Imanol Unanue Gual: "Contributions to the Mathematical Modeling of Estimation of Distribution Algorithms and Pseudo - Boolean Functions".

Zuzendariak_Directores:  José Antonio Lozano Alonso / María Merino Maestre.

2023_10_27, 11:00  Sala Ada Lovelace.

Abstract:

"The objective of Combinatorial Optimization Problems is to obtain a feasible solution which maximizes or minimizes a fitness function defined over a discrete search space. Due to the fact that most of these problems cannot be solved by an exhaustive analysis, their resolution are often approached by heuristic algorithms. However, there is no algorithm that outperforms any other algorithm for all Combinatorial Optimization Problem instances. Therefore, given a problem instance, the idilic goal is to know which algorithm is the most efficient one to solve it. The main research lines to achieve the goal are to study the definition of Combinatorial Optimization Problems and the range of possible instances generated by the problems and to study the design and characteristic of the algorithms. In this thesis, both lines have been addressed. On the one hand, we study pseudo-Boolean functions and several well-known binary-based Combinatorial Optimization Problems. On the other hand, we present a mathematical modeling to study Estimation of Distribution Algorithms designed to solve permutation-based Combinatorial Optimization Problems. The main motivation has been to continue making progress in this field for a better comprehension of the relations between Combinatorial Optimization Problems and optimization algorithms."