Multicriteria optimization: scalarization tecniques

In this work, we briefly present the notations about multicriteria optimization problem and then focus our attention on scalarization techniques. Multicriteria optimization presents issues at the analyst that are very different from the usual problem that we can find when we deal with a single objective optimization problem; for this reason, we need new tools and definitions for solving it. One of this issue consist in ordering a vector of functions and for this purpose we need to introduce the concept of cone and all related theorems. The core of the work, however, is about scalarization methods. Those techniques consist in transforming the multiobjective optimization problem into a scalar one that is easier to solve. The most important and used method – the weighted sum method – is presented in depth, together with another general method – the Pascoletti-Serafini one – that is also used to highlight the pitfalls of other scalarization techniques. During the work, various issues about multicriteria optimization are introduced and discussed