Tesis "On the use of surrogate models as informed operators to improve the efficiency of multi-objective evolutionary algorithms in expensive problems"
Alumno: Alan Díaz Manríquez
Asesor: Dr. Gregorio Toscano Pulido
Sinodales: Dr. Fernando López Irarragorri, Dr. Alfredo Arias Montaño, Dr. Gerardo de la Fraga, Dr. Eduardo Arturo Rodríguez Tello
Most real-world problems are multi-objective. Although the operations research, and evolutionary multi-objective optimization communities have proposed a number of approaches to handle these problems, little effort has been placed in developing hybrid approaches. Also, in spite of their success, current multi-objective approaches remain unable to handle computationally expensive real-world optimization problems.
In this dissertation, we propose an informed operator that transforms a multi-objective problem into a single-objective formulation through the use of classical techniques for multi-objective optimization. The underlying single objective optimization problem is handled with the Nelder-Mead algorithm. However, in order to avoid a raise in the fitness function evaluations, we decided to use surrogate models. Nonetheless, since the selection of the right surrogate model is an important decision that can increase the performance of the proposed approach, we decided to perform a study on several surrogate models commonly accepted in the literature of evolutionary algorithms.
This study is also intended to serve as starting point in the design of new multi-objective evolutionary algorithms that require the use of surrogate models. Having the informed operator and the method to create surrogate models, a simplified stand-alone algorithm was proposed in order to evaluate the performance of such operator. Additionally, the intelligent operator was embedded into two evolutionary algorithms, the Non-dominated Sorting Genetic Algorithm-II and the Differential Evolution for Multi-objective Optimization.
Results indicate that our informed operator is able to improve the convergence of those approaches that it is attached to, since the standalone approach and the two MOEAs that incorporated it outperformed some of the best multi-objective evolutionary algorithms known to date. Also, it is worth noting that both hybrid MOEAs also outperformed their original versions while reducing the number of fitness function evaluations required to obtain good approximations of the true Pareto fronts.