Must-Expand Nodes in Multi-Objective Search [Extended Abstract]

Shawn Skyler, Shahaf S. Shperberg, Dor Atzmon, Ariel Felner, Oren Salzman, Shao-Hung Chan, Han Zhang, Sven Koenig, William Yeoh, Carlos Hernández Ulloa

Abstract: This extended abstract presents a theoretical analysis of node expansions in Multi-Objective Search. We define three categories of nodes, Must-Expand Nodes, Maybe-Expand Nodes, and Never-Expand Nodes. Our analysis establishes that regardless of the Ordering Function or Multi-Objective Search algorithm used, any Multi-Objective Search algorithm must expand all Must-Expand Nodes, some or none of Maybe-Expand Nodes, and none of Never-Expand Nodes. In addition, we conduct experimental evaluations of various Ordering Functions, revealing that they all expand the same number of nodes and compare their efficiency at finding solutions at various stages of the search.