Number partitioning is a classic problem in artificial intelligence. And balanced multi-way number partitioning problem (BMNP) aims to partition a set of numbers into multiple subsets, such that (1) each subset contains the same number of numbers and (2) the subset sums are equal. The BMNP problem has various applications in real world scenarios, including task allocation, CPU scheduling, file placement in data center, multi-source data processing, etc. In this paper, we consider the problem of diversity-aware balanced multi-way number partitioning (DBMNP). DBMNP differs from BMNP, in that each number is associated with a type attribute. In addition to the two goals of BMNP, DBMNP also requires that the types of numbers in each subset are as diversified as possible. To solve the problem, we propose three heuristic algorithms to minimize the difference between subset sums and at the same time maximize diversify of each subset. Extensive experiments are conducted to evaluate the effectiveness of our proposed algorithms.

数字划分是人工智能中的经典问题。平衡多路号码分配问题（BMNP）的目的是将一组号码划分为多个子集，以使（1）每个子集包含相同数量的数字，以及（2）子集总和相等。BMNP问题在现实世界中具有多种应用，包括任务分配，CPU调度，数据中心中的文件放置，多源数据处理等。在本文中，我们考虑了具有多样性感知的平衡多路号码划分问题（DBMNP）。DBMNP与BMNP不同，因为每个数字都与类型属性相关联。除了BMNP的两个目标外，DBMNP还要求每个子集中的数字类型尽可能多样化。为了解决这个问题 我们提出了三种启发式算法，以最小化子集和之间的差异，同时最大化每个子集的多样性。进行了广泛的实验，以评估我们提出的算法的有效性。