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Gene-Similarity Normalization in a Genetic Algorithm for the Maximum k -Coverage Problem

Author

Listed:
  • Yourim Yoon

    (Department of Computer Engineering, College of Information Technology, Gachon University, 1342 Seongnamdaero, Sujeong-gu, Seongnam-si, Gyeonggi-do 13120, Korea)

  • Yong-Hyuk Kim

    (School of Software, Kwangwoon University, 20 Kwangwoon-ro, Nowon-gu, Seoul 01897, Korea)

Abstract

The maximum k -coverage problem (MKCP) is a generalized covering problem which can be solved by genetic algorithms, but their operation is impeded by redundancy in the representation of solutions to MKCP. We introduce a normalization step for candidate solutions based on distance between genes which ensures that a standard crossover such as uniform and n -point crossovers produces a feasible solution and improves the solution quality. We present results from experiments in which this normalization was applied to a single crossover operation, and also results for example MKCPs.

Suggested Citation

  • Yourim Yoon & Yong-Hyuk Kim, 2020. "Gene-Similarity Normalization in a Genetic Algorithm for the Maximum k -Coverage Problem," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:513-:d:340708
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    References listed on IDEAS

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    1. Yong-Hyuk Kim & Alberto Moraglio & Ahmed Kattan & Yourim Yoon, 2014. "Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-10, April.
    2. Masoud Yaghini & Mohammad Karimi & Mohadeseh Rahbar, 2015. "A set covering approach for multi-depot train driver scheduling," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 636-654, April.
    3. Dorit S. Hochbaum & Anu Pathria, 1998. "Analysis of the greedy approach in problems of maximum k‐coverage," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(6), pages 615-627, September.
    4. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    5. U Aickelin, 2002. "An indirect genetic algorithm for set covering problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(10), pages 1118-1126, October.
    6. Beasley, J. E. & Chu, P. C., 1996. "A genetic algorithm for the set covering problem," European Journal of Operational Research, Elsevier, vol. 94(2), pages 392-404, October.
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    Cited by:

    1. Jaeyoung Yang & Yong-Hyuk Kim & Yourim Yoon, 2022. "A Memetic Algorithm with a Novel Repair Heuristic for the Multiple-Choice Multidimensional Knapsack Problem," Mathematics, MDPI, vol. 10(4), pages 1-15, February.

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