scalarizationbased

Scalarization refers to a process in which a problem with multiple objectives is transformed into a single-objective problem. This is often done in the context of multi-objective optimization, where decisions need to be made that affect several criteria simultaneously. By converting the multi-objective problem into a scalar one, standard single-objective optimization techniques can be applied.

There are several common methods for scalarization. A widely used approach is the weighted sum method, where each objective function is multiplied by a weight, and these weighted objectives are then summed together to form a single scalar objective function. The weights reflect the relative importance assigned to each objective. Another technique is the epsilon-constraint method, where one objective is optimized while the other objectives are treated as constraints, often with upper bounds set by a parameter epsilon.

The choice of scalarization method and the specific parameters used (like weights or epsilon values) can significantly influence the solution obtained. Scalarization is a powerful tool for simplifying complex decision-making scenarios and finding trade-offs between competing objectives. It's particularly relevant in fields such as engineering design, economics, and operations research, where optimizing multiple, often conflicting, goals is a common challenge. The resulting scalar problem is then solved using algorithms designed for single-objective optimization.