Summary

In many real world problems, there are hierarchical decision-making structures, where a higher level agent (leader) makes decisions anticipating the optimal reaction of a lower level agent (follower). These scenarios are modeled by binivel optimization, in which the problem of the upper level is resolved subject to the fact that the lower level decisions are optimal with respect to their own objective. The inherent complexity of these models, not convex, not differentiability, and the presence of multiple optics, makes it difficult to use classical methods. In this context, the Binivel Evolutionary Optimization (OEB) has emerged as a robust computational approach to addressing high-complexity binivel problems. This tutorial focuses on the multi-objective case, where the top, the lower, or both, consider multiple conflicting criteria. The main challenges associated will be discussed, including the definition of feasibility in the presence of multiple optimal responses, the spread of optimality between levels, and the maintenance of diversity in Pareto-type solutions sets under a hierarchical structure. It will also analyse how modern Artificial Intelligence techniques can be integrated into evolutionary algorithms to improve search space exploration, approximate lower level reaction functions and reduce computational cost. The tutorial will include replicable computational examples, illustrating practical implementations and algorithmic design patterns. Finally, applications and

Public objective

In many real world problems, there are hierarchical decision-making structures, where a higher level agent (leader) makes decisions anticipating the optimal reaction of a lower level agent (follower). These scenarios are modeled by binivel optimization, in which the problem of the upper level is resolved subject to the fact that the lower level decisions are optimal with respect to their own objective. The inherent complexity of these models, not convex, not differentiability, and the presence of multiple optics, makes it difficult to use classical methods. In this context, the Binivel Evolutionary Optimization (OEB) has emerged as a robust computational approach to addressing high-complexity binivel problems. This tutorial focuses on the multi-objective case, where the top, the lower, or both, consider multiple conflicting criteria. The main challenges associated will be discussed, including the definition of feasibility in the presence of multiple optimal responses, the spread of optimality between levels, and the maintenance of diversity in Pareto-type solutions sets under a hierarchical structure. It will also analyse how modern Artificial Intelligence techniques can be integrated into evolutionary algorithms to improve search space exploration, approximate lower level reaction functions and reduce computational cost. The tutorial will include replicable computational examples, illustrating practical implementations and algorithmic design patterns. Finally, applications and

Pre- requirements

People interested in optimization.

Technical requirements

It is desirable that you have taken some optimization course and have programming bases.