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ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Author

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  • Stefka Fidanova

    (Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25A, 1113 Sofia, Bulgaria)

  • Krassimir Todorov Atanassov

    (Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 105, 1113 Sofia, Bulgaria)

Abstract

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

Suggested Citation

  • Stefka Fidanova & Krassimir Todorov Atanassov, 2021. "ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem," Mathematics, MDPI, vol. 9(13), pages 1-7, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1456-:d:579308
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    References listed on IDEAS

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    1. Diaz, Juan Esteban & Handl, Julia & Xu, Dong-Ling, 2018. "Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system," European Journal of Operational Research, Elsevier, vol. 266(3), pages 976-989.
    2. Marius Posta & Jacques Ferland & Philippe Michelon, 2012. "An exact method with variable fixing for solving the generalized assignment problem," Computational Optimization and Applications, Springer, vol. 52(3), pages 629-644, July.
    3. M. Dawande & J. Kalagnanam & P. Keskinocak & F.S. Salman & R. Ravi, 2000. "Approximation Algorithms for the Multiple Knapsack Problem with Assignment Restrictions," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 171-186, June.
    4. Woodcock, Andrew J. & Wilson, John M., 2010. "A hybrid tabu search/branch & bound approach to solving the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 207(2), pages 566-578, December.
    5. Zhen, Lu & Wang, Kai & Wang, Shuaian & Qu, Xiaobo, 2018. "Tug scheduling for hinterland barge transport: A branch-and-price approach," European Journal of Operational Research, Elsevier, vol. 265(1), pages 119-132.
    6. Martello, Silvano & Monaci, Michele, 2020. "Algorithmic approaches to the multiple knapsack assignment problem," Omega, Elsevier, vol. 90(C).
    7. Geir Dahl & Njål Foldnes, 2006. "LP based heuristics for the multiple knapsack problem with assignment restrictions," Annals of Operations Research, Springer, vol. 146(1), pages 91-104, September.
    8. Dimitrov, Nedialko B. & Solow, Daniel & Szmerekovsky, Joseph & Guo, Jia, 2017. "Emergency relocation of items using single trips: Special cases of the Multiple Knapsack Assignment Problem," European Journal of Operational Research, Elsevier, vol. 258(3), pages 938-942.
    9. Martin Feuerman & Harvey Weiss, 1973. "A Mathematical Programming Model for Test Construction and Scoring," Management Science, INFORMS, vol. 19(8), pages 961-966, April.
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