The Routing Protocol for Low Power and Lossy Networks (RPL) uses objective functions to construct routes that optimize or constrain the routes it selects and uses. This specification describes the Minimum Rank with Hysteresis Objective Function (MRHOF), an objective function that selects routes that minimize a metric, while using hysteresis to reduce churn in response to small metric changes. MRHOF works with metrics that are additive along a route, and the metric it uses is determined by the metrics RPL Destination Information Object (DIO) messages advertise.