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Hybrid Scheduling Problems (HSPs) combine temporal and finite-domain variables via hybrid constraints that dictate that specific bounds on temporal constraints rely on assignments to finite-domain variables. Hybrid constraint tightening (HCT) reformulates hybrid constraints to apply the tightest consistent temporal bound possible, assisting in search space pruning. The contribution of this paper is to empirically evaluate the HCT approach using a state-of-the-art Satisfiability Modulo Theory solver on realistic, interesting problems related to developing scheduling agents to assist people with cognitive impairments. We demonstrate that HCT leads to orders of magnitude reduction of search complexity. The success of HCT is enhanced as we apply HCT to hybrid constraints involving increasing numbers of finite-domain variables and finite-domains with increasing size, as well as hybrid constraints expressing increasing temporal precision. We show that while HCT reduces search complexity for all but the simplest problems, the relative effectiveness is dampened on problems with partially conditional temporal constraints and hybrid constraints with increasing temporal disjunctions. Finally, we present our preliminary investigations that indicate that HCT can assist in increasing communication efficacy in a multiagent setting.

Evaluating hybrid constraint tightening for scheduling agents