In our previous research we suggested an approach to maximizing agents preferences over schedules of multiple tasks with temporal and precedence constraints. The proposed approach is based on Expected Utility Theory. In this paper we address two mutually dependent questions: (a) what are the properties of the problem domain that can facilitate efficient maximization algorithms, and (b) what criteria determine attractiveness of one or another potential solution to the agent. We discuss different ways of exploring the problem domain. We show that naive optimization approaches often fail to find solutions for risk-averse agents and propose ways of using properties of the domain to improve upon naive approaches.
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