Optimal toll design: a lower bound framework for the asymmetric traveling salesman problem

Optimal toll design: a lower bound framework for the asymmetric traveling salesman problem

We propose a framework of lower bounds for the asymmetric traveling salesman problem (TSP) based on approximating the dynamic programming formulation with different basis vector sets. We discuss how several well-known TSP lower bounds correspond to intuitive basis vector choices and give an economic interpretation wherein the salesman must pay tolls as he travels between cities. We then introdu...

Lower bounding procedure for the asymmetric quadratic traveling salesman problem

In this paper we consider the Asymmetric Quadratic Traveling Salesman Problem. Given a directed graph and a function that maps every pair of consecutive arcs to a cost, the problem consists in finding a cycle that visits every vertex exactly once and such that the sum of the costs is minimum. We propose an extended Linear Programming formulation that has a variable for each cycle in the graph. ...

Asymmetric Traveling Salesman Problem

The asymmetric traveling salesman problem (ATSP) is one of the most fundamental problems in combinatorial optimization. An instance of ATSP is a directed complete graph G = (V,E) with edge weights w : E → N that satisfy the triangle inequality, i. e., w(a, c) ≤ w(a, b) +w(b, c) for all distinct vertices a, b, c ∈ V . The goal is to find a Hamiltonian cycle of minimum weight. The weight of a Ham...

The Asymmetric Traveling Salesman Problem

The Asymmetric Quadratic Traveling Salesman Problem

The quadratic traveling salesman problem asks for a tour of min-imal costs where the costs are associated with each two arcs that are traversedin succession. This structure arises, e. g., if the succession of two arcs representsthe costs of loading processes in transport networks or a switch between dif-ferent technologies in communication networks. Based on a quadratic integer<...