Our research deals with the optimization version of the set partition problem, where the objective is to minimize the absolute difference between the sums of the two disjoint partitions. Although this problem is known to be NP-hard and requires exponential time to solve, we propose a less demanding version of this problem where the goal is to find a locally optimal solution. In our approach, we consider the local optimality in respect to any movement of at most two elements. To accomplish this, we developed an algorithm that can generate a locally optimal solution in at most $O(N^2)$ time and $O(N)$ space. Our algorithm can handle arbitrary input precisions and does not require positive or integer inputs. Hence, it can be applied in various problem scenarios with ease.

翻译：我们的研究涉及设定分割问题的优化版本, 其目的在于最大限度地缩小两个断开分割之间的绝对差额。 虽然这个问题已知为NP硬型, 需要指数时间来解决, 但我们建议了一个不那么苛刻的版本, 目标是找到一个本地最佳解决方案。 在我们的方法中, 我们考虑对最多两个元素的任何移动的本地最佳性。 为了实现这一目标, 我们开发了一个算法, 它可以产生一个本地最佳解决方案, 最多在$O( N)2) 和$O( N) 空间。 我们的算法可以处理任意输入精度, 不需要正或整数输入。 因此, 它可以轻松地应用于各种问题情景中 。</s>