Multiobjective Optimization Strategies: A Comparative Analysis Focused on Direct Vector Methods
Date:
Group photo taken after the thematic session on optimization.
Summary: Multiobjective optimization addresses complex problems in which multiple, often conflicting objectives must be considered simultaneously, and the main challenge is to find solutions that represent the best trade-off among them. This talk presents an overview of the main strategies for tackling such problems, organized into three distinct approaches.
We discuss Scalarization Methods, which transform multiobjective problems into single-objective problems using techniques such as weighted sums, highlighting both their simplicity and the limitation of typically producing only one solution per run.
In contrast, we explore Full-Front Approximation Methods, which aim to generate a set of trade-off solutions, or a Pareto front, often using evolutionary and genetic algorithms to provide a global view of possible optimal solutions in a single run.
Finally, the main focus is on Direct Vector Optimization Methods, where the problem is handled directly in vector form, without the need for scalarization or population-based strategies. We present concepts such as the generalization of the gradient to a vector of objectives and the determination of descent directions that optimize simultaneously or identify the best local compromise, with examples including the Multiobjective Gradient Method and the Multiobjective Newton Method.
The presentation aims to provide a clear understanding of different multiobjective optimization philosophies, with a deeper dive into direct vector methods, which represent a powerful extension of classical optimization approaches to the vector setting.