Multi-objective Optimization - Scalarizing Multiobjective Optimization Problems

Scalarizing Multiobjective Optimization Problems

Scalarizing a multiobjective optimization problem means formulating a single-objective optimization problems such that optimal solutions to the single-objective optimization problem are Pareto optimal solutions to the multiobjective optimization problem. With different parameters for the scalarization, different Pareto optimal solutions are produced. A well-known example is the so-called linear scalarization (see, e.g.,)

$\min_{x\in X} \sum_{i=1}^k w_if_i(x),$