Optimization Methods for Redundancy Allocation in Hybrid Structure Large Binary Systems

Petru Cașcaval and Florin Leon ()
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Petru Cașcaval: Faculty of Automatic Control and Computer Engineering, “Gheorghe Asachi” Technical University of Iasi, Bd. Mangeron 27, 700050 Iasi, Romania
Florin Leon: Faculty of Automatic Control and Computer Engineering, “Gheorghe Asachi” Technical University of Iasi, Bd. Mangeron 27, 700050 Iasi, Romania

Mathematics, 2022, vol. 10, issue 19, 1-33

Abstract: This paper addresses the issue of optimal redundancy allocation in hybrid structure large binary systems. Two aspects of optimization are considered: (1) maximizing the reliability of the system under the cost constraint, and (2) obtaining the necessary reliability at a minimum cost. The complex binary system considered in this work is composed of many subsystems with redundant structure. To cover most of the cases encountered in practice, the following kinds of redundancy are considered: active redundancy, passive redundancy, hybrid standby redundancy with a hot or warm reserve and possibly other cold ones, triple modular redundancy (TMR) structure with control facilities and cold spare components, static redundancy: triple modular redundancy or 5-modular redundancy (5MR), TMR/Simplex with cold standby redundancy, and TMR/Duplex with cold standby redundancy. A classic evolutionary algorithm highlights the complexity of this optimization problem. To master the complexity of this problem, two fundamentally different optimization methods are proposed: an improved evolutionary algorithm and a zero-one integer programming formulation. To speed up the search process, a lower bound is determined first. The paper highlights the difficulty of these optimization problems for large systems and, based on numerical results, shows the effectiveness of zero-one integer programming.

Keywords: redundancy allocation; hybrid structure binary systems; Markov chains; evolutionary algorithms; RELIVE algorithm; zero-one integer programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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