We give polynomial time algorithms to compute the third and fourth moments about the mean of tour costs over the solution space of the general symmetric Travelling Salesman Problem (TSP). These algorithms complement previous work on the population variance and provide a tractable method to compute the skewness and kurtosis of the probability distribution of tour costs. The methodology is genera...

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...

Ant Colony Optimization (ACO) has been proved to be one of the most effective algorithms to solve a wide range of combinatorial optimization (or NP-hard) problems as the Travelling Salesman Problem (TSP). The first step of an ACO algorithm is setting the parameters that drive the algorithm. The basic parameters that are used in ACS algorithms are; number of ants, the relative importance (or wei...

This paper investigates the effect of the cost matrix standard deviation of Travelling Salesman Problem (TSP) instances on the performance of a class of combinatorial optimisation heuristics. Ant Colony Optimisation (ACO) is the class of heuristic investigated. Results demonstrate that for a given instance size, an increase in the standard deviation of the cost matrix of instances results in an...

We proposed a new search heuristic using the scuba diving metaphor. This approach is based on the concept of evolvability and tends to exploit neutrality which exists in many real-world problems. Despite the fact that natural evolution does not directly select for evolvability, the basic idea behind the scuba search heuristic is to explicitly push evolvability to increase. A comparative study o...