Erratum: A hybrid genetic algorithmic approach to the maximally diverse grouping problem

Fan, Zhi‐Ping; Chen, Y.; Ma, Jian; Zeng, Shi

doi:10.1057/jors.2010.92

Cited by 13 publications

(3 citation statements)

References 24 publications

(22 reference statements)

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“…Regarded as an extension of the MDGP, the MDGP's objective is to distribute students into unique, non-overlapping groups, thereby maximizing the sum of differences between each pair of individuals within the same group [59]. As this problem has attracted significant attention, there have been extensive research initiatives and algorithmic solutions proposed to tackle the MDGP formulation [58,60,61]. However, the key limitations of the MDGP approach include challenges in scalability as the computational complexity grows exponentially with the number of objects and groups [62], and sensitivity to the quality of input data, which influences the quality of obtained solutions [62].…”

Section: Literature Reviewmentioning

confidence: 99%

Leveraging Multi-Criteria Integer Programming Optimization for Effective Team Formation

Singh,

Huynh,

Nguyen

et al. 2023

Preprint

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The research addresses a critical aspect of organizational settings – team formation – which is vital for effective team-based learning. In many organizational environments, successful teamwork depends on the composition of teams that consider various criteria, such as skill levels, background, and personality traits. Meanwhile, maintaining fairness and equity among teams is crucial to ensure equal opportunities for all team members. Our research framework lies in its ability to model a diverse range of factors, while simultaneously maximizing within-team diversity and minimizing conflict levels. In this study, we introduce a novel application of multi-criteria integer programming (MCIP) that diverges from traditional and single-objective optimization methods to address the complexity of team formation with a focus on multiple criteria. This approach offers a comprehensive solution that accommodates multiple criteria simultaneously. The contributions of this paper are: 1) An innovative optimization model for team formation that addresses the complex task of maximizing intra-group diversity while minimizing inter-group diversity. 2) Addressing the challenge of forming balanced and diverse student teams and providing educators with a practical tool for effective team formation.

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Section: Literature Reviewmentioning

confidence: 99%

Leveraging Multi-Criteria Integer Programming Optimization for Effective Team Formation

Singh,

Huynh,

Nguyen

et al. 2023

Preprint

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“…The problem belongs to the N P-hard computational complexity class, and heuristics are available to tackle it [7]. A hybrid genetic algorithm was proposed in [8]. There, the authors suggested Tabu Search combined with strategic oscillations.…”

Section: Related Workmentioning

confidence: 99%

Solving the Max-Diversity Orthogonal Regrouping Problem by an Integer Linear Programming Model and a GRASP/VND with Path-Relinking Approach

et al. 2021

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Students from Master of Business Administration (MBA) programs are usually split into teams. In light of the generalistic nature of MBA programs, diversity within every team is desirable in terms of gender, major, age and other criteria. Many schools rotate the teams at the beginning of every term so that each student works with a different set of peers during every term, thus training his or her adaptation skills and expanding the peer network. Achieving diverse teams while avoiding–or minimizing—the repetition of student pairs is a complex and time-consuming task for MBA Directors. We introduce the Max-Diversity Orthogonal Regrouping (MDOR) problem to manage the challenge of splitting a group of people into teams several times, pursuing the goals of high diversity and few repetitions. We propose a hybrid Greedy Randomized Adaptive Search Procedure/Variable Neighborhood Descent (GRASP/VND) heuristic combined with tabu search and path relinking for its resolution, as well as an Integer Linear Programming (ILP) formulation. We compare both approaches through a set of real MBA cohorts, and the results show that, in all cases, the heuristic approach significantly outperforms the ILP and manually formed teams in terms of both diversity and repetition levels.

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“…Correspondingly, the swap neighborhood of y includes all solutions ȳ such that (2)-(4) are fulfilled, y i = ȳi for all items i ∈ I\{j, j ′ }, ȳj ′ = y j , and ȳj = y j ′ . These two neighborhoods are used in most of the advanced solution methods for the MDGP, including the five advanced algorithms mentioned before as well as for example Baker and Powell (2002), Chen et al (2011), Fan et al (2011), Palubeckis et al (2011), Rodriguez et al (2013), Urošević (2014), andSchulz (2023). In the paper at hand, we present a new efficient method enhancing the neighborhood decomposition (ND) method described in Lai et al (2021a) to evaluate the two neighborhoods faster than in the standard implementation which simply evaluates the entire neighborhood and the ND implementation.…”

Section: Introductionmentioning

confidence: 99%

Efficient neighborhood evaluation for the Maximally Diverse Grouping Problem

Schulz

2023

Preprint

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The Maximally Diverse Grouping Problem is one of the well-known combinatorial optimization problems with applications in the assignment of students to groups or courses. Due to its NP-hardness several (meta)heuristic solution approaches have been presented in the literature. Most of them include the insertion of an item of one group into another group and the swap of two items currently assigned to different groups as neighborhoods. The paper presents a new efficient implementation for both neighborhoods and compares it with the standard implementation in which all inserts/swaps are evaluated as well as the neighborhood decomposition approach. The results show that the newly presented approach is clearly superior for larger instances allowing for up to 160% more iterations in comparison to the standard implementation and up to 76% more iterations in comparison to the neighborhood decomposition approach. Moreover, the results can also be used for (meta)heuristic algorithms for other grouping or clustering problems.

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Erratum: A hybrid genetic algorithmic approach to the maximally diverse grouping problem

Cited by 13 publications

References 24 publications

Leveraging Multi-Criteria Integer Programming Optimization for Effective Team Formation

Leveraging Multi-Criteria Integer Programming Optimization for Effective Team Formation

Solving the Max-Diversity Orthogonal Regrouping Problem by an Integer Linear Programming Model and a GRASP/VND with Path-Relinking Approach

Efficient neighborhood evaluation for the Maximally Diverse Grouping Problem

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