Otimização multimodal baseada em métodos unimodais e de clusterização

• Autor(a) principal: Almeida, Deise Mara Barbosa de
• Data de Publicação: 2016
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13691
• topic: Global optimization; Multimodal problems; Clustering; Otimização matemática; Analise global (Matematica) Métodos de simulação; Solução de problemas Métodos de simulação; Otimização global; Problema multimodal; Agrupamento; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

Optimization problems which have two or more global optimal solutions are known as global multimodal problems. Obtaining all global solutions for this kind of problems can be important and lead to a hard task. This work proposes two methodologies that links optimization methods and clustering to find all optimal solutions of a global multimodal problem. We run a given number of iterations of the evolutionary algorithm Harmony Search to create small groups around each point of global optimum to a n-dimensional function. Then, we use Laplacian Eigenmap to identify these clusters and represent them in a space of smaller dimension, possibly. Subsequently, we classify each cluster using k-means in reduced dimension or by smoothing the distance matrix and we obtain an estimate to each global optimum point. After that, we use the Hooke-Jeeves deterministic algorithm to obtain a global optimum point from each of the estimates. To verify the proposed methodology we use test functions, initially defined in a two-dimensional space. Thereafter, we use functions defined on spaces of higher dimension. The methodologies were also applied to a real engineering problem which corresponds to the refrigerant system ammonia + R-125. The results indicate that the methodologies are able to construct good approximations of the optimum points.