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A primogenitary linked quad tree data structure and its application to discrete multiple criteria optimization

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  • Minghe Sun

Abstract

A data structure called the primogenitary linked quad tree is developed. Each node in the data structure has a pointer to its parent, a pointer to its immediate existing younger sibling, a pointer to its eldest existing son, and an integer as its successorship to its parent. To access any other son of a node, the first-born existing son must be accessed first. The siblings of the same parent are managed as a linked list. This data structure is an extension or enhancement of the traditional quad tree data structure. The primogenitary linked quad tree is applied to discrete multiple criteria optimization for the identification, storage, and retrieval of nondominated criterion vectors. Algorithms managing this data structure are developed and implemented. Major advantages of using the primogenitary linked quad tree instead of the traditional quad tree are savings in memory or storage space and savings in execution time. Examples are provided to demonstrate the application. A computational experiment is conducted to test the performances of the data structure and the algorithms. Computational results show that this data structure uses only a small fraction of the CPU time used by the traditional quad tree to perform the same task. Using this data structure, the identification, storage and retrieval of nondominated criterion vectors become an easy task for discrete multiple criteria optimization problems with many criteria and hundreds of thousands criterion vectors. This data structure can also be used for storage and retrieval of data with composite keys in other applications. Copyright Springer Science + Business Media, LLC 2006

Suggested Citation

  • Minghe Sun, 2006. "A primogenitary linked quad tree data structure and its application to discrete multiple criteria optimization," Annals of Operations Research, Springer, vol. 147(1), pages 87-107, October.
    • Handle: RePEc:spr:annopr:v:147:y:2006:i:1:p:87-107:10.1007/s10479-006-0063-2
    DOI: 10.1007/s10479-006-0063-2
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    References listed on IDEAS

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    1. Sun, Minghe & Steuer, Ralph E., 1996. "InterQuad: An interactive quad tree based procedure for solving the discrete alternative multiple criteria problem," European Journal of Operational Research, Elsevier, vol. 89(3), pages 462-472, March.
    2. Sun, Minghe, 2005. "Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures," European Journal of Operational Research, Elsevier, vol. 162(2), pages 468-483, April.
    3. Minghe Sun & Ralph E. Steuer, 1996. "Quad-Trees and Linear Lists for Identifying Nondominated Criterion Vectors," INFORMS Journal on Computing, INFORMS, vol. 8(4), pages 367-375, November.
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    Cited by:

    1. Nathan Adelgren & Pietro Belotti & Akshay Gupte, 2018. "Efficient Storage of Pareto Points in Biobjective Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 324-338, May.
    2. Minghe Sun & Zhen-Yu Chen & Zhi-Ping Fan, 2014. "A Multi-task Multi-kernel Transfer Learning Method for Customer Response Modeling in Social Media," Working Papers 0161mss, College of Business, University of Texas at San Antonio.
    3. Sun, Minghe, 2011. "A primogenitary linked quad tree approach for solution storage and retrieval in heuristic binary optimization," European Journal of Operational Research, Elsevier, vol. 209(3), pages 228-240, March.
    4. Minghe Sun, 2008. "A Tabu Search Heuristic Procedure for the Capacitated Facility Location Problem," Working Papers 0050, College of Business, University of Texas at San Antonio.

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