A global optimization algorithm using trust-region methods and clever multistart

• Autor(a) principal: Cordeiro, Tiago Alexandre Barrinha
• Data de Publicação: 2021
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10362/135864
• topic: Global Optimization; Trust-region Methods; Multistart Strategies; Optimization with Derivatives; Domínio/Área Científica::Ciências Naturais::Matemáticas

Global optimization is an important scientific domain, not only due to the algorithmic challenges associated with this area, but also due to its practical application in different areas of knowledge, from Biology to Aerospace Engineering. In this work we develop an algorithm based on trust-region methods for solving global optimization problems with derivatives, using a clever multistart strategy, testing its efficiency and effectiveness by comparison with other global optimization algorithms. Based on an idea applied to the resolution of problems in derivative-free optimization, this algorithm seeks to reduce the computational effort that the search for a global optimum requires, by comparing points that are relatively close to each other, using as comparison radius the one associated with the trust-region method, retaining only the most promising ones, which will continue to be explored. The proposed method has the added benefit of not only reporting the global optimum but also a list of local optima that may be of interest, depending on the context of the problem in question.