Local Optima Markov Chains: A New Tool for Landscape-aware Analysis of Algorithm Dynamics

Landscape analysis is a very useful tool in optimization to understand the structure of the search space of a problem when there is some kind of distance or neighborhood de.ned over the solutions. Local Optima Networks (LON) have been proposed to serve as a summary of the landscape of a problem. LONs are graphs where the nodes are the local optima of the search space according to a particular neighborhood and edges join local optima when one can be reached from the other using some kind of perturbation followed by hill climbing. In this paper we enhance local optima networks to include precise information on the transition probabilities among local optima, yielding a Markov Chain for the visited local optima during the search. The new analysis tool, called Local Optima Markov Chain (LOMA), is built on top of the static landscape information depending on the problem and includes information about algorithm dynamics. We show how LOMAs can be used to compute metrics that are out of the reach of other landscape-aware tools, thus o.ering more information to understand algorithm dynamics.