Solving the maximally diverse grouping problem by skewed general variable neighborhood search

The maximally diverse grouping problem requires finding a partition of a given set of elements into a fixed number of mutually disjoint subsets (or groups) in order to maximize the overall diversity between elements of the same group. In this paper we develop a new variant of variable neighborhood search for solving the problem. The extensive computational results show that our new heuristic significantly outperforms the current state of the art. Moreover, the best known solutions have been improved on 531 out of 540 test instances from the literature.

[1]  P. Hansen,et al.  Variable neighbourhood search: methods and applications , 2010, Ann. Oper. Res..

[2]  Michael J. Pazzani,et al.  Mining for proposal reviewers: lessons learned at the national science foundation , 2006, KDD '06.

[3]  Barrie M. Baker,et al.  Assigning pupils to tutor groups in a comprehensive school , 2001, J. Oper. Res. Soc..

[4]  Dragan Urošević.  VARIABLE NEIGHBORHOOD SEARCH FOR MAXIMUM DIVERSE GROUPING PROBLEM , 2014 .

[5]  R. R. Weitz,et al.  An empirical comparison of heuristic and graph theoretic methods for creating maximally diverse groups, VLSI design, and exam scheduling , 1997 .

[6]  Jian Ma,et al.  A hybrid grouping genetic algorithm for reviewer group construction problem , 2011, Expert Syst. Appl..

[7]  V. Lotfi,et al.  A Three Phased Approach To Final Exam Scheduling , 1989 .

[8]  Dmitry Krass,et al.  Constrained group balancing: Why does it work , 2010, Eur. J. Oper. Res..

[9]  Joyendu Bhadury,et al.  Maximizing Workforce Diversity In Project Teams: A Network Flow Approach. , 2000 .

[10]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[11]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[12]  Nenad Mladenovic,et al.  Mic'2001 -4th Metaheuristics International Conference Design of Balanced Mba Student Teams , 2022 .

[13]  Abraham Duarte,et al.  Tabu search and GRASP for the maximum diversity problem , 2007, Eur. J. Oper. Res..

[14]  Micael Gallego,et al.  Tabu search with strategic oscillation for the maximally diverse grouping problem , 2013, J. Oper. Res. Soc..

[15]  Francisco J. Rodríguez,et al.  An artificial bee colony algorithm for the maximally diverse grouping problem , 2013, Inf. Sci..

[16]  R. R. Weitz,et al.  On a Heuristic for the Final Exam Scheduling Problem , 1996 .

[17]  Vahid Lotfi,et al.  A Final-Exam-Scheduling Package , 1991 .

[18]  Y. Chen,et al.  Erratum: A hybrid genetic algorithmic approach to the maximally diverse grouping problem , 2011, J. Oper. Res. Soc..

[19]  R. R. Weitz,et al.  An empirical comparison of heuristic methods for creating maximally diverse groups , 1998, J. Oper. Res. Soc..

[20]  John Mingers,et al.  Creating student groups with similar characteristics: A heuristic approach , 1995 .

[21]  F. Glover,et al.  Heuristic algorithms for the maximum diversity problem , 1998 .

[22]  Thomas A. Feo,et al.  A class of bounded approximation algorithms for graph partitioning , 1990, Networks.