Multi-objective optimization: Difference between revisions

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=== Scalarizing ===
[[File:NonConvex.gif|thumb|Linear scalarization approach is an easy method used to solve multi-objective optimization problem. It consists in aggregating the different optimization functions in a single function. However, this method only allows to find the supported solutions of the problem (i.e. points on the convex hull of the objective set). This animation shows that when the outcome set is not convex, all efficient solutions cannot be found]]
 
Scalarizing a multi-objective optimization problem is an a priori method, which means formulating a single-objective optimization problem such that optimal solutions to the single-objective optimization problem are Pareto optimal solutions to the multi-objective optimization problem.<ref name="HwangMasud1979" /> In addition, it is often required that every Pareto optimal solution can be reached with some parameters of the scalarization.<ref name="HwangMasud1979" /> With different parameters for the scalarization, different Pareto optimal solutions are produced. A general formulation for a scalarization of a multi-objective optimization problem is