, a Steiner tour is a cycle passing at least once through each vertex of S . In this paper we investigate naturally submodular graphs: graphs for which the length function of the Steiner tours is submodular. We provide two characterizations of naturally submodular graphs, an 0(n) time algorithm for identifying such graphs...

Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP)expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...

We present a new lifting approach for strengthening arbitrary clique tree inequalities that are known to be facet defining for the symmetric traveling salesman problem in order to get stronger valid inequalities for the symmetric quadratic traveling salesman problem (SQTSP). Applying this new approach to the subtour elimination constraints (SEC) leads to two new classes of facet defining inequa...

The Generalized Traveling Salesman Problem is one of a well known complex combinatorial optimization problems. Equality-Generalized Traveling Salesman Problem is a particular case of it. Themain objective of the problem it is to find a minimum cost tour passing through exactly one node from each cluster of a large-scale undirected graph. Multi-agent approaches are successfully used nowadays for...