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

Paulo Figueroa-Torrez, Orlando Durán (), Broderick Crawford and Felipe Cisternas-Caneo
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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

Mathematics, 2023, vol. 11, issue 16, 1-23

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.

Keywords: cell formation problem; alternative routing; grouping machines; machine reliability; black widow optimization algorithm; metaheuristics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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