Fitness Landscape and the Behavior of Heuristics

This paper focuses on using the tness landscape paradigm in order to gain a better understanding of the behavior of local search heuristics in order to solve NP-hard problems. We concentrate ourselves on the symmetric planar TSP and we compare experimental facts about landscapes associated with the well-known 2-change and city-swap operators. We measure the \\tness-distance correlation" (FDC), i.e. the correlation between the tness of sampled points and their distance to a global optimum. We show that the 2-change landscapes have greater FDC values than the city-swap. We relate this with the fact that 2-change hill-climbers walks terminate on solutions quite close to the global optimum, whereas city-swap walks are unable to reduce the distance to the optimum (distances are measured in terms of operator metric). This connrms former propositions about the importance of a good FDC, and examplify the existence of non artiicial problems exhibiting this property. The diierence in FDC seems to be an alternative explanation to the usual auto-correlation measures when it comes to explain the diierence in performance between these two operators. Furthermore, an operator showing a good FDC value points to the possible use of intensifying search techniques, relying on a reened use of the operator itself.