Wanner Elizabeth F, Guimarães Frederico G, Takahashi Ricardo H C, Fleming Peter J
Departamento de Matemática, Universidade Federal de Ouro Preto, Morro do Cruzeiro, Ouro Preto, MG, Brazil.
Evol Comput. 2008 Summer;16(2):185-224. doi: 10.1162/evco.2008.16.2.185.
This paper proposes a local search optimizer that, employed as an additional operator in multiobjective evolutionary techniques, can help to find more precise estimates of the Pareto-optimal surface with a smaller cost of function evaluation. The new operator employs quadratic approximations of the objective functions and constraints, which are built using only the function samples already produced by the usual evolutionary algorithm function evaluations. The local search phase consists of solving the auxiliary multiobjective quadratic optimization problem defined from the quadratic approximations, scalarized via a goal attainment formulation using an LMI solver. As the determination of the new approximated solutions is performed without the need of any additional function evaluation, the proposed methodology is suitable for costly black-box optimization problems.
本文提出了一种局部搜索优化器，作为多目标进化技术中的附加算子，它能够以较低的函数评估成本帮助找到帕累托最优曲面的更精确估计。新算子采用目标函数和约束的二次近似，这些近似仅使用常规进化算法函数评估已生成的函数样本构建。局部搜索阶段包括求解由二次近似定义的辅助多目标二次优化问题，该问题通过使用线性矩阵不等式（LMI）求解器的目标达成公式进行标量化。由于新近似解的确定无需任何额外的函数评估，因此所提出的方法适用于代价高昂的黑箱优化问题。
