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Radiotherapy aims to deliver ablative dose to the tumour with minimal normal tissue exposure - this requires accurate alignment of treatment beam with patient anatomy. Organ motion during treatment violates such alignment, and may compromise treatment efficacy significantly. One motion management strategy is to adaptively reposition and reshape the beam aperture in response to real-time motion, subject to deliverability constraints. In this work, we introduce an optimization framework and investigate a systematic control method for Multi-leaf collimator (MLC) leaf sequencing by explicitly defining the optimality of a leaf configuration with the composite effect of overdose and underdose cost. Given an estimate of the instantaneous motion, the planning beam aperture is transformed to generate an ideal aperture, which is then mapped to the deliverable space defined by the physical constraints (finite MLC leaf width and the restrictive track-wise convex topology due to paired leaf structure). Such projection is obtained via minimizing the aforementioned dose composite dose discrepancy cost. The key contribution of this work is the holistic optimization framework seeking a deliverable MLC configuration that is closest to the ideal aperture, where closeness is defined rigorously as the cumulative cost in terms of underdose to tumor target and overdose to healthy tissue. The optimization framework proposed here is general enough to account for an arbitrary planning aperture, and (nonlinear) deformation motion. It is particularly flexible to incorporate inhomogeneous underdose/overdose cost to reflex difference in organ radiosensitivity. We illustrate automatic adaptation features based on overdose/underdose tradeoff, with examples where (1) the tumor target and the organ at risk exhibits differential motion, and (2) rotational motion results in undeliverable aperture, to demonstrate the automatic adaptation based on overdose/underdose tradeoff. The proposed framework can- be naturally extended to incorporate more complex physical constraints, and to adjust for accumulative dose discrepancy.