可变序结构下最优元的标量化

Scalarization of Optimal Element under Variable Ordering Structure

摘要: 在多目标优化问题中，将多目标问题转化为单目标问题被称为标量化。许多学者提出了不同形式的标量化函数，并进行了深入研究。然而，线性标量化需要凸性或广义凸性等较强的条件。因此，本文依据可变序结构下最优元的不同概念，利用一个非线性标量化函数得到了其推广函数φ_a,r(y)、Φ_a,r(y)及其性质。最后，利用这些函数将向量优化问题转化为数值优化问题，并给出了向量优化问题解的刻画。

Abstract: In multi-objective optimization problems, it is called scalarization to transform multi-objective problems into single objective problems. Many scholars have proposed different types of scalarization function and studied them. However, linear scalarization needs strong conditions such as convexity or generalized convexity. Therefore, in this paper, according to the different concepts of the optimal element under the variable order structure, we obtain generalization function φ_a,r(y), Φ_a,r(y) and its properties by using a nonlinear scalarization function. Finally, the vector optimization problem is transformed into a numerical optimization problem by using these functions, and the characterizations of the solutions of the vector optimization problem are given.