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A Binary Black Widow Optimization Algorithm for Addressing the Cell Formation Problem Involving Alternative Routes and Machine Reliability

Author

Listed:
  • Paulo Figueroa-Torrez

    (Escuela de Ingeniería Industrial, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Orlando Durán

    (Escuela de Ingeniería Mecánica, Pontificia Universidad Católica de Valparaíso, Valparaíso 2340025, Chile)

  • Broderick Crawford

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

  • Felipe Cisternas-Caneo

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

Abstract

The Cell Formation Problem (CFP) involves the clustering of machines to enhance productivity and capitalize on various benefits. This study addresses a variant of the problem where alternative routes and machine reliability are included, which we call a Generalized Cell Formation Problem with Machine Reliability (GCFP-MR). This problem is known to be NP-Hard, and finding efficient solutions is of utmost importance. Metaheuristics have been recognized as effective optimization techniques due to their adaptability and ability to generate high-quality solutions in a short time. Since BWO was originally designed for continuous optimization problems, its adaptation involves binarization. Accordingly, our proposal focuses on adapting the Black Widow Optimization (BWO) metaheuristic to tackle GCFP-MR, leading to a new approach named Binary Black Widow Optimization (B-BWO). We compare our proposal in two ways. Firstly, it is benchmarked against a previous Clonal Selection Algorithm approach. Secondly, we evaluate B-BWO with various parameter configurations. The experimental results indicate that the best configuration of parameters includes a population size ( P o p ) set to 100, and the number of iterations ( M a x i t e r ) defined as 75. Procreating Rate ( P R ) is set at 0.8, Cannibalism Rate ( C R ) is set at 0.4, and the Mutation Rate ( P M ) is also set at 0.4. Significantly, the proposed B-BWO outperforms the state-of-the-art literature’s best result, achieving a noteworthy improvement of 1.40%. This finding reveals the efficacy of B-BWO in solving GCFP-MR and its potential to produce superior solutions compared to alternative methods.

Suggested Citation

  • Paulo Figueroa-Torrez & Orlando Durán & Broderick Crawford & Felipe Cisternas-Caneo, 2023. "A Binary Black Widow Optimization Algorithm for Addressing the Cell Formation Problem Involving Alternative Routes and Machine Reliability," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3475-:d:1215221
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    References listed on IDEAS

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    1. Javid Jouzdani & Farnaz Barzinpour & Mohammad Ali Shafia & Mohammad Fathian, 2014. "Applying Simulated Annealing To A Generalized Cell Formation Problem Considering Alternative Routings And Machine Reliability," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-26.
    2. 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.
    3. Burbidge, John L., 1996. "The first step in planning group technology," International Journal of Production Economics, Elsevier, vol. 43(2-3), pages 261-266, June.
    4. Marcelo Becerra-Rozas & José Lemus-Romani & Felipe Cisternas-Caneo & Broderick Crawford & Ricardo Soto & Gino Astorga & Carlos Castro & José García, 2022. "Continuous Metaheuristics for Binary Optimization Problems: An Updated Systematic Literature Review," Mathematics, MDPI, vol. 11(1), pages 1-32, December.
    5. Das, K. & Lashkari, R.S. & Sengupta, S., 2007. "Reliability consideration in the design and analysis of cellular manufacturing systems," International Journal of Production Economics, Elsevier, vol. 105(1), pages 243-262, January.
    6. Amir Shabani & Behrouz Asgarian & Saeed Asil Gharebaghi & Miguel A. Salido & Adriana Giret, 2019. "A New Optimization Algorithm Based on Search and Rescue Operations," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-23, November.
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