论文标题
新型双目标优化算法最大程度地降低了功能的最大和总和
Novel bi-objective optimization algorithms minimizing the max and sum of vectors of functions
论文作者
论文摘要
我们研究一个双向目标优化问题，对于给定的积极数字$ n $旨在查找$ x = \ {x_0，\ cdots，x_ {k-1} \} \ in \ in \ mathbb {r}^{r}^{k}^{k} _} _ {\ ge ge 0} $ { $ k $的最大函数的最大函数，$ \ max_ {i = 0}^{k-1} f_i（x_i）$，以及目标型二类$ k $函数的总和，$ \ sum_ {i = 0}^{k-1}^{k-1} g_i（x_i）$。这个问题是在优化高性能计算平台上的性能和能源的应用程序中出现的。我们首先提出了一种算法，该算法解决了一个目标一型功能均连续且严格增加的情况，并且目标型两种功能的所有功能都是线性增加的。然后，我们提出了一种算法解决问题的版本，其中$ n $是一个积极的整数，所有功能都是离散的，并由有限集表示，没有任何假设。两种算法都是多项式复杂性。
We study a bi-objective optimization problem, which for a given positive real number $n$ aims to find a vector $X = \{x_0,\cdots,x_{k-1}\} \in \mathbb{R}^{k}_{\ge 0}$ such that $\sum_{i=0}^{k-1} x_i = n$, minimizing the maximum of $k$ functions of objective type one, $\max_{i=0}^{k-1} f_i(x_i)$, and the sum of $k$ functions of objective type two, $\sum_{i=0}^{k-1} g_i(x_i)$. This problem arises in the optimization of applications for performance and energy on high performance computing platforms. We first propose an algorithm solving the problem for the case where all the functions of objective type one are continuous and strictly increasing, and all the functions of objective type two are linear increasing. We then propose an algorithm solving a version of the problem where $n$ is a positive integer and all the functions are discrete and represented by finite sets with no assumption on their shapes. Both algorithms are of polynomial complexity.
