Reliability–redundancy allocation problem considering optimal redundancy strategy using parallel genetic algorithm
Introduction
Reliability is now a matter of greater concern than in the past, because the increasing complexity of modern engineering and service systems has led to a dramatic rise in their susceptibility to faults. Methods to enhance the reliability of a system involve (i) the improvement of component reliability, (ii) the installation of redundant components in parallel, (iii) combinations of (i) and (ii), and (iv) component replacement with substitutable components [1], [2].
Reliability optimization problems, using the approaches for improving the system reliability mentioned above, optimize reliability objective(s), e.g., the maximization of system reliability or minimization of required resources subject to some design constraints. That is, they suggest design choices to the system design engineers such as for components, redundancy levels, and redundant configuration. Generally, reliability optimization problems are divided into reliability allocation problem, redundancy allocation problem, and reliability–redundancy allocation problem (RRAP). The RRAP is a composite of the other two problems and determines the reliabilities and the redundancy levels of components to maximize system reliability under design constraints such as those for cost, volume, or weight.
The design strategies used to improve system reliability by installing redundant components are divided into two main approaches: active and standby redundancy. In an active redundant system, both the primary and secondary components are exposed to operating stresses. Hence, their failure potentials are regarded as equivalent, and secondary components may break before they are employed. A standby system commonly requires additional equipment, called a fault detector/switch, for detecting the failure of a primary component and activating a standby component. The standby redundancy strategies, based on the standby status of the redundant components, are classified as hot, warm, and cold standby. The cold standby of them is most effective to improve system reliability because it is assumed that standby components are completely shielded against operating stresses. In addition, hot or warm standby is mostly suitable for particular systems. Hot standby is chiefly used for uninterruptible or near-uninterruptible systems such as uninterruptible power supplies or network servers and routers. Examples of warm standby systems are power plants, redundant hard disks, and wireless sensors networks, which require the ability to switch to a primary component [3]. Thus, in general systems, either active or cold standby has been mainly considered as the redundancy strategy for improving the reliability of a system, and the advantageous strategy depends on the reliabilities of a fault detector/switch and components, in addition to redundancy levels. However, most studies on reliability optimization have considered only active redundancy as the redundant configuration.
One of the research areas regarding RRAP is to develop methods for solving it efficiently because it was determined to be an NP-hard problem in [4]. Recently, numerous studies using meta-heuristics as well as hybrid forms have been reported. These studies include ones employing genetic algorithms (GAs) [5], [6], [7], [8], ant colony optimization (ACO) [9], [10], simulated annealing (SA) [11], immune algorithms [12], [13], artificial bee colonies [14], [15], particle swarm optimization (PSO) [16], [17], cuckoo search (CS) algorithms [18], [19], and imperialist competitive algorithms [20]. The hybrid algorithms include neural networks—GA [21], [22], SA–GA [23], harmony search (HS)–PSO [24], differential evolution (DE)–HS [25], CS–GA [26], DE–PSO [27]. In recent years, Liu and Quin [28], [29] proposed a modified PSO algorithm and hybrid tabu search–DE algorithm, respectively. Huang [30] suggested a particle-based simplified swarm optimization algorithm, which is a hybrid form of PSO and simplified swarm optimization. He et al. [31], Liu [32], and Zhu and Liu [33] proposed a novel artificial fish swarm algorithm, an improved bat algorithm and a hybrid TS–interior search algorithm, respectively. Khorshidi et al. [34] investigated the best combination of imperialist competitive algorithm's parameters for RRAP on series–parallel system. Zhang and Chen [35] suggested the multi-objective PSO algorithm for RRAP under different operating or environmental conditions. Additionally, recent interesting studies on redundancy allocation problem (RAP), similar to RRAP, involve the following: Teimouri et al. [36] suggested the memory-based electromagnetism-like mechanism (MBEM) and obtained superior results in the benchmarks and large-size example for RAP. It is worthy of notice that MBEM is a powerful algorithm designed for continuous solution spaces. Mousavi et al. [37] proposed the RAP for series–parallel system considering quantity discounts and the improved fruit fly optimization algorithm to solve the problem. Khorshidi et al. [38] suggested the problem to decide upon both redundancy levels and maintenance activities for optimizing system reliability and costs in multi-state weighted k-out-of-n system. Guilani et al. [39] proposed the simulation-based optimization approach for the RAP of a system composed of components with increasing failure rates.
While studies on the RRAP focus on active redundant systems, Ardakan and Hamadani [5] presented a RRAP considering cold standby redundancy for the first time. However, they used an approximated reliability function for the cold standby system based on [40] and did not consider active redundancy. Therefore, this paper proposes an exact reliability model for cold standby with an imperfect fault detector/switch modeled using a continuous time Markov chain (CTMC). In addition, a RRAP with a choice of redundancy strategies is suggested, and in the RRAP, the optimal strategies for individual subsystems are additionally considered to be the decision variables. New examples that modify the resource constraints of popular benchmarks are also recommended. Finally, a parallel genetic algorithm (PGA) to solve them with a non-linear objective function and constraints is presented.
The remainder of this article is organized as follows: In Section 2, the basic formulation for a RRAP is introduced, and the reliability model for a cold standby system with an imperfect fault detector/switch is presented. Section 3 proposes the PGA for solving the RRAP with a non-linear objective function and constraints. Section 4 analyzes the results of numerical experiments to demonstrate the advantage of the new reliability model, the performance of PGA, and the improvement in system reliability enabled by the ability to choose the optimal redundancy strategy for individual subsystems. Finally, the conclusions are presented in Section 5.
Section snippets
Reliability–redundancy allocation problem
To maximize the reliability of an overall system under design constraints, a RRAP determines the component reliability and redundancy levels for individual subsystems. It is formulated by mixed integer programming with linear or nonlinear constraints, and represented as follows:where depends on system configuration such as series, series–parallel, or complex configuration. Variables ri and ni are the decision variables of an RRAP.
Parallel genetic algorithm
GAs have been used most frequently to address in the optimization problem, and their performance has been verified. In this study, a PGA for solving RRAP is proposed, as shown in Fig. 3. It is composed of some unit GAs such that they independently search for the solution to a problem and periodically cooperate among themselves by communicating the useful information of each group. The main purpose of the parallelization is to prevent them from prematurely converging to a local optimum and
Numerical experiments
The experiments in this study were conducted using popular benchmark problems: a series system (benchmark 1, Fig. 8), series–parallel system (benchmark 2, Fig. 9), and complex system (benchmark 3, Fig. 10). They are composed of five subsystems with parallel redundant components. Thus, the system reliability functions of the individual benchmarks are Eqs. (15), (16), (17), respectively, where .
Conclusion
This article presents the exact reliability function for a cold standby redundant system with an imperfect detector/switch modeled using CTMC. The approximating error of the previous model (Eq. (6)) was numerically evaluated using well-known RRAP benchmark problems and was a meaningful level to sufficiently influence the determination of the system structure. Therefore, the proposed reliability model in this paper can be clearly recommended for designing a large-scale or high reliability system.
References (45)
- et al.
Optimal sequencing of warm standby elements
Comput Ind Eng
(2013) On the computational complexity of reliability redundancy allocation in a series system
Oper Res Lett
(1992)- et al.
Multiobjective optimization by genetic algorithmsapplication to safety systems
Reliab Eng Syst Saf
(2001) - et al.
Alternatives and challenges in optimizing industrial safety using genetic algorithms
Reliab Eng Syst Saf
(2004) - et al.
Basics of genetic algorithms optimization for rams applications
Reliab Eng Syst Saf
(2006) - et al.
Ant system for reliability optimization of a series system with multiple-choice and budget constraints
Reliab Eng Syst Saf
(2005) - et al.
New methods to minimize the preventive maintenance cost of series-parallel systems using ant colony optimization
Reliab Eng Syst Saf
(2005) Ias based approach for reliability redundancy allocation problems
Appl Math Comput
(2006)- et al.
An effective immune based two-phase approach for the optimal reliability–redundancy allocation problem
Appl Math Comput
(2011) - et al.
Solving reliability redundancy allocation problems using an artificial bee colony algorithm
Comput Oper Res
(2011)
An efficient two phase approach for solving reliability–redundancy allocation problem using artificial bee colony technique
Comput Oper Res
An improved particle swarm optimization algorithm for reliability problems
ISA Trans
Improved cuckoo search for reliability optimization problems
Comput Ind Eng
Modified imperialist competitive algorithm based on attraction and repulsion concepts for reliability–redundancy optimization
Expert Syst Appl
An effective global harmony search algorithm for reliability problems
Expert Syst Appl
A coevolutionary differential evolution with harmony search for reliability–redundancy optimization
Expert Syst Appl
A hybrid cuckoo search and genetic algorithm for reliability–redundancy allocation problems
Comput Ind Eng
A particle-based simplified swarm optimization algorithm for reliability redundancy allocation problems
Reliab Eng Syst Saf
A novel artificial fish swarm algorithm for solving large-scale reliability–redundancy application problem
ISA Trans
Improved bat algorithm for reliability–redundancy allocation problems
Int J Secur Appl
Multi-objective reliability redundancy allocation in an interval environment using particle swarm optimization
Reliab Eng Syst Saf
An efficient memory-based electromagnetism-like mechanism for the redundancy allocation problem
Appl Soft Comput
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