Determining Linearity of Optimal Plans by Operator Schema Analysis

Analysing the structures of solution plans generated by AI Planning engines is helpful in improving the generative planning process, as well as shedding light in the study of its theoretical foundations. We investigate a specific property of solution plans, that we called linearity, which refers to a situation where each action achieves an atom (or atoms) for a directly following action, or achieves goal atom(s). Similarly, linearity can be defined for parallel plans where each action in a set of actions executed at some time step, achieves either goal atom(s) or atom(s) for some action executed in the directly following time step. In this paper, we present a general and problem-independent theoretical framework focusing on the analysis of planning operator schema, namely relations of achiever, clobberer and independence, in order to determine whether solvable planning problems using a given operator schema have as solutions optimal (parallel) plans which are linear. The findings presented in this paper deepen current theoretical knowledge, provide helpful information to engineers of new planning domain models, and suggest new ways of improving the performance of state-of-theart (optimal) planning engines.