A Quantum Genetic Algorithm Framework For The MaxCut Problem

• Ano de defesa: 2025
• Autor(a) principal: ARAÚJO, Paulo André Viana de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Pernambuco; UFPE; Brasil; Programa de Pos Graduacao em Ciencia da Computacao
• Palavras-chave em Português: Computação quântica; Otimização combinatória; Graph Theory
• Link de acesso: https://repositorio.ufpe.br/handle/123456789/64777

The MaxCut problem is a fundamental problem in Combinatorial Optimization, with sig- nificant implications across diverse domains such as logistics, network design, and statistical physics. The algorithm represents innovative approaches that balance theoretical rigor with practical scalability. The proposed method introduces a Quantum Genetic Algorithm (QGA) using a Grover-based evolutionary framework and divide-and-conquer principles. By partition- ing graphs into manageable subgraphs, optimizing each independently, and applying graph contraction to merge the solutions, the method exploits the inherent binary symmetry of Max- Cut to ensure a more efficient and robust approximation performance. Theoretical analysis establishes a foundation for a better performance of the algorithm, while empirical evalua- tions provide quantitative evidence of its effectiveness. On complete graphs, the proposed method consistently achieves the true optimal MaxCut values, outperforming the Semidefi- nite Programming (SDP) approach, which provides up to 99.7% of the optimal solution for larger graphs. On Erdős-Rényi random graphs, the QGA demonstrates competitive perfor- mance, achieving median solutions within 92-96% of the SDP results. These results showcase the potential of the QGA framework to deliver competitive solutions, even under heuristic constraints, while demonstrating its promise for scalability as quantum hardware evolves.