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Multicriteria optimization problems occur in many real life applications, forexample in cancer radiotherapy treatment and in particular in intensitymodulated radiation therapy (IMRT). In this work we focus on optimizationproblems with multiple objectives that are ranked according to theirimportance. We solve these problems numerically by combining lexicographicoptimization with our recently proposed level set scheme, which yields asequence of auxiliary convex feasibility problems; solved here via projectionmethods. The projection enables us to combine the newly introducedsuperiorization methodology with multicriteria optimization methods to speed upcomputation while guaranteeing convergence of the optimization. We demonstrateour scheme with a simple 2D academic example (used in the literature) and alsopresent results from calculations on four real head neck cases in IMRT(Radiation Oncology of the Ludwig-Maximilians University, Munich, Germany) fortwo different choices of superiorization parameter sets suited to yield fastconvergence for each case individually or robust behavior for all four cases.

Speedup of lexicographic optimization by superiorization and its applications to cancer radiotherapy treatment