Multi-objective Reliability Redundancy Allocation Research Articles

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.

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

A Generalized Multiobjective Reliability Redundancy Allocation With Uncertainties

Multi-objective reliability-redundancy allocation problem (MORRAP) needs to maximize system reliability and minimize cost, weight, and volume with underlining constraints. In the systems’ design and analysis phase, uncertainties can occur from various sources, such as manufacturing variability, environmental conditions, user behavior, etc. To deal with this, we present a generalization of the traditional MORRAP under multiple empirical and ambiguous circumstances, named interval type-2 fuzzy multiobjective reliability redundancy allocation problem (IT2FMORRAP). The newly formulated IT2FMORRAP considers optimizing goals as reliability, cost, and weight for a series-parallel system with interval type-2 fuzzy number. The mathematical formulation is established under which the proposed IT2FMORRAP model reduces to T1FMORRAP (type-1 fuzzy MORRAP), IVMORRAP (interval-valued MORRAP), and classical MORRAP. An Enhanced Karnik-Mendel and NSGA-II algorithm-based solving strategy is developed for the proposed IT2FMORRAP. The real-world dataset is considered to demonstrate the efficacy of the solution method for the proposed problem. A K-mean clustering technique identifies the best solution sets from the knee region of the generated Pareto fronts. An experimental study on commonly used performance metrics reveals that IT2FMORRAP performs significantly better than T1FMORRAP and crisp MORRAP. Further, the statistical analysis also confirms the hypothesis established in the empirical research. Finally, a comparative performance study has been conducted with notable state-of-the-art papers from the literature to encounter an appropriate establishment for the proposed work in the domain.

Multi-objective reliability redundancy allocation using MOPSO under hesitant fuzziness

Enhancing reliability in complex systems often leads to allocating redundant elements and identifying the system configuration by connecting various stages. Most of the redundancy allocation problems depend on critical decisions taken on various uncertainties present in the system. This study presents the modeling of the redundancy allocation under hesitant fuzzy environment as a multi-objective problem. The multi-objective mathematical framework of series–parallel configuration has been proposed for identifying the system performance to obtain optimal cost against enhanced reliability of the power station coal feeding system incorporating the system’s weight and volume restrictions. A sequence of algorithms is presented involving the hesitant alternative of hesitant fuzzy situation based multi-objective particle swarm optimization to illustrate the optimal solutions to improve the system performance in crisp and hesitant fuzzy environments.

NSGA-II Based Analysis of Fuzzy Multi-objective Reliability–Redundancy Allocation Problem Using Various Membership Functions

In the broadest sense, reliability is a measure of performance of the system under the stated conditions. The reliability–redundancy allocation problem gives a highly reliable system in the presence of optimal redundant components. This design is the most preferred by the design engineer. During the designing phase of the system, all the design data involved in the system are not very precise. Various types of uncertainties such as expert’s information character, qualitative statements, vagueness, incompleteness, unclear system boundaries, inability to evaluate the relative importance of the objectives, etc., are typical for many practical problems. Fuzzy set theory is an efficient technique to tackle such types of uncertainties in the system design problem. In this paper, the goals of the fuzzy multi-objective reliability–redundancy allocation problem are specified by various membership functions such as linear, quadratic, parabolic, and hyperbolic. An efficient multi-objective evolutionary algorithm, namely, NSGA-II is employed to solve it. The Pareto-optimal fronts for the various membership functions are shown in both the membership and objective spaces. Fuzzy ranking method then finds the best compromise solution for each membership function. Finally, the performance of membership functions is ranked by the data envelopment analysis by taking cost criteria (cost, weight, and volume) as inputs and benefit criteria (reliability and maximum satisfaction level) as outputs of the system. The effectiveness of the proposed approach is illustrated by a numerical example of the over-speed protection system for a gas turbine. A comparative analysis of the proposed approach is given with the existing approach.

Multi-objective reliability redundancy allocation problem considering two types of common cause failures

Common cause failures actuate simultaneous failure in the components of system and can incredibly reduce the reliability of the system. So the evaluation of common cause failure rates and its effect on system reliability is very much significant. When common cause failures are considered, failure rate of the components are not independent. The influence of common cause failure (CCF) to system reliability has motivated to consider common cause failures in reliability redundancy allocation problem. So, a novel multi-objective reliability redundancy allocation problem is formulated here with the objectives of maximizing system reliability and minimizing system cost in the presence of common cause failures. In this article, two types of common causes are highlighted, namely fatal and non-fatal CCFs, in addition to random failures. These types of failures lead to simultaneous failure of multiple components because of a common cause. An attempt has been made for the first time to solve the multi-objective optimization problem using two meta-heuristic algorithms which gives the Pareto optimal solution. Since the rapid advancements in Science and Technology encouraged the researchers for the optimal design of complex systems considering different environmental situations, two numerical evidences based on complex systems has been considered here. The results indicate the reduction of optimal redundancy with two types of CCF when compared to random failure alone.

Multiobjective optimization of reliability–redundancy allocation problems for serial parallel-series systems based on importance measure

For complex equipment, designers are challenged to reduce the expense while satisfying high requirements of system reliability. This article focuses on the multiobjective reliability–redundancy allocation problem for serial parallel-series systems to balance the conflicts between system reliability and design cost. The multiobjective reliability–redundancy allocation problem model for serial parallel-series systems is established with constraints on system reliability and design cost. An importance measure–based and harmony search–based multiobjective particle swarm optimization algorithm is proposed to solve the multiobjective model effectively based on the importance measure–based harmony search and multiobjective particle swarm optimization algorithm. The performance of the importance measure–based and harmony search-based multiobjective particle swarm optimization algorithm is verified by comparison with the nondominated sorting genetic algorithm and importance measure–based multiobjective particle swarm optimization algorithm. In Experiment 1, the performance of the importance measure–based and harmony search-based multiobjective particle swarm optimization algorithm is better than that of the nondominated sorting genetic algorithm and importance measure–based multiobjective particle swarm optimization, and the importance measure–based and harmony search-based multiobjective particle swarm optimization algorithm also can get the Pareto front with better uniformity. Compared to the nondominated sorting genetic algorithm, four cases with different constraints of system reliability and design cost are considered in Experiment 2, and the importance measure–based and harmony search–based multiobjective particle swarm optimization algorithm applies to the systems with the lower system reliability constraints and the higher design cost constraints.

Type-2 fuzzy reliability–redundancy allocation problem and its solution using particle-swarm optimization algorithm

In this paper, the fuzzy multi-objective reliability redundancy allocation problem (FMORRAP) is proposed, which maximizes the system reliability while simultaneously minimizing the system cost under the type 2 fuzzy uncertainty. In the proposed formulation, the higher order uncertainties (such as parametric, manufacturing, environmental, and designers uncertainty) associated with the system are modeled with interval type 2 fuzzy sets (IT2 FS). The footprint of uncertainty of the interval type 2 membership functions (IT2 MFs) accommodates these uncertainties by capturing the multiple opinions from several system experts. We consider IT2 MFs to represent the subsystem reliability and cost, which are to be further aggregated using extension principle to evaluate the total system reliability and cost according to their configurations, i.e., series parallel and parallel series. We proposed a particle swarm optimization (PSO) based novel solution approach to solve the FMORRAP. To demonstrate the applicability of two formulations, namely, series parallel FMORRAP and parallel series FMORRAP, we performed experimental simulations on various numerical data sets. The decision makers/system experts assign different importance to the objectives (system reliability and cost), and these preferences are represented by sets of weights. The optimal results are obtained from our solution approach, and the Pareto optimal front is established using these different weight sets. The genetic algorithm (GA) was implemented to compare the results obtained from our proposed solution approach. A statistical analysis was conducted between PSO and GA, and it was found that the PSO based Pareto solution outperforms the GA.

Efficient reliability–redundancy allocation with uniform importance measure in presence of correlated failure

ABSTRACTThe problem of designing optimal system architecture (including the redundancy level and the corresponding reliability of each component) which maximizes reliability through resource constraints has been attracted increasing attention in recent years. In this paper, a hybrid method in which an effective co-evolutionary particle swarm optimization combined with harmony search algorithm is proposed to solve the reliability–redundancy optimization problem in the presence of correlated component failures. Another main objective which is considered is decreasing the role of critical component in system reliability. So two different scenarios for reliability–redundancy optimization problem were investigated. The first scenario is reliability–redundancy optimization in the presence of correlation between subsystem failures and the second scenario is considering the multi-objective reliability redundancy allocation problem where the reliability of the system and the uniformity of importance measure of each subsystem are considered as two different objectives. To show the effectiveness of the proposed method, numerical results of some sample systems are illustrated. In addition, some numerical results of two different types of RRAP are reported. The obtained simulation results show that the proposed approach is better in comparison of previously reported in the recent literature.

Multi-objective Reliability-Redundancy Allocation Problem with Interval Type-2 Fuzzy Uncertainty

The multiobjective reliability redundancy allocation problem (MORRAP) aims to ensure high system reliability in the presence of optimally redundant components. This is one of the most important design considerations for system designers. Due to the associated uncertainty in component parameters, precise computations of overall system reliability, cost, and weight, etc., are difficult during design time. Hence, these parameters are befitting to be modeled as fuzzy quantities. As type-1 fuzzy numbers have limitations in representing higher order uncertainties, so this paper models the component parameters viz., reliability, cost, and weight with interval type-2 fuzzy numbers. Thus, we propose a novel formulation of MORRAP, termed as interval type-2 fuzzy multiobjective optimization problem (IT2FMORRAP). A popular multiobjective evolutionary algorithm, viz., nondominated sorting genetic algorithm II, is used to solve the proposed IT2FMORRAP, for which we have developed two novel algorithms in this paper. Numerical examples are included to demonstrate the solution approach. On comparing the outcomes with earlier results, we have found that the proposed IT2FMORRAP outperforms classical as well as other type-1 fuzzy-number-based approaches.

Multi-objective reliability redundancy allocation in an interval environment using particle swarm optimization

Most of the existing works addressing reliability redundancy allocation problems are based on the assumption of fixed reliabilities of components. In real-life situations, however, the reliabilities of individual components may be imprecise, most often given as intervals, under different operating or environmental conditions. This paper deals with reliability redundancy allocation problems modeled in an interval environment. An interval multi-objective optimization problem is formulated from the original crisp one, where system reliability and cost are simultaneously considered. To render the multi-objective particle swarm optimization (MOPSO) algorithm capable of dealing with interval multi-objective optimization problems, a dominance relation for interval-valued functions is defined with the help of our newly proposed order relations of interval-valued numbers. Then, the crowding distance is extended to the multi-objective interval-valued case. Finally, the effectiveness of the proposed approach has been demonstrated through two numerical examples and a case study of supervisory control and data acquisition (SCADA) system in water resource management.

Entropy based region reducing genetic algorithm for reliability redundancy allocation in interval environment

This research paper presents a multi-objective reliability redundancy allocation problem for optimum system reliability and system cost with limitation on entropy of the system which is very essential for effective sustainability. Both crisp and interval-valued system parameters are considered for better realization of the model in more realistic sense. We propose that the system cost of the redundancy allocation problem depends on reliability of the components. A subpopulation and entropy based region reducing genetic algorithm (GA) with Laplace crossover and power mutation is proposed to determine the optimum number of redundant components at each stage of the system. The approach is demonstrated through the case study of a break lining manufacturing plant. A comprehensive study is conducted for comparing the performance of the proposed GA with the single-population based standard GA by evaluating the optimum system reliability and system cost with the optimum number of redundant components. Set of numerical examples are provided to illustrate the effectiveness of the redundancy allocation model based on the proposed optimization technique. We present a brief discussion on change of the system using graphical phenomenon due to the changes of parameters of the system. Comparative performance studies of the proposed GA with the standard GA demonstrate that the proposed GA is promising to solve the reliability redundancy optimization problem providing better optimum system reliability.

A practical approach for solving multi-objective reliability redundancy allocation problems using extended bare-bones particle swarm optimization

This paper proposes a practical approach, combining bare-bones particle swarm optimization and sensitivity-based clustering for solving multi-objective reliability redundancy allocation problems (RAPs). A two-stage process is performed to identify promising solutions. Specifically, a new bare-bones multi-objective particle swarm optimization algorithm (BBMOPSO) is developed and applied in the first stage to identify a Pareto-optimal set. This algorithm mainly differs from other multi-objective particle swarm optimization algorithms in the parameter-free particle updating strategy, which is especially suitable for handling the complexity and nonlinearity of RAPs. Moreover, by utilizing an approach based on the adaptive grid to update the global particle leaders, a mutation operator to improve the exploration ability and an effective constraint handling strategy, the integrated BBMOPSO algorithm can generate excellent approximation of the true Pareto-optimal front for RAPs. This is followed by a data clustering technique based on difference sensitivity in the second stage to prune the obtained Pareto-optimal set and obtain a small, workable sized set of promising solutions for system implementation. Two illustrative examples are presented to show the feasibility and effectiveness of the proposed approach.

A new multi-objective particle swarm optimization method for solving reliability redundancy allocation problems

In this paper, a new dynamic self-adaptive multi-objective particle swarm optimization (DSAMOPSO) method is proposed to solve binary-state multi-objective reliability redundancy allocation problems (MORAPs). A combination of penalty function and modification strategies is used to handle the constraints in the MORAPs. A dynamic self-adaptive penalty function strategy is utilized to handle the constraints. A heuristic cost-benefit ratio is also supplied to modify the structure of violated swarms. An adaptive survey is conducted using several test problems to illustrate the performance of the proposed DSAMOPSO method. An efficient version of the epsilon-constraint (AUGMECON) method, a modified non-dominated sorting genetic algorithm (NSGA-II) method, and a customized time-variant multi-objective particle swarm optimization (cTV-MOPSO) method are used to generate non-dominated solutions for the test problems. Several properties of the DSAMOPSO method, such as fast-ranking, evolutionary-based operators, elitism, crowding distance, dynamic parameter tuning, and tournament global best selection, improved the best known solutions of the benchmark cases of the MORAP. Moreover, different accuracy and diversity metrics illustrated the relative preference of the DSAMOPSO method over the competing approaches in the literature.

Multi-objective reliability-redundancy allocation problem using particle swarm optimization

This paper considers the multi-objective reliability redundancy allocation problem of a series system where the reliability of the system and the corresponding designing cost are considered as two different objectives. Due to non-stochastic uncertain and conflicting factors it is difficult to reduce the cost of the system and improve the reliability of the system simultaneously. In such situations, the decision making is difficult, and the presence of multi-objectives gives rise to multi-objective optimization problem (MOOP), which leads to Pareto optimal solutions instead of a single optimal solution. However in order to make the model more flexible and adaptable to human decision process, the optimization model can be expressed as fuzzy nonlinear programming problems with fuzzy numbers. Thus in a fuzzy environment, a fuzzy multi-objective optimization problem (FMOOP) is formulated from the original crisp optimization problem. In order to solve the resultant problem, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker regarding cost and reliability goals and then particle swarm optimization is applied to solve the resulting fuzzified MOOP under a number of constraints. The approach has been demonstrated through the case study of a pharmaceutical plant situated in the northern part of India.

Solving binary-state multi-objective reliability redundancy allocation series-parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA

In this paper, a procedure based on efficient epsilon-constraint method and data envelopment analysis (DEA) is proposed for solving binary-state multi-objective reliability redundancy allocation series-parallel problem (MORAP). In first module, a set of qualified non-dominated solutions on Pareto front of binary-state MORAP is generated using an efficient epsilon-constraint method. In order to test the quality of generated non-dominated solutions in this module, a multi-start partial bound enumeration algorithm is also proposed for MORAP. The performance of both procedures is compared using different metrics on well-known benchmark instance. The statistical analysis represents that not only the proposed efficient epsilon-constraint method outperform the multi-start partial bound enumeration algorithm but also it improves the founded upper bound of benchmark instance. Then, in second module, a DEA model is supplied to prune the generated non-dominated solutions of efficient epsilon-constraint method. This helps reduction of non-dominated solutions in a systematic manner and eases the decision making process for practical implementations.