Redundancy Allocation Problem Research Articles

Application of the NSGA-II algorithm to a multi-period inventory-redundancy allocation problem in a series-parallel system

In this paper, we formulate a mixed-integer binary non-linear programming model to study a series-parallel multi-component multi-periodic inventory-redundancy allocation problem (IRAP). This IRAP is a novel redundancy allocation problem (RAP) because components (products) are purchased under an all unit discount (AUD) policy and then installed on a series-parallel system. The total budget available for purchasing the components, the storage space, the vehicle capacities, and the total weight of the system are limited. Moreover, a penalty function is used to penalize infeasible solutions, generated randomly. The overall goal is to find the optimal number of the components purchased for each subsystem so that the total costs including ordering cost, holding costs, and purchasing cost are minimized while the system reliability is maximized, simultaneously. A non-dominated sorting genetic algorithm-II (NSGA-II), a multi-objective particle swarm optimization (MOPSO), and a multi-objective harmony search (MOHS) algorithm are applied to obtain the optimal Pareto solutions. While no benchmark is available in the literature, some numerical examples are generated randomly to evaluate the results of NSGA-II on the proposed IRAP. The results are in favor of NSGA-II.

New parallel swarm algorithm for smart sensor systems redundancy allocation problems in the Internet of Things

In recent years, various smart sensor systems have been integrated into the “Internet of Things (IOT)” with the advancement of sensing technology. A redundancy allocation is the safest, most convenient, and most economical way to increase the reliability of smart sensor systems. To solve the smart sensor systems redundancy allocation problem (RAP) in IOT, a cooperative parallel simplified swarm algorithm (pSSO) is presented in this study. This pilot study includes several innovative points. First, research is conducted to use the RAP in IOT. Second, the proposed pSSO is the first parallel algorithm to solve the RAP and the first one to parallelize the simplified swarm optimization (SSO) with the Taguchi method. A simple real-life example regarding shopping and shipping in TAOBAO is given to describe the way how to model the IOT used the RAP. As proof of the success of the proposed pSSO, detailed computational results from solving a series-parallel redundancy allocation problem with a mix of components is presented. The computational results reflect the efficiency of the pSSO proposed.

Multi-objective redundancy allocation problem for a system with repairable components considering instantaneous availability and strategy selection

Many Studies have been conducted on Redundancy Allocation Problem (RAP), but only a few of them have considered designing systems which operate for a certain period of time. Such temporary systems are not meant to operate for a long period of time (e.g. a manufacturing cell designed to produce a unique product with a small window of opportunity). Due to this fact, the investigation of the reliability at an infinite time will not be helpful; instead designing a system which perform optimally in a short period of time is of importance. additionally RAP's are inherently complex and classified as NP-Hard, as a result most proposed approaches, consider a set of simplified assumptions. Among these assumptions are the calculation of availability in the steady state (a time in which a system becomes completely stable), the use of non-repairable components, and setting predetermined configuration strategy (parallel, cold or warm standby subsystems). Unfortunately, these simplified assumptions do not conform to the real world conditions. Therefore, this article intends to develop an integrated algorithm to solve the reliability design problem considering instantaneous availability, repairable components, and the selection of configuration strategies based on the Markov processes and NSGA-II algorithm.

Efficient solution concepts and their application in uncertain multiobjective programming

Based on uncertainty theory, we investigate the relations among efficiency concepts of the multiobjective programming (MOP) with uncertain vectors. We first propose the uncertain MOP model, and study its convexity. Then, we define different efficiency concepts such as expected-value efficiency, expected-value proper efficiency, and establish their relations under the assumed conditions, which are illustrated through two numerical examples. Finally, in the uncertain environment, we apply the theoretical results to a redundancy allocation problem with two objectives in reparable parallel-series systems, and discuss how to obtain different types of efficient solutions according to the decision-maker's preferences.

A new model for reliability optimization of series-parallel systems with non-homogeneous components

In discussions related to reliability optimization using redundancy allocation, one of the structures that has attracted the attention of many researchers, is series-parallel structure. In models previously presented for reliability optimization of series-parallel systems, there is a restricting assumption based on which all components of a subsystem must be homogeneous. This constraint limits system designers in selecting components and prevents achieving higher levels of reliability. In this paper, a new model is proposed for reliability optimization of series-parallel systems, which makes possible the use of non-homogeneous components in each subsystem. As a result of this flexibility, the process of supplying system components will be easier. To solve the proposed model, since the redundancy allocation problem (RAP) belongs to the NP-hard class of optimization problems, a genetic algorithm (GA) is developed. The computational results of the designed GA are indicative of high performance of the proposed model in increasing system reliability and decreasing costs.

Allocation and sequencing in 1-out-of-N heterogeneous cold-standby systems: Multi-objective harmony search with dynamic parameters tuning

A redundancy allocation is a famous problem in reliability sciences. A lot of researcher investigated about this problem, but a few of them focus on heterogeneous 1-out-of-N: G cold-standby redundancy in each subsystem. This paper considers a redundancy allocation problem (RAP) and standby element sequencing problem (SESP) for 1-out-of-N: G heterogeneous cold-standby system, simultaneously. Moreover, here, maximizing reliability of cold-standby allocation and minimizing cost of buying and time-independent elements are considered as two conflict objectives. This problem is NP-Hard and consequently, devizing a metaheuristic to solve this problem, especially for large-sized instances, is highly desirable. In this paper, we propose a multi-objective harmony search. Based on Taguchi experimental design, we, also, present a new parameters tuning method to improve the proposed algorithm.

A novel strategy for redundant components in reliability--redundancy allocation problems

ABSTRACTThis article presents a new interpretation and formulation of the Reliability–Redundancy Allocation Problem (RRAP) and demonstrates that solutions to this new problem provide distinct advantages compared with traditional approaches. Using redundant components is a common method to increase the reliability of a system. In order to add the redundant components to a system or a subsystem, there are two traditional types of strategies called active and standby redundancy. Recently a new redundancy strategy, called the “mixed” strategy, has been introduced. It has been proved that in the Redundancy Allocation Problem (RAP), this new strategy has a better performance compared with active and standby strategies alone. In this article, the recently introduced mixed strategy is implemented in the RRAP, which is more complicated than the RAP, and the results of using the mixed strategy are compared with the active and standby strategies. To analyze the performance of the new approach, some benchmark problems on the RRAP are selected and the mixed strategy is used to optimize the system reliability in these situations. Finally, the reliability of benchmark problems with the mixed strategy is compared with the best results of the systems when active or standby strategies are considered. The final results show that the mixed strategy results in an improvement in the reliability of all the benchmark problems and the new strategy outperforms the active and standby strategies in RRAP.

Two-stage simplified swarm optimization for the redundancy allocation problem in a multi-state bridge system

The redundancy allocation problem involves configuring an optimal system structure with high reliability and low cost, either by alternating the elements with more reliable elements and/or by forming them redundantly. The multi-state bridge system is a special redundancy allocation problem and is commonly used in various engineering systems for load balancing and control. Traditional methods for redundancy allocation problem cannot solve multi-state bridge systems efficiently because it is impossible to transfer and reduce a multi-state bridge system to series and parallel combinations. Hence, a swarm-based approach called two-stage simplified swarm optimization is proposed in this work to effectively and efficiently solve the redundancy allocation problem in a multi-state bridge system. For validating the proposed method, two experiments are implemented. The computational results indicate the advantages of the proposed method in terms of solution quality and computational efficiency.

A redundancy strategy for minimizing cost in systems with non-disjoint subsystems under reliability constraint

The present paper solves a redundancy allocation problem under reliability constraint. To improve the system reliability, use of redundancy, i.e., use of additional components above the minimum number of components required for the system to operate, is a common practice. But it increases the total cost of the system as well. Thus the problem of allocating redundancy to coherent systems with competing choices of system-components needs to be optimally resolved so that the cost of adding redundancy is minimized. In this paper the problem of redundancy allocation is solved by minimizing the total cost subject to meeting a pre-assigned reliability target. The decision variables here are the number of redundancies. The methodology developed here can be applied to any coherent system, simple or complex. The computational complexity increases with the increase in complexity of the system design. The methodology of solving the redundancy allocation problem developed here yields a deterministic optimal solution, which is a polynomial time solution of an established NP-hard problem. Numerical examples have been included to illustrate the method developed here. The sensitivity of the optimal solution, augmented system reliability and related cost of using redundancy has been studied with respect to the specified reliability targets. No assumption about the form of the component life distribution has been made in the study.

Reliability optimization problems with multiple constraints under fuzziness

In reliability optimization problems diverse situation occurs due to which it is not always possible to get relevant precision in system reliability. The imprecision in data can often be represented by triangular fuzzy numbers. In this manuscript, we have considered different fuzzy environment for reliability optimization problem of redundancy. We formulate a redundancy allocation problem for a hypothetical series-parallel system in which the parameters of the system are fuzzy. Two different cases are then formulated as non-linear programming problem and the fuzzy nature is defuzzified into crisp problems using three different defuzzification methods viz. ranking function, graded mean integration value and α-cut. The result of the methods is compared at the end of the manuscript using a numerical example.

A multi-objective multi-state series-parallel redundancy allocation model using tuned meta-heuristic algorithms

ABSTRACTIn this paper, we study a series-parallel multi-objective multi-state redundancy allocation problem (MSRAP) with known performance levels and corresponding state probabilities. The problem is comprised of multiple subsystems in series and each subsystem is comprised of multiple components in parallel. The system components have a range of performance level from complete working to complete failure. The subsystems contain homogenous redundant components and the component prices come under an all-unit discount policy if a unique brand (type) is chosen for purchasing all subsystem components. Each component is characterised by its cost, weight and availability. The goals are to find the optimal combination of the components in each subsystem that maximises system availability and minimises the total cost under a weight constraint. We propose a multi-objective harmony search (MOHS) algorithm, a non-dominated sorting genetic algorithm (NSGA-II), and a multi-objective genetic algorithm (MOGA) to solve this problem. In addition, the Taguchi method is utilised to tune the parameters in each algorithm. We use a number of numerical examples to demonstrate the applicability and exhibit the efficacy of the three algorithms. The results show that the MOHS outperforms the NSGA-II and MOGA with respect to all of the considered metrics.

System redundancy optimization with uncertain stress-based component reliability: Minimization of regret

System reliability design optimization models have been developed for systems exposed to changing and diverse stress and usage conditions. Uncertainty is addressed through defining a future operating environment where component stresses have shifted or changed for different future usage scenarios. Due to unplanned variations or changing environments and operating stresses, component and system reliability often cannot be predicted or estimated without uncertainty. Component reliability can vary due to a relative increase/decrease of stresses or operating conditions. The uncertain parameters of stresses have been incorporated directly into the new decision-making model. Risk analysis perspectives, including risk-neutral and risk-averse, are considered as system reliability objective functions. A regret function is defined, and minimization of the maximum regret provides an objective function based on random future usage stresses. This is an entirely new formulation of the redundancy allocation problem, but it is a relevant one for some problem domains. The redundancy allocation problem is solved to select the best design solution when there are multiple choices of components and system-level constraints. Nonlinear programming and a neighborhood search heuristic method are recommended to obtain the integer solutions for risk-based formulations.

Reliability Analysis and Redundancy Allocation for a One-Shot System Containing Multifunctional Components

Enabling more than one function in a component provides a new cost-effective way to develop a highly reliable system. In this paper, we study the reliability of a one-shot system containing multifunctional components. Such systems have attracted increasing attention in many areas, such as ad hoc sensor networks. We derive the expressions for system reliability and reliability of each function, and formulate a redundancy allocation problem (RAP) with the objective of maximizing system reliability. Unlike constructing a system with single-functional components, the number of copies of a specific function to be included in each multifunctional component (i.e., functional redundancy) needs to be determined as part of the design. Moreover, a start-up strategy for turning on specific functions in these components must be decided prior to system operation. We develop a heuristic algorithm and include it in a two-stage genetic algorithm (GA) to solve the new RAP. We also apply a Tabu search (TS) method for solving such NP-hard problems. Our numerical studies illustrate that the two-stage GA and the TS method are quite effective in searching for high-quality solutions.

Design and analysis of the redundancy allocation problem using a greedy technique

We present a very computationally light and fast approximation algorithm and then verify it with genetic algorithm and simulated annealing. We show that our algorithm is on par with GA and SA in terms of output produced while having a tightly bounded time complexity. Our algorithm works best when there is a strong positive correlation between the reliability of a component and its cost. We present two algorithms with the same essence. One of them is system cost bounded and the other is target reliability bounded. Our proposed algorithm works on a subsystem level redundancy instead of component level redundancy.

A penalty guided stochastic fractal search approach for system reliability optimization

Modern industry requires components and systems with high reliability levels. In this paper, we address the system reliability optimization problem. A penalty guided stochastic fractal search approach is developed for solving reliability allocation, redundancy allocation, and reliability–redundancy allocation problems. Numerical results of ten case studies are presented as benchmark problems for highlighting the superiority of the proposed approach compared to others from literature.

Redundancy allocation problem of a system with increasing failure rates of components based on Weibull distribution: A simulation-based optimization approach

The redundancy allocation problem (RAP) is a useful method to enhance system reliability. In most works involving RAP, failure rates of the system components are assumed to follow either exponential or k-Erlang distributions. In real world problems however, many systems have components with increasing failure rates. This indicates that as time passes by, the failure rates of the system components increase in comparison to their initial failure rates. In this paper, the redundancy allocation problem of a series–parallel system with components having an increasing failure rate based on Weibull distribution is investigated. An optimization method via simulation is proposed for modeling and a genetic algorithm is developed to solve the problem.

Local Search Optimization for a Multi-state Series-parallel System

Generally, the redundancy allocation problem is characterized as a kind of NP-hard combinatorial optimization problem, which is difficult to solve with the classical method because it has exponentially increasing complexity with the augmented size. In this paper, we propose the efficient approach with two phases that is comprised of particle swarm optimization (PSO), which can efficiently represent the region search, and a local search, to solve the adjacent domains of best particle, which is great useful to improve optimization efficiency, and the parameter of local search is also studied.

Efficient Stochastic Approximation Monte Carlo Sampling for Heterogeneous Redundancy Allocation Problem

Existing optimization methods to heterogeneous redundancy allocation problem often suffer from the local-trap problem in optimization, due to the rugged energy landscapes. In this paper, a new optimization paradigm based on the Markov chain Monte Carlo sampling is proposed for solving the heterogeneous redundancy allocation for multi-state systems. We address this in an optimization-by-sampling framework, and propose to sample the intricate distribution over the combinatorial space by a doubly adaptive sampling approach, where the target adaptation favors free random walk on the rugged energy landscape to substantially alleviate the local-trap problem by updating the target distribution on-the-fly, while the proposal adaptation helps improve the sampling efficiency by learning the proposal distribution based on chain history in optimization. Experimental results performed on a range of benchmark instances demonstrated the superiority of the proposed optimization approach compared with the state-of-the-art alternatives in terms of the solution quality or computational efficiency.

Multi-objective optimization of IT service availability and costs

The continuous provision of highly available IT services is a crucial task for IT service providers in order to fulfill service level agreements with customers. Although the introduction of redundant components increases availability, the associated cost may be very high. Therefore, decision makers in the IT service design stage face a trade-off between cost and availability in order to define suitable service level objectives. Although this task can be seen as a redundancy allocation problem, the existing definitions in this area are not transferable to IT service design due to the assumption of independent component failures, which has been identified as unrealistic in IT systems.In this paper, a multi-objective redundancy allocation problem for IT service design is defined. Therefore, a Petri net Monte Carlo simulation is developed that estimates the availability and costs of a specific design. In order to provide (sub)optimal solutions to an IT service redundancy allocation problem, two meta-heuristics, namely a genetic algorithm and tabu search, are adapted. The approach is utilized to optimize the IT service design of an application service provider in terms of availability and cost to demonstrate its feasibility and suitability.

Developing a bi-objective optimization model for solving the availability allocation problem in repairable series–parallel systems by NSGA II

Bi-objective optimization of the availability allocation problem in a series–parallel system with repairable components is aimed in this paper. The two objectives of the problem are the availability of the system and the total cost of the system. Regarding the previous studies in series–parallel systems, the main contribution of this study is to expand the redundancy allocation problems to systems that have repairable components. Therefore, the considered systems in this paper are the systems that have repairable components in their configurations and subsystems. Due to the complexity of the model, a meta-heuristic method called as non-dominated sorting genetic algorithm is applied to find Pareto front. After finding the Pareto front, a procedure is used to select the best solution from the Pareto front.