Predicting Heuristic Search Performance with PageRank Centrality in Local Optima Networks

Previous studies have used statistical analysis of fitness landscapes such as ruggedness and deceptiveness in order to predict the expected quality of heuristic search methods. Novel approaches for predicting the performance of heuristic search are based on the analysis of local optima networks (LONs). A LON is a compressed stochastic model of a fitness landscape's basin transitions. Recent literature has suggested using various LON network measurements as predictors for local search performance.

In this study, we suggest PageRank centrality as a new measure for predicting the performance of heuristic search methods using local search. PageRank centrality is a variant of Eigenvector centrality and reflects the probability that a node in a network is visited by a random walk. Since the centrality of high-quality solutions in LONs determines the search difficulty of the underlying fitness landscape and since the big valley property suggests that local optima are not randomly distributed in the search space but rather clustered and close to one another, PageRank centrality can serve as a good predictor for local search performance. In our experiments for NK-models and the traveling salesman problem, we found that the PageRank centrality is a very good predictor for the performance of first-improvement local search as well as simulated annealing, since it explains more than 90% of the variance of search performance. Furthermore, we found that PageRank centrality is a better predictor of search performance than traditional approaches such as ruggedness, deceptiveness, and the length of the shortest path to the optimum.