As we have already pointed out in the introduction to this book, many problems arising in applications are from its structure multiobjective. Nevertheless these problems are often treated as a single objective optimization problem in practice. This was for instance done in intensity modulated radiotherapy (IMRT). Here, an optimal treatment plan for the irradiation of a cancer tumor has to be found for a patient. The aim is to destroy or at least reduce the tumor while protecting the surrounding healthy tissue from unnecessary damage. For a detailed problem description we refer to [3, 36, 63, 143, 146, 170, 223].
Regarding the natural structure this problem is multiobjective, i. e. there are two or more competing objectives which have to be minimized at the same time. On the one hand there exists the target that the tumor has to be irradiated sufficiently high such that it is destroyed. On the other hand the surrounding organs and tissue, which is also affected by this treatment, should be spared. Thereby the physician has to weight the risk of the unavoidable damage of the surrounding to the tumor against each other. He can decide on the reduction of the irradiation dose delivered to one organ by allowing a higher dose level in another organ.