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Binarization Technique Comparisons of Swarm Intelligence Algorithm: An Application to the Multi-Demand Multidimensional Knapsack Problem

Author

Listed:
  • José García

    (Escuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile)

  • Paola Moraga

    (Escuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile)

  • Broderick Crawford

    (Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile)

  • Ricardo Soto

    (Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile)

  • Hernan Pinto

    (Escuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile)

Abstract

In order to minimize execution times, improve the quality of solutions, and address more extensive target situations, optimization techniques, particularly metaheuristics, are continually improved. Hybridizing procedures are one of these noteworthy strategies due to their wide range of applications. This article describes a hybrid algorithm that combines the k-means method to produce a binary version of the cuckoo search and sine cosine algorithms. The binary algorithms are applied on the NP -hard multi-demand multidimensional knapsack problem. This problem is of particular interest because it has two types of constraints. The first group of constraints is related to the capacity of the knapsacks, and a second type is associated with the demand that must be met. Experiments were undertaken to acquire insight into the contribution of the k-means technique and the local search operator to the final results. Additionally, a comparison is made with two other types of binarization, the first based on a random method and the second based on the percentile concept. The results reveal that the k-means hybrid algorithm consistently provides superior results in most cases studied. In particular, incorporating the local search operator improved the results by an average of 0.23%. On the other hand, when comparing the results with 100 items and 30-30 restrictions, k-means was 1.06% better on average than the random operator.

Suggested Citation

  • José García & Paola Moraga & Broderick Crawford & Ricardo Soto & Hernan Pinto, 2022. "Binarization Technique Comparisons of Swarm Intelligence Algorithm: An Application to the Multi-Demand Multidimensional Knapsack Problem," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3183-:d:905812
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    References listed on IDEAS

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    1. Paola Cappanera & Marco Trubian, 2005. "A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 82-98, February.
    2. Lai, Xiangjing & Hao, Jin-Kao & Yue, Dong, 2019. "Two-stage solution-based tabu search for the multidemand multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 274(1), pages 35-48.
    3. José García & José V. Martí & Víctor Yepes, 2020. "The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm," Mathematics, MDPI, vol. 8(6), pages 1-22, May.
    4. Broderick Crawford & Ricardo Soto & Gino Astorga & José García & Carlos Castro & Fernando Paredes, 2017. "Putting Continuous Metaheuristics to Work in Binary Search Spaces," Complexity, Hindawi, vol. 2017, pages 1-19, May.
    5. José García & Gino Astorga & Víctor Yepes, 2021. "An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics," Mathematics, MDPI, vol. 9(3), pages 1-20, January.
    6. George J. Beaujon & Samuel P. Marin & Gary C. McDonald, 2001. "Balancing and optimizing a portfolio of R&D projects," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(1), pages 18-40, February.
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