Mathematical Programming Models for Optimizing Partial-Order Plan Flexibility

A partial-order plan (POP) compactly encodes a set of sequential plans that can be dynamically chosen by an agent at execution time. One natural measure of the quality of a POP is its flexibility, which is defined to be the total number of sequential plans it embodies (i.e., its linearizations). As this criteria is hard to optimize, existing work has instead optimized proxy functions that are correlated with the number of linearizations. In this paper, we develop and strengthen mixed-integer linear programming (MILP) models for three proxy functions: two from the POP literature and a third novel function based on the temporal flexibility criteria from the scheduling literature. We show theoretically and empirically that none of the three proxy measures dominate the others in terms of number of sequential plans. Compared to the state-of-the-art MaxSAT model for the problem, we empirically demonstrate that two of our MILP models result in equivalent or slightly better solution quality with savings of approximately one order of magnitude in computation time.