The balanced maximally diverse grouping problem with integer attribute values

Author:

Schulz ArneORCID

Abstract

AbstractThe paper considers the assignment of items to groups according to their attribute values such that the groups are as balanced as possible. Although the problem is in general NP-hard, we prove that it can be solved in pseudo-polynomial time if attribute values are integer. We point out a relation to partition and more general to multi-way number partitioning. Furthermore, we introduce a mixed-integer programming (MIP) formulation, a variable reduction technique, and an efficient lower bound for the objective value. Our computational results show that the lower bound meets the optimal objective value in the most of our instances of realistic size. Hence, the MIP solves instances with several thousand items within seconds to optimality.

Funder

Universität Hamburg

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Theory and Mathematics,Control and Optimization,Discrete Mathematics and Combinatorics,Computer Science Applications

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Capacitated Clustering Problem;Journal of Communications Technology and Electronics;2024-07-29

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