Multicriteria optimization with a multiobjective golden section line search

• 成果类型: Article
• 署名作者: Vieira, Douglas A. G.; Takahashi, Ricardo H. C.; Saldanha, Rodney R.
• 署名单位: Universidade Federal de Minas Gerais; Universidade Federal de Minas Gerais
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-010-0347-9
• 发表日期: 2012
• 页码: 131-161
• 关键词: genetic algorithm; computation; points

摘要

This work presents an algorithm for multiobjective optimization that is structured as: (i) a descent direction is calculated, within the cone of descent and feasible directions, and (ii) a multiobjective line search is conducted over such direction, with a new multiobjective golden section segment partitioning scheme that directly finds line-constrained efficient points that dominate the current one. This multiobjective line search procedure exploits the structure of the line-constrained efficient set, presenting a faster compression rate of the search segment than single-objective golden section line search. The proposed multiobjective optimization algorithm converges to points that satisfy the Kuhn-Tucker first-order necessary conditions for efficiency (the Pareto-critical points). Numerical results on two antenna design problems support the conclusion that the proposed method can solve robustly difficult nonlinear multiobjective problems defined in terms of computationally expensive black-box objective functions.