The Travelling Salesman Problem (TSP) is a classical NPhard optimisation problem. There exist, however, special cases of the TSP that can be solved in polynomial time. Many of the well-known TSP special cases have been characterized by imposing special four-point conditions on the underlying distance matrix. Probably the most famous of these special cases is the TSP on a Monge matrix, which is ...

We discuss geometric special cases of optimization problems on graphs where the n vertices are represented as points in IR d and where the lengths of the edges are measured according to a norm with a polyhedral unit ball. We derive algorithms whose running time is polynomial in n (and depends exponentially on the number of faces of the unit ball). We consider the maximum travelling salesman pro...

The combination of local optimisation heuristics and genetic algorithms has been shown to be an effective approach for finding near-optimum solutions to the Travelling Salesman Problem (TSP). In problem domains where the problem can be represented geometrically, such as networks and chemical structures, the combination of local optimisation operators and phenotype genetic operators has also bee...

In this paper, we present a novel approach named "ACO-PSO-TSPGPU" to run PSO and ACO on Graphical Processing Units (GPUs) and applied to TSP (Parallel-PSO&ACO-A-TSP). Both algorithms are implemented on GPUs. Well-known benchmark problems for many heuristic and meta heuristic algorithms presented by Travelling Salesman Problem (TSP) are known as NP hard complex problems.TSP was investigated usin...

We report for the first time on finding shortest path solutions for the travelling salesman problem (TSP) using hybrid “in materio” computation: a technique that uses search algorithms to configure materials for computation. A single-walled carbon nanotube (SWCNT) / polymer composite material deposited on a micro-electrode array is configured using static voltages so that voltage output reading...

In optimization problem, Genetic Algorithm (GA) and Ant Colony Optimization Algorithm (ACO) have been known as good alternative techniques. GA is designed by adopting the natural evolution process, while ACO is inspired by the foraging behaviour of ant species. This paper presents a hybrid GA-ACO for Travelling Salesman Problem (TSP), called Genetic Ant Colony Optimization (GACO). In this metho...

Travelling Salesman Problem (TSP) belongs to the class of NP-Complete problems. It has been proved that evolutionary algorithms are effective and efficient, with respect to the traditional methods for solving NP-Complete problems like TSP, with avoidance trapping in local minima areas. Artificial Bee Colony (ABC) is a new swarm-based optimization algorithm, which inspired by the foraging behavi...

This chapter presents a rigorous Design of Experiments (DOE) approach for determining whether a problem characteristic affects the performance of a heuristic. Specifically, it reports a study on the effect of the cost matrix standard deviation of symmetric Travelling Salesman Problem (TSP) instances on the performance of Ant Colony Optimisation (ACO) heuristics. Results demonstrate that for a g...