On Random Symmetric Travelling Salesman Problems

The Landscape of the Traveling Salesman Problem

The landscapes of Traveling Salesman Problems are investigated by random walk techniques. The autocorrelation functions for diierent metrics on the space of tours are calculated. The landscape turns out to be AR(1) for symmetric TSPs. For asymmetric problems there can be a random contribution superimposed on an AR(1) behaviour.

Random-key cuckoo search for the travelling salesman problem

Combinatorial optimization problems are typically NP-hard, and thus very challenging to solve. In this paper, we present the random key cuckoo search (RKCS) algorithm for solving the famous Travelling Salesman Problem (TSP). We used a simplified random-key encoding scheme to pass from a continuous space (real numbers) to a combinatorial space. We also consider the displacement of a solution in ...

Improvements to the Or-opt heuristic for the symmetric travelling salesman problem

Several variants and generalizations of the Or-opt heuristic for the Symmetric Traveling Salesman Problem are developed and compared on random and planar instances. Some of the proposed algorithms are shown to significantly improve upon the standard 2-opt and Or-opt heuristics.

On Complexity of Optimal Recombination for the Travelling Salesman Problem

Computational complexity of optimal recombination for the Travelling Salesman Problem is considered both in symmetric and in general cases. Strong NP-hardness of these optimal recombination problems is proven and solving approaches are considered.

On random symmetri travelling salesman problems