Redundancy Allocation Problem Research Articles

Application of RRAP reliability optimization as a test of nature-inspired algorithms

This paper presents a discussion on the application of two swarm intelligence algorithms, Cuckoo Search (CS) and Firey Algorithm (FA), to maximize the reliability of two complex systems with resource constraints, which have been well-known in the literature. The reliability of the systems is also evaluated using several classical methods. The results indicate that although the CS algorithm, which utilizes Lévy flight, is eective, the FA rey algorithm outperformed it in the presented optimization tasks, within the given parameter range. These ndings contribute to the ongoing discussion on using nature-inspired algorithms for solving Reliability Redundancy Allocation Problem (RRAP) problems, and the two test scenarios used in the study can be useful for validating other algorithms in RRAP problems. The paper introduces metrics and methods for analyzing and comparing the performance of algorithms in RRAP optimization, including the comparison of criterion function values and other parameters introduced in the paper. Additionally, the paper discusses statistical analyses of variance (ANOVA) with post-hoc RIR Tuckey tests.

Redundancy allocation problem with a mix of components for a multi-state system and continuous performance level components

Redundancy allocation problem with a mix of components for a multi-state system and continuous performance level components

Integrating Statistical Simulation and Optimization for Redundancy Allocation in Smart Grid Infrastructure

It is a critical issue to allocate redundancy to critical smart grid infrastructure for disaster recovery planning. In this study, a framework to combine statistical prediction methods and optimization models for the optimal redundancy allocation problem is presented. First, statistical simulation methods to identify critical nodes of very large-scale smart grid infrastructure based on the topological features of embedding networks are developed, and then a linear integer programming model based on generalized assignment problem (GAP) for the redundancy allocation of critical nodes in smart grid infrastructure is presented. This paper aims to contribute to the field by employing a general redundancy allocation problem (GRAP) model from high-order nonlinear to linear model transformation. The model is specifically implemented in the context of smart grid infrastructure. The innovative linear integer programming model proposed in this paper capitalizes on the logarithmic multiplication property to reframe the inherently nonlinear resource allocation problem (RAP) into a linearly separable function. This reformulation markedly streamlines the problem, enhancing its suitability for efficient and effective solutions. The findings demonstrate that the combined approach of statistical simulation and optimization effectively addresses the size limitations inherent in a sole optimization approach. Notably, the optimal solutions for redundancy allocation in large grid systems highlight that the cost of redundancy is only a fraction of the economic losses incurred due to weather-related outages.

Markov-based reliability model for a mixed redundant system and parallel genetic algorithm with knowledge archives for a redundancy allocation problem

Markov-based reliability model for a mixed redundant system and parallel genetic algorithm with knowledge archives for a redundancy allocation problem

A new model for reliability redundancy allocation problem with component mixing

Reliability Redundancy Allocation Problem (RRAP) is a well-known problem in reliability optimization. In most of the previous research in RRAP, it is assumed that the components allocated to each subsystem are of the same type. This assumption limits the possible choices for the subsystem. In this paper, a new RRAP is proposed where the components allocated to each subsystem can be non-identical, and the redundancy strategy is a decision variable that can be active, standby, mixed, or none. In the proposed RRAP, both the active and the standby components can be independently of different types, which has not been considered in any of the previous studies. Since RRAP is an NP-hard problem, an adapted genetic algorithm is presented to search for the optimal solution of the proposed problem. Finally, some well-known problems are investigated to compare the proposed model with the previous ones. The obtained results show that the proposed RRAP can improve the reliability of the system in different cases by 10 % to 63 % in terms of the maximum possible improvement index.

Multi-task optimization in reliability redundancy allocation problem: A multifactorial evolutionary-based approach

Evolutionary multi-task optimization attempts to solve multiple optimization problems simultaneously by modeling the solution structures of two or more problems within a single encoding. In this paper, we report a novel way for evolutionary multi-task optimization in the reliability redundancy allocation problem exploiting the concepts of the popular multifactorial evolutionary algorithm (MFEA). We demonstrate the working of the proposed method considering two test sets and show how they can be concurrently solved using the MFEA. In the first test set, we consider two optimization tasks (case studies): the complex (bridge) system and the series-parallel system. In the second test set, there are two optimization tasks: the over-speed protection system for the gas turbine and the life support system in a space capsule. The common attributes between the two systems, within a set, complement each other to enhance the evolution process through implicit knowledge transfer. We present the comparative results considering existing evolutionary methods such as particle swarm optimization, genetic algorithm, simulated annealing, differential evolution, and ant colony optimization. Results are analyzed and compared using the average reliability, best reliability, computation time, performance ranking, and the popular statistical significance test of analysis of variance. The outcome shows that our proposed approach can solve the multiple case studies of RRAP simultaneously without compromising the solution quality. Moreover, our MFEA based solution method tops the rank among all approaches and provides significant improvement in computation time where it gains 28.02% and 14.43% of improvement in computation time for first and second test set, respectively, when compared with genetic algorithm. The percentage improvements in the computational time of the MFEA significantly increases when it is compared with other approaches.

Optimization of time based fuzzy multi-objective reliability redundancy allocation problem for [formula omitted] system using tuning and neighborhood based fuzzy MOPSO algorithm

In this paper, a time based fuzzy multi objective reliability redundancy allocation problem (FMORRAP) is proposed for the xj−out−of−m series–parallel system. The main objective is to maximize the system reliability with minimization of system cost and system repairing cost by optimizing the number of redundant components at each stage. The objectives are achieved by satisfying entropy constraints with limited redundant components at each stage and same for the whole system. Here the uncertainty of reliability, cost and repairing cost of each component is maintained by using triangular fuzzy number (TFN). The decreasing factor of component reliability and cost follows the change in the length of radius for the inverse logarithmic spiral with respect to time. Similarly the increasing factor of component repairing cost follows the same for the logarithmic spiral. Tuning and Neighborhood based Fuzzy Multi-Objective Particle Swarm Optimization (TNF-MOPSO) algorithm is proposed to solve fuzzy multi-objective optimization problems (MOOP). The proposed problem and proposed algorithm are illustrated by using a bench mark problem. The proposed algorithm produced better membership of objective functions for most of the time values and high satisfaction level of reliability for all values of the time parameter. It also outperforms the standard approaches MOPSO and NF-MOPSO.

A novel reliability redundancy allocation problem formulation for complex systems

Reliability Redundancy Allocation Problem (RRAP) aims to optimize system design with respect to certain resource constraints. For the most of RRAP studies, it is commonly assumed that the subsystems form a series-parallel or bridge structure, while the redundant components in the same subsystem are placed in parallel. To generalize system structures, this paper proposes a novel RRAP for complex systems. The complex system structure is modeled with a graph, where the vertices and edges represent the components and connections between them, respectively. To calculate the system reliability from its structure graph, an automated calculation method based on functionality multi-graph is put forward. The components are classified into various clusters based on the system functionalities they provide, then a multi-graph is constructed by fusing the vertices in the same cluster into a hyper-vertex. Spanning trees are derived from functionality multi-graph, and a validity test is performed to identify valid system configurations. On this basis, a factoring theorem-based algorithm is devised to calculate system reliability. Comparative experiments are carried out on six benchmark problems, the results of which compare favorably to previous RRAP studies. A case study of security system design is also conducted to demonstrate the practicality of our proposed method.

An efficient simulation optimization method for the redundancy allocation problem with a chance constraint

We explore the Redundancy Allocation Problem (RAP) under the objective of minimizing the cost of a production system of general topology in which system reliability is treated as a chance constraint. A novel simulation optimization-based solution method grounded in the concepts of the trust region and response surface methodology is proposed to efficiently solve the generalized RAP (GRAP) under random system survival times. The generalizability of the RAP model and efficiency of the solution method allows for our approach to be utilized in a wide variety of real-world applications. We demonstrate in a series of numerical experiments based on production systems of varying complexity that the finite convergence of the proposed method is much more efficient than the commonly-used genetic algorithm. It is shown that on a simple bridge network, only the proposed algorithm can find the true optimal solution to the GRAP under an allotted computational budget. On a complex network which includes series, parallel, and logical relationships, the proposed algorithm is also shown to find solutions to the GRAP which have substantially lower total system cost than those found by GA under a wide variety of scenarios.

Optimization of time-dependent fuzzy multi-objective reliability redundancy allocation problem for n-stage series–parallel system

Optimization of time-dependent fuzzy multi-objective reliability redundancy allocation problem for n-stage series–parallel system

Solving Redundancy Allocation Problems using Jaya Algorithm

Reliability-based design is related to the performance analysis of engineering systems. The redundancy allocation problem is one of the most common problems in the reliability-based design approach. The redundancy allocation problem determines the redundancy level of components in a system to maximize system reliability, subject to several constraints. In recent years, obtaining solutions to reliability-related redundancy allocation problems by means of evolving meta-heuristic algorithms has appealed to researchers due to the several drawbacks of classical mathematical methods. Meta-heuristics have shown the potential of obtaining precise solution in optimization problems and many techniques have been applied in the literature for optimal redundancy allocation. In this paper, a recently developed Jaya optimization algorithm is proposed to be applied for redundancy allocation to maximize system reliability. The Jaya algorithm is a simple, population-based intelligent meta-heuristic algorithm consisting of a single phase and an algorithm-specific parameter-less algorithm. This paper aims to present an application of the Jaya algorithm for searching the optimal solution of two redundancy allocation problems from the literature with nonlinear constraints so that system reliability is maximized. The first problem is the over speed protection system for a gas turbine, whose control system is modelled as a four-stage series system. The objective is to determine the optimal level of redundancy of the valves of the protection system under cost and weight constraints. The second one is the redundancy allocation problem of a five-stage series system with volume, weight, and cost constraints. The results are validated by comparing them with two other meta-heuristics.

Optimization of the redundancy allocation problem: Genetic algorithm and Monte Carlo simulation with discrete events

Sistem güvenilirliği, iletişim ve elektronik sistemler gibi ileri teknolojiye sahip modern mühendislik sistemlerinin tasarımı ve analizinde yaygın olarak kullanılan önemli ölçütlerden biridir. Günlük hayatımıza giren, çoğu çalışma alanında ve sosyal yaşamda kullandığımız uygulamaları doğrudan etkileyen altyapı tasarım problemlerinin bir kısmı güvenilirlik ölçütünü dikkate alan eniyileme problemi olarak tanımlanmaktadır. Bu nedenle bu tür problemlerin çözümü, farklı disiplinlerde çalışan birçok araştırmacının yoğun ilgisini çekmektedir. Sistem güvenilirliğinin eniyilenmesi için alan yazında yaygın olarak kullanılan Yedek Bileşen Tahsis Problemi (YBTP), sistemde yer alan bileşenlere paralel olarak yerleştirilen kullanıma hazır bileşenler ile yeni sistemlerin tasarlanması olarak tanımlanabilir. Böylece, güvenilirlik başarım ölçütü dikkate alınarak daha yüksek güvenilirlik değerine sahip sistem tasarımlarının elde edilmesi sağlanabilmektedir. Sistem özelliklerine bağlı olarak seçilen uygun yöntemle sistemin güvenilirlik değeri elde edilir. Bu çalışmada, artan arıza ve tamir oranlarının dikkate alındığı YBTP’de sistem güvenilirliğini gerçekçi bir yaklaşımla tahmin etmek için Kesikli Olaylı Benzetim (KOB) modeli, sistemin eniyilenmesi için ise Genetik Algoritma (GA) geliştirilmiştir. KOB modelinin geçerliliği test problemleri üzerinde gösterilmiştir. Önerilen yaklaşımla, YBTP için daha yüksek güvenilirliğe sahip sistem tasarımlarının daha düşük maliyetlerle elde edilebilmesi sağlanmıştır.

Redundancy Allocation of Components with Time-Dependent Failure Rates

The Redundancy Allocation Problem (RAP) is well-known in the field of reliability optimization. In this paper, RAP is investigated assuming that the distribution of the time to failure of the components has the form of an Erlang distribution with a time-dependent rate parameter and considering that the choice of redundancy for each subsystem can be none, active, standby or mixed. A genetic algorithm is used to solve the problem of optimal allocation. To analyze the effect of the time dependence, some numerical examples are worked out. Then, a case study of RAP from the literature is analyzed. The obtained results show that time dependence of the failure time distribution parameters can lead to significant differences in the optimal redundancy allocation.

Strategy selection for multi-objective redundancy allocation problem in a k-out-of-n system considering the mean time to failure

Strategy selection for multi-objective redundancy allocation problem in a k-out-of-n system considering the mean time to failure

A Markov chain-based genetic algorithm for solving a redundancy allocation problem for a system with repairable warm standby components

Many studies have been conducted on designing systems based on the redundancy allocation problem (RAP). However, considering repairable warm-standby components (which are subject to failure even in an idle state) is somewhat neglected by researchers due to the complex mathematical models. One of the crucial aspects of these systems is considering the probability of failure when switching to a standby component or subsystem. This study tries to highlight these imperfect switching and switch selection strategies in the redundancy allocation designs. In this regard, this article is dedicated to developing two RAP models (a single objective and a bi-objective) with warm standby repairable components by proposing a solving approach based on the genetic algorithm (GA) and Markov chains. Since the model’s objective functions minimize the system’s mean time to failure (MTTF) and cost, we discussed how imperfect switches affect the total system’s cost and mean time to failure for the proposed RAPs. Finally, we adopted a GA and a non-dominated sorting genetic algorithm (NSGA-II) to solve the proposed models due to the models’ complexity. Solving these models clearly indicates the critical role of selecting an appropriate switching strategy on the system’s costs and reliability.

Reliable design optimization for industrial hybrid energy systems with uncertain sustainable energy

More and more attention has been paid to the industrial hybrid energy systems which comprise fossil energy and renewable energy for achieving carbon neutrality. Wherein, the uncertainty of renewable energy, fluctuation of energy requirement from process units, and failure rate of energy conversion devices have significant effects on the reliability of industrial hybrid energy systems and thus restrict the application and promotion. How to simultaneously address these issues for realizing the reliable design of industrial hybrid energy systems has been a matter of great concern and challenge. Hence, a systematic reliable design optimization method is presented in this study to tackle these challenges. In this study, the two-stage stochastic programming method is implemented to conduct the uncertain optimization in dealing with the uncertainty of renewable energy and fluctuation of energy requirement, while a mixed stand-by redundancy allocation problem is proposed for simultaneously enhancing the reliability and minimizing the number of stand-by devices. A multi-objective mixed integer non-linear programming framework using reliability and total annual cost as the dual objectives is then formulated and applied to a refinery site for the reliable design optimization of the industrial hybrid energy system. According to the solution results, compared to the minimum total annual cost scheme without stand-by redundancy, the maximum reliability of the industrial hybrid energy system can reach 0.9878 using the stand-by redundancy strategy. As a result, the reliability can be significantly enhanced by 44%, with only a 5% increment of the total annual cost. Moreover, a Pareto frontier under multi-objective optimization is constructed, and the optimization schemes at the Pareto frontier can realize the trade-off between reliability and the total annual cost of the industrial hybrid energy system. Subsequently, a reliability-gain index is proposed to further evaluate the trade-off schemes and thus guide the choice of appropriate design schemes.

A novel binary-addition simplified swarm optimization for generalized reliability redundancy allocation problem

Abstract Network systems are commonly used in various fields, such as power grids, Internet of Things, and gas networks. The reliability redundancy allocation problem is a well-known reliability design tool that needs to be developed when the system is extended from a series-parallel structure to a more general network structure. Therefore, this study proposes a novel reliability redundancy allocation problem, referred to as the general reliability redundancy allocation problem, to be applied in network systems. Because the general reliability redundancy allocation problem is NP-hard, a new algorithm referred to as binary-addition simplified swarm optimization is proposed in this study. Binary-addition simplified swarm optimization combines the accuracy of the binary addition tree algorithm with the efficiency of simplified swarm optimization, which can effectively reduce the solution space and speed up the time required to find high-quality solutions. The experimental results show that binary-addition simplified swarm optimization outperforms three well-known algorithms: the genetic algorithm, particle swarm optimization, and simplified swarm optimization in high-quality solutions and high stability on six network benchmarks.

Redundancy allocation under state‐dependent distributional uncertainty of component lifetimes

In this paper, we consider a redundancy allocation problem in a series‐parallel system with uncertain component lifetimes of multiple states, which involves multitype components and mixed redundancy strategy. We develop a distributionally robust redundancy allocation model using state‐dependent ambiguity set, which describes the mean, expected cross‐deviation, and the support conditional on each state of the component lifetime distribution. Our structural analysis of the worst‐case system reliability function identifies a concave equivalent for the conditional worst‐case reliability function in each state and achieves an averaged finite piece‐wise affine representation for the overall worst‐case system reliability function, which enjoys valuable operational insights for reliability evaluation and scalable optimization of the redundancy designs. Furthermore, we analyze the reliability guarantees for the worst‐case reliability in optimality under possible misspecification of ambiguity‐set parameters, which admit the structure of “Reliability Target + Target Surplus + Estimated Elasticity,” and insightfully imply that the auxiliary dual variables obtained via solving the design problem can be regarded as the scale of elasticity. Computationally, the redundancy design problem can be linearized and reformulated as a mixed 0–1 second‐order cone program. Exploiting the above finite piece‐wise affine structure of the worst‐case reliability function, the design problem also admits a practical iterative decomposition scheme with finite convergence, which is more scalable especially for the possible situations of large number of states in practice. Finally, numerical experiments including a case with real‐life data of braking system components well justify the value of state information incorporated by our model in producing favorable cost‐effective redundancy designs for reliability operations.

Hybridization in nature inspired algorithms as an approach for problems with multiple goals: An application on reliability–redundancy allocation problems

This paper focuses on approaching reliability–redundancy allocation problems, using hybrid schemes that consist of individual nature inspired algorithms. The aim is to investigate if hybridization is an efficient way to approach problems with multiple goals. Therefore, known algorithms that have been successfully applied to reliability and redundancy allocation problems in literature are implemented as part of hybrid schemes in this study. The idea behind that is to study whether an efficient hybrid scheme is the outcome of the hybridization of (individual) efficient algorithms. The performance of the nine proposed schemes and the individual algorithms is tested on ten well-known artificial and real-world case studies, from the field of reliability engineering. The numerical results are compared to others from literature highlighting the efficiency of the proposed hybrid schemes and consequently, support the hypothesis that hybridization can enhance the performance of optimization methods. The experimental results demonstrate that among the nine hybrid schemes, the one consisting of Bat Algorithm and Firefly Algorithm shows the best performance.

Techno-Economic Green Optimization of Electrical Microgrid Using Swarm Metaheuristics

In electrical power engineering, elements such as reliability analysis, modeling, and optimization for complex systems are of the utmost importance. Although there exist myriad studies regarding reliability optimization with conventional methods, researchers are still seeking to find more efficient and accurate methods to address the issue of the redundancy allocation problem. To that effect, an ideal power energy management approach is put forward for the operation of a hybrid microgrid system with different kinds of productions. In the present study, we suggest three algorithms in order to optimize the series-parallel power energy system: the Firefly (FA), Bat (BA), and Interior Search (ISA) algorithms. Moreover, the reliability estimate of the system is solved with the Ushakov algorithm (UMGF). The components may completely fail, which decreases their performance rate. Furthermore, the optimization results are achieved using objective functions that include the total cost of the system, emission gases (NOX, SO2, and CO2) of the power production from fuel cells, diesel generators, and gas turbines, and take into consideration the dependability indices. Devices used in power subsystems are characterized based on their dependabilities, performances, capital costs, and maintenance costs. Reliability hinges on a functioning system, which naturally entails meeting customer demand; as a result, it is influenced by the accumulated batch curve. This method provides an idea with regards to the economic cost optimization of microgrid systems. Finally, we present the results of numeric simulations.