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We review the field of multi-criteria optimization for radiation therapytreatment planning. Special attention is given to the technique known as Paretosurface navigation, which allows physicians and treatment planners tointeractively navigate through treatment planning options to get anunderstanding of the tradeoffs (dose to the target versus over-dosing ofimportant nearby organs) involved in each patient's plan. We also describe goalprogramming and prioritized optimization, two other methods designed to handlemultiple conflicting objectives. Issues related to nonconvexities, both interms of dosimetric goals and the fact that the mapping from controllablehardware parameters to patient doses is usually nonconvex, are discussed atlength since nonconvexities have a large impact on practical solutiontechniques for Pareto surface construction and navigation. A general planningstrategy is recommended which handles the issue of nonconvexity by firstfinding an ideal Pareto surface with radiation delivered from many presetangles. This can be cast as a convex optimization problem. Once a high qualitysolution is selected from the Pareto surface, a sparse version (which can meanfewer beams, fewer segments, less leaf travel for arc therapy techniques, etc.)is obtained using an appropriate sparsification heuristic. We end by discussingissues of efficiency regarding the planning and the delivery of radiationtherapy.

Multi-criteria optimization methods in radiation therapy planning: a review of technologies and directions