Ruggedness and Neutrality

Fitness landscapes have been proposed as a theoretical construct for investigating and explaining a range of phenomena from biology, physics and combinatorial optimization. A simple definition of a fitness landscape can be given as a triple (V, E, f), where V is a set of vertices, E is a set of undirected edges between the vertices of V, and f:V is an arbitrary function. The vertices of V are called configurations and two configurations are called neighbors, if there is an edge in E between the corresponding vertices of V. The function f is called the fitness function, and the values of the function on a particular vertex x V is called the fitness of the vertex. In combinatorial optimization, landscape properties may prove to be useful in explaining why some problems are difficult and why some heuristics or exact algorithms perform better than others for a given problem. The Traveling Salesman Problem (TSP) is a prototypical problem in combinatorial optimization and one that has been a subject of extensive research. It is known that small modifications to the basic TSP problem can cause significant differences in the performance of alternative solution techniques [1]. The hypothesis is that the differences can be explained by the properties of the corresponding landscapes, in this particular case, by correlation between the neighboring configurations.