Cost-Based Heuristics and Node Re-Expansions across the Phase Transition

Recent work aimed at developing a deeper understanding of suboptimal heuristic search has demonstrated that the use of a cost-based heuristic function in the presence of large operator cost ratio and the decision to allow re-opening of visited nodes can have a significant effect on search effort. In parallel research, phase transitions in problem solubility have proved useful in the study of problem difficulty for many computational problems and have recently been shown to exist in heuristic search problems. In this paper, we show that the impact on search effort associated with a larger operator cost ratio and the number of node re-expansions is concentrated almost entirely in the phase transition region. Combined with previous work connecting local minima in the search space with such behavior, these observations lead us to hypothesize a relationship between the phase transition and the existence of local minima.