整数规划在最大化多样性分组问题中的应用
An Integer Programming Formulation for the Maximally Diverse Grouping Problem
AI总结：
本文提出一种新的整数线性规划方法，突破传统限制，为评估启发式方法在更广泛应用中的性能提供基准。
摘要：
最大化多样性分组问题（MDGP）是将一组元素分配到互不重叠的组中，以最大化元素间总体多样性的问题。由于MDGP是NP难的，大多数研究集中在启发式解决方案上，而不是精确解决方案。一方面，尽管启发式方法在实践中很常见，但它们不保证全局最优解。另一方面，将问题重新表述为整数线性规划的问题，可以使用精确解决方案方法求解，但这些研究要么限制于等大小的组，要么限制于使用曼哈顿距离。本文提出了一种新的整数线性规划公式，不受上述两种限制的影响，因此可以用于在更广泛的应用中建立启发式方法性能的有用基准。
英文摘要：
The Maximally Diverse Grouping Problem (MDGP) is the problem of assigning a set of elements to mutually disjoint groups in order to maximise the overall diversity between the elements. Because the MDGP is NP-complete, most studies have focused on heuristic solution approaches, as compared to exact solution approaches, to the problem. On the one hand, heuristic solution approaches, although common in practice, do not guarantee a global optimal solution. On the other hand, studies that have reformulated the problem as an integer linear programme, which can be solved using exact solution approaches, are either restricted to groups of equal size or restricted to the use of the Manhattan distance. The present paper presents a new integer linear programming formulation that is not subjected to either of these restrictions, and can therefore be used to establish useful benchmarks for the performance of heuristics in a broader range of applications moving forward.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
