What does "Scalarization" mean?
Table of Contents
Scalarization is a method used in multi-objective optimization, where multiple goals are considered at the same time. Instead of trying to solve each goal separately, scalarization combines them into a single goal. This makes it easier to find the best overall solution.
How It Works
In scalarization, a utility function is created. This function helps to balance the different goals by comparing them to a reference point. The idea is to maximize the utility, which represents how well the goals are being met.
Types of Utility Functions
There are different types of utility functions that can be used in scalarization. Some common types include Cobb-Douglas, Leontief, and CES functions. Each of these types has its own way of combining the goals into a single value.
Benefits
One of the main benefits of scalarization is that it can help to identify the best solutions while simplifying the problem. It can also lead to good results when applied to real-world scenarios, such as selecting the best investment portfolio based on multiple financial goals.
Key Observation
In some cases, it may not be necessary to directly deal with certain constraints when using scalarization. If certain conditions are met, the process can be simplified, allowing for a quicker way to find the best solutions.