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An evolutionary computation approach to solving repairable multi-state multi-objective redundancy allocation problems

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Abstract

The redundancy allocation problem (RAP) is an optimization problem for maximizing system reliability at a predetermined time. Among the several extensions of RAPs, those considering multi-state and repairable components are the closest ones to real-life availability engineering problems. However, despite their practical implications, this class of problems has not received much attention in the RAP literature. In this paper, we propose a multi-objective nonlinear mixed-integer mathematical programming to model repairable multi-state multi-objective RAPs (RMMRAPs) where a series of parallel systems experiencing repairs, partial failures, and component degrading through time is considered. The performance of a component depends on its state and may decrease/increase due to minor and major failures/repairs which are modeled by a Markov process. The proposed RMMRAP allows for configuring multiple components and redundancy levels in each sub-system while evaluating multiple objectives (i.e., availability and cost). A customized version of the non-dominated sorting genetic algorithm (NSGA-II), where constraints are handled using a combination of penalty functions and modification strategies, is introduced to solve the proposed RMMRAP. The performance of the proposed NSGA-II and that of an exact multi-objective mathematical solution procedure, known as the epsilon-constraint method, are compared on several benchmark RMMRAP instances. The results obtained show the relative dominance of the proposed customized NSGA-II over the epsilon-constraint method.

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Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their insightful comments and suggestions.

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Authors and Affiliations

  1. Business Systems and Analytics Department, Distinguished Chair of Business Systems and Analytics, La Salle University, Philadelphia, PA, 19141, USA

    Madjid Tavana

  2. Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098, Paderborn, Germany

    Madjid Tavana

  3. Department of Industrial Engineering, South-Tehran Branch, Islamic Azad University, Tehran, Iran

    Kaveh Khalili-Damghani & Zeynab Oveisi

  4. Department of Mathematics and Statistics, York University, Toronto, Canada

    Debora Di Caprio

  5. Polo Tecnologico IISS G. Galilei, Bolzano, Italy

    Debora Di Caprio

Authors
  1. Madjid Tavana
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  2. Kaveh Khalili-Damghani
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  3. Debora Di Caprio
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  4. Zeynab Oveisi
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Corresponding author

Correspondence to Kaveh Khalili-Damghani.

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Tavana, M., Khalili-Damghani, K., Di Caprio, D. et al. An evolutionary computation approach to solving repairable multi-state multi-objective redundancy allocation problems. Neural Comput & Applic 30, 127–139 (2018). https://doi.org/10.1007/s00521-016-2676-y

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  • DOI: https://doi.org/10.1007/s00521-016-2676-y

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