[论文解读] The Guided Team-Partitioning Problem: Definition, Complexity, and Algorithm

Sanaz Bahargam, Theodoros Lappas+1 more|arXiv (Cornell University)|Apr 30, 2019

Mobile Crowdsensing and Crowdsourcing被引用 4

一句话总结

本文提出了引导式团队划分（Guided Team-Partitioning, GTP）问题，该问题将人群划分为若干团队，使得每个团队的质心尽可能接近给定的目标向量，从而实现可控且公平的团队构成。作者证明了GTP问题是NP难的，并提出了高效的启发式算法，在真实和合成数据集上均表现出优于基线方法的解决方案质量与运行时间。

ABSTRACT

A long line of literature has focused on the problem of selecting a team of individuals from a large pool of candidates, such that certain constraints are respected, and a given objective function is maximized. Even though extant research has successfully considered diverse families of objective functions and constraints, one of the most common limitations is the focus on the single-team paradigm. Despite its well-documented applications in multiple domains, this paradigm is not appropriate when the team-builder needs to partition the entire population into multiple teams. Team-partitioning tasks are very common in an educational setting, in which the teacher has to partition the students in her class into teams for collaborative projects. The task also emerges in the context of organizations, when managers need to partition the workforce into teams with specific properties to tackle relevant projects. In this work, we extend the team formation literature by introducing the Guided Team-Partitioning (GTP) problem, which asks for the partitioning of a population into teams such that the centroid of each team is as close as possible to a given target vector. As we describe in detail in our work, this formulation allows the team-builder to control the composition of the produced teams and has natural applications in practical settings. Algorithms for the GTP need to simultaneously consider the composition of multiple non-overlapping teams that compete for the same population of candidates. This makes the problem considerably more challenging than formulations that focus on the optimization of a single team. In fact, we prove that GTP is NP-hard to solve and even to approximate. The complexity of the problem motivates us to consider efficient algorithmic heuristics, which we evaluate via experiments on both real and synthetic datasets.

研究动机与目标

• 为解决团队组建研究中仅关注单个团队优化的空白，特别是在需要将整个群体划分为多个非重叠团队的场景中。
• 形式化引导式团队划分（GTP）问题，要求团队质心被引导至特定目标向量，以确保团队构成的均衡或符合预期。
• 分析GTP的计算复杂度，并证明其求解和近似均属于NP难问题。
• 设计并评估适用于GTP的高效启发式算法，确保其可扩展性并生成高质量解。
• 通过在真实和合成数据上的实验，展示GTP在教育和组织场景中的实际应用价值。

提出的方法

• 将GTP建模为带约束的优化问题，目标是最小化团队质心与目标向量之间平方距离的总和。
• 提出GuidedSplit算法，一种启发式方法，通过平衡质心接近度与团队规模约束，迭代地将个体分配至团队。
• 在划分过程中使用凸优化子程序（ConvexOpt）来优化团队质心，提升其与目标向量的对齐程度。
• 集成基于匈牙利算法的匹配步骤，以在需要时将聚类中心分配给目标向量，确保最优目标分配。
• 设计一种贪心变体（BTF_Greedy）和一种基线方法（BTF_CVX）用于对比，两者均采用带目标约束的迭代优化。
• 使用合成数据和真实世界数据集评估性能，通过质心-目标距离衡量解决方案质量，通过运行时间效率评估效率。

实验结果

研究问题

• RQ1 引导式团队划分问题是否为NP难问题？是否可在常数因子内近似？
• RQ2 能否设计出高效启发式算法，在保持计算效率的同时有效将团队构成引导至指定目标向量？
• RQ3 所提出的算法在解决方案质量与运行时间方面，相较于现有的聚类与团队组建基线方法表现如何？
• RQ4 参数如聚类数量和每次迭代中移除的点数对算法性能有何影响？
• RQ5 在哪些真实世界场景中，引导式划分显著优于标准聚类或团队组建方法？

主要发现

• 已证明GTP问题在求解和常数因子近似方面均为NP难，确立了其计算上的不可解性。
• 所提出的GuidedSplit算法在最小化质心-目标距离方面，显著优于k-means、k_targets、Random及基线方法。
• GuidedSplit的运行时间与其他启发式方法相当，当团队平衡时，其运行时间随群体规模呈次线性增长；由于每次迭代中需移除点，聚类数量增加时运行时间也随之上升。
• k_means基线在大规模数据集上表现出高运行时间与较差性能，主要由于聚类严重失衡，尤其在n = 5000时更为明显。
• 当ℓ = 0（无凸优化）时，BTF_CVX与BTF_Greedy因每次迭代需运行ConvexOpt或贪心步骤n次，故运行速度慢于其他方法。
• k_targets基线因使用预定义质心作为种子，初始聚类更均衡，故在运行时间上优于k_means。