New Advances in Estimation of Distribution Algorithms for Quantum Machine Learning and Industrial Scenarios

• Autores: Vicente Pérez Soloviev
• Directores de la Tesis: Concha Bielza Lozoya (dir. tes.) , Pedro Larrañaga Múgica (codir. tes.)
• Lectura: En la Universidad Politécnica de Madrid ( España ) en 2025
• Idioma: inglés
• Tribunal Calificador de la Tesis: José Antonio Gámez Martín (presid.) , Juan Antonio Fernández del Pozo de Salamanca (secret.) , Roberto Santana Hermida (voc.) , John McCall (voc.) , Andrés Gómez Tato (voc.)
• Programa de doctorado: Programa de Doctorado en Inteligencia Artificial por la Universidad Politécnica de Madrid
• Calificación: Sobresaliente Cum Laude
• Enlaces
  • Tesis en acceso abierto en: Archivo Digital UPM
• Resumen

  • Evolutionary algorithms span a wide range of domains, including Industry 4.0, machine learning, and quantum machine learning (QML) due to their ease of implementation, scalability, and interpretability. This PhD dissertation focuses on estimation of distribution algorithms (EDAs), which use probabilistic models (PMs) to sample new solutions. Bayesian networks (BNs) graphically represent conditional dependencies between variables, and their embedding into EDAs can reveal patterns and enhance solution quality. In this PhD thesis we first focus on the application of these approaches in industrial problems. First, we extend an EDA with Gaussian BNs to optimize solvent mixtures for cost-effective dissolution in a laboratory. The EDA explores an initial search space provided by the experts in which several constraints are required (expert knowledge) and includes a parameter to balance exploration. Results indicate that maximizing exploration replicates expert proposals, while decreasing leads to more cost-effective solutions. This methodology was later extended to a multi-objective (MO) problem in designing experiments for fuel fabrication in a laboratory. To reduce resource use, we developed a framework based on EDAs to propose experimental formulas, where some objectives cannot be evaluated analytically and are predicted with surrogate models. A posteriori analysis revealed previously unknown dependencies between fuel components. Traditional EDAs for continuous domains usually involve assuming Gaussians. Moreover, the EDA baseline updates a PM based on the top individuals from the previous iteration, risking local optima convergence. We introduce a semiparametric EDA, relaxing the Gaussianity assumption by using semiparametric BNs, where kernel estimated and Gaussian nodes coexist, determined dynamically by the algorithm. Our approach incorporates information from multiple past iterations to learn the PM. Empirical results show statistically significant improvements over other methods. EDAs share similarities with some QML algorithms. This dissertation secondly combines EDAs with quantum computing (QC) for various optimization tasks. On the one hand, quantum-inspired methods lead to classical algorithms assisted by QC. We introduce a quantum-inspired EDA, replacing the PM with a quantum circuit. Results indicate that quantum noise improves the results. We also compare computational costs across different topologies and identify the ideal one for our EDA. On the other hand, variational quantum algorithms (VQAs) are QC methodologies assisted by classical optimizers. VQAs aim to minimize a given energy function by optimizing the parameters of the quantum parametric circuit (ansatz). Our first contribution in this field applies VQAs for BN structure learning. We analyze the algorithm's noise resilience across different types of noises, showing competitive results. Due to current quantum device limitations, we employed the Digital Annealer for larger BNs. We propose the use of EDAs for the parameter optimization of the ansatz by benchmarking different EDAs in different scenarios. Our results show that EDAs offer competitive results compared to other gradient-based / -free approaches in terms of CPU time and accuracy, with and without quantum noise simulation. Quantum architecture search involves optimizing not only the parameters but also the architecture of the ansatz. To manage this complex multi-level optimization, we use an EDA assisted by a surrogate model to rank solutions by expected energy. We also address both accuracy and barren plateau occurrence by framing it as a MO problem. Results show that our approach, effectively enhances the trainability of known architectures while maintaining strong performance. Finally, we introduce EDAspy, a Python open-source library designed to advance EDA research. Noting the lack of EDA implementations, we offer over ten variants and supports creating custom EDAs with various components.