scalarisering

Scalarization is a technique used in multi-objective optimization to convert a problem with multiple, often conflicting objectives into a single-objective problem. This is achieved by combining the individual objectives into a single scalar function. The goal is to find a solution that optimizes this scalar function, which ideally corresponds to a good compromise or a Pareto optimal solution for the original multi-objective problem.

There are various methods for scalarization. One common approach is the weighted sum method, where each objective function is multiplied by a positive weight and then summed up. The weights reflect the relative importance assigned to each objective. Another method is the epsilon-constraint method, where one objective is optimized while the other objectives are treated as constraints, with upper bounds specified by epsilon values. Other scalarization techniques include the Tchebycheff method and the goal programming method.

The choice of scalarization method and the specific parameters used (e.g., weights or epsilon values) can significantly influence the set of solutions obtained. Different scalarizations might lead to different Pareto optimal solutions. Therefore, scalarization is often employed iteratively, with different parameter settings to explore the Pareto front and identify a preferred solution based on decision-maker preferences. The success of scalarization depends on effectively representing the trade-offs between objectives in a single scalar value.