In this article, we introduce the Maximum Diversity Assortment Selection Problem (MDASP), which is a generalization of the two-dimensional Knapsack Problem (2D-KP). Given a set of rectangles and a rectangular container, the goal of 2D-KP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. MDASP is to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized. Thereby, diversity is defined as the minimum or average normalized Hamming distance of all assortment pairs. MDASP was the topic of the 11th AIMMS-MOPTA Competition in 2019. The methods described in this article and the resulting computational results won the contest. In the following, we give a definition of the problem, introduce a mathematical model and solution approaches, determine upper bounds on the diversity, and conclude with computational experiments conducted on test instances derived from the 2D-KP literature.

在本文中，我们介绍了最大多样性分类选择问题（MDASP），它是二维背包问题（2D-KP）的概括。给定一组矩形和一个矩形容器，2D-KP的目标是确定可以放置在容器中而不会重叠（即可行的分类）的矩形子集，从而覆盖最大面积。MDASP将确定一组可行的分类，每个分类涵盖容器的某个最小阈值，以使它们之间的多样性最大化。因此，多样性被定义为所有分类对的最小或平均归一化汉明距离。MDASP是2019年第11届AIMMS-MOPTA竞赛的主题。本文描述的方法和由此产生的计算结果赢得了比赛。在下面的，