The induced generalized OWA operator

We present the induced generalized ordered weighted averaging (IGOWA) operator. It is a new aggregation operator that generalizes the OWA operator by using the main characteristics of two well known aggregation operators: the generalized OWA and the induced OWA operator. Then, this operator uses generalized means and order inducing variables in the reordering process. With this formulation, we get a wide range of aggregation operators that include all the particular cases of the IOWA and the GOWA operator, and a lot of other cases such as the induced ordered weighted geometric (IOWG) operator and the induced ordered weighted quadratic averaging (IOWQA) operator. We further generalize the IGOWA operator by using quasi-arithmetic means. The result is the Quasi-IOWA operator. Finally, we also develop a numerical example of the new approach in a financial decision making problem

Automating Intensity Modulated Radiation Therapy Treatment Planning by using Hierarchical Optimization

The intensity modulated radiation therapy (IMRT) optimizes the beam’s intensity to deliver the prescribed dose to the target while minimizing the radiation exposure to normal structures. The IMRT optimization is a complex optimization problem because of the multiple conflicting objectives in it. Due to the complexity of the optimization, the IMRT treatment planning is still a trial and error process. Hierarchical optimization was proposed to automate the treatment planning process, but its potential has not been demonstrated in a clinical setting. Moreover, hierarchical optimization is slower than the traditional optimization. The dissertation studied a sampling algorithm to reduce the hierarchical optimization time, customized an open source optimization solver to solve the nonlinear optimization formulation and demonstrated the potential of hierarchical optimization to automate the treatment planning process in a clinical setting. We generated the treatment plans of 31 prostate patients by hierarchical optimization using the same criteria as used by planners to prepare the treatment plans at Memorial Sloan Kettering Cancer Center. We found that hierarchical optimization produced the same or better treatment plans than that produced by a planner using the Eclipse treatment planning system. Therefore, the dissertation demonstrated that hierarchical optimization could automate the treatment planning process and shift the paradigm of the treatment planning from manual trial and error to an ideal automated process