Travelling and touring problems

Touring machines

In considering what to ask Lewis Wolpert’s good fairy godmother of science [1], I am reminded of John von Neumann, a pioneer of computer science. In 1946 he wrote to Norbert Wiener, the father of cybernetics, bemoaning the fact that Turing, Pitts and McCulloch had shown that anything the brain can do can be mimicked by a universal neural mechanism — a Turing machine [2]. Inverting the argument,...

Solving Capacity Problems as Asymmetric Travelling Salesman Problems

The railway capacity optimization problem deals with the maximization of the number of trains running on a given network per unit time. In this study, we frame this problem as a typical asymmetrical Travelling Salesman Problem (ATSP), with the ATSP nodes representing the train arrival /departure events and the ATSP total cost representing the total time-interval of the schedule. The application...

Heuristics for sparse general travelling salesman problems

The well-known travelling salesman problem can be expressed in graphtheoretic terms as follows : find a minimum-weight Hamiltonian cycle in a connected edge-weighted graph G(N, A). vVe concentrate here on the problem where G is large and sparse, i.e., where INI is 500 or more and IAI is O( INI). Such graphs arise frequently in practice, where G represents a road network, and each node (city) is...

On Random Symmetric Travelling Salesman Problems

Let the edges of the complete graph Kn be assigned independent uniform [0; 1] random edge weights. Let ZTSP and Z2FAC be the weights of the minimum length travelling salesman tour and minimum weight 2-factor respectively. We show that whp jZTSP Z2FAC j = o(1). The proof is via by the analysis of a polynomial time algorithm that nds a tour only a little longer than Z2FAC .

On random symmetri travelling salesman problems