Described embodiments relate to determining an objective function to be used for mapping radiation beams to a patient body volume. The objective function has a first term related to at least one target volume and a second term related to at least one non-target volume. The second term is zero only when a product of the weight of a beamlet mapped to pass through a non-target volume portion and the dose deposited by said beamlet is equal to a first predetermined average dose constraint value for the respective non-target volume portion, for all beamlets mapped to pass through the at least one non-target volume. This limit aims to reduce the occurrence of negative beam weights. In another embodiment, the objective function has a smoothing term for biasing the weight of beamlets towards a uniform distribution within the respective beam. Radiotherapy is delivered based on the objective function.