Reliability Redundancy Allocation Problem Research Articles

Fuzzy Multi-Objective Software Reliability Redundancy Allocation Based on MEDA-BFA Algorithm

Software reliability allocation problem is a major problem in engineering design practices. A fuzzy multi-objective software reliability allocation model is established by analyzing the software redundancy architecture and considering some fuzzy factors to reliability. Then, the MEDA-BFA algorithm is proposed based on estimation of distribution to solve software reliability redundancy allocation problem. Finally, experimental results show that the proposed intelligence algorithm can solve multi-objective software reliability allocation effectively and correctly, can help decision makers decide between software reliability and cost.

Two metaheuristics for solving the reliability redundancy allocation problem to maximize mean time to failure of a series–parallel system

The redundancy allocation problem is one of the main branches of reliability optimization problems. Traditionally, the redundancy allocation model has focused mainly on maximizing system reliability at a predetermined time. Hence, in this study, we develop a more realistic model, such that the mean time to failure of a system is maximized. To overcome the structural complexity of the model, the Monte Carlo simulation method is applied. Two metaheuristics, Simulated Annealing (SA) and Genetic Algorithm (GA), are proposed to solve the problem. In addition, the design of experiments and response surface methodology are employed for tuning the GA and SA parameters. The metaheuristics are compared, based on their computation time and accuracy, in 30 test problems. Finally, the results are analyzed and discussed, and some conclusions are drawn.

Modified imperialist competitive algorithm based on attraction and repulsion concepts for reliability-redundancy optimization

System reliability analysis and optimization are important to efficiently utilize available resources and to develop an optimal system design architecture. System reliability optimization has been solved by using optimization techniques including meta-heuristics. Meanwhile, the development of meta-heuristics has been an active research field of the reliability optimization wherein the redundancy, the component reliability, or both are to be determined. In recent years, a broad class of stochastic meta-heuristics, such as simulated annealing, genetic algorithm, tabu search, ant colony, and particle swarm optimization paradigms, has been developed for reliability-redundancy optimization of systems. Recently, a new kind of evolutionary algorithm called Imperialist Competitive Algorithm (ICA) was proposed. The ICA is based on imperialistic competition where the populations are represented by countries, which are classified as imperialists or colonies. However, the trade-off between the exploration (i.e. the global search) and the exploitation (i.e. the local search) of the search space is critical to the success of the classical ICA approach. An improvement in the ICA by implementing an attraction and repulsion concept during the search for better solutions, the AR-ICA approach, is proposed in this paper. Simulations results demonstrates the AR-ICA is an efficient optimization technique, since it obtained promising solutions for the reliability redundancy allocation problem when compared with the previously best-known results of four different benchmarks for the reliability-redundancy allocation problem presented in the literature.

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.

An effective immune based two-phase approach for the optimal reliability–redundancy allocation problem

Abstract Highly reliable systems can reduce loss of money and time in practice. System reliability can be enhanced by: (i) increasing component reliabilities and/or (ii) providing redundancy at the component level. A trade-off between these two options is necessary for nonlinear-constrained reliability optimization. The problem of maximizing system reliability through component reliability choices and component redundancy is called as reliability–redundancy allocation problem, and it is a difficult but realistic nonlinear mixed-integer optimization problem. In this paper, under nonlinear constraints of weight, cost, and volume, we propose a new immune based two-phase approach to solve the reliability–redundancy allocation problem. In the first phase, an immune based algorithm (IA) is developed to solve the allocation problem, and in the second phase we present a new procedure to improve the solutions by IA. Numerical results of four benchmark problems are reported and compared. As shown, the solutions by the new proposed approach are all superior to those best solutions by typical approaches in the literature.

Solving reliability redundancy allocation problems using an artificial bee colony algorithm

This paper proposed a penalty guided artificial bee colony algorithm (ABC) to solve the reliability redundancy allocation problem (RAP). The redundancy allocation problem involves setting reliability objectives for components or subsystems in order to meet the resource consumption constraint, e.g. the total cost. RAP has been an active area of research for the past four decades. The difficulty that one is confronted with the RAP is the maintenance of feasibility with respect to three nonlinear constraints, namely, cost, weight and volume related constraints. In this paper nonlinearly mixed-integer reliability design problems are investigated where both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously so as to maximize the reliability of the system. The reliability design problems have been studied in the literature for decades, usually using mathematical programming or heuristic optimization approaches. To the best of our knowledge the ABC algorithm can search over promising feasible and infeasible regions to find the feasible optimal/near-optimal solution effectively and efficiently; numerical examples indicate that the proposed approach performs well with the reliability redundant allocation design problems considered in this paper and computational results compare favorably with previously-developed algorithms in the literature.

Self-Organizing Migrating Strategies Applied to Reliability-Redundancy Optimization of Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The reliability-redundancy allocation problem is a mixed-integer programming problem. It has been solved by using optimization techniques such as dynamic programming, integer programming, mixed-integer non-linear programming, heuristics, and meta-heuristics. Meanwhile, the development of meta-heuristics has been an active research area in optimizing system reliability wherein the redundancy, the component reliability, or both are to be determined. In recent years, a broad class of stochastic algorithms, such as simulated annealing, evolutionary computation, and swarm intelligence algorithms, has been developed for reliability-redundancy optimization of systems. Recently, a new class of stochastic optimization algorithm called SOMA (Self-Organizing Migrating Algorithm) has emerged. SOMA works on a population of potential solutions called specimen, and is based on the self-organizing behavior of groups of individuals in a “social environment”. This paper introduces a modified SOMA approach based on a Gaussian operator to solve reliability-redundancy optimization problems. In this context, three examples of mixed integer programming in reliability-redundancy design problems are evaluated. In this application domain, SOMA was found to outperform the previously best-known solutions available. </para>

Reliability Optimization of Entropy Based Series-Parallel System Using Global Criterion Method

In this paper, we have considered a series-parallel system to find out optimum system reliability with an additional entropy objective function. Maximum system reliability of series-parallel system is depending on proper allocation of redundancy component in different stage. The goal of entropy based reliability redundancy allocation problem is to find optimal number of redundancy component in each stage such a manner that maximize the system reliability subject to available total system cost. Global criterion method is used to analyze entropy based reliability optimization problem with different weight function of objective functions. Numerical examples have been provided to illustrate the model.

Reliability‐redundancy optimization using simulated annealing algorithms

PurposeThis paper aims to present a simulated annealing (SA) algorithm to search the optimal solution of reliability‐redundancy allocation problems (RRAP) with nonlinear resource constraints.Design/methodology/approachThe developed SA algorithm is coded in C++ and is applied to reliability design problems which include the series system (P1(a) and P1(b)), the series‐parallel system (P2), and the complex (bridge) system (P3). The numerical experiments are executed on an IBM‐PC compatible with a Pentium IV 2.0 GHz. The results are compared with those of previous studies.FindingsThe SA algorithm can find better solutions comparable to the previous studies in all problems except the problem P1(b). The difference on the order of 10−4 between the best and worst for all problems indicates good solution convergence of the SA algorithm. Note that the CPU times for these problems are within a few seconds by Pentium IV 2.0 GHz (P1(a) =2.78 sec, P1(b) =3.37 sec, P2=1.38 sec, and P3=1.40 sec).Originality/valueThe application of the SA is expanded to the RRAP, which can help reliability engineers design the system reliability.

IAs based approach for reliability redundancy allocation problems

Nonlinearly mixed-integer reliability design problems are investigated in this paper where both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously so as to maximize the reliability of system. The reliability design problems have been studied in the literature for decades, usually using mathematical programming or heuristic/metaheuristic optimization approaches. The difficulties confronted for both methodologies are to maintain feasibility with respect to three nonlinear constraints, namely, cost, weight and volume related constraints. A penalty guided artificial immune algorithm is presented for solving such mixed-integer reliability design problems. It can search over promising feasible and infeasible regions to find the feasible optimal/near optimal solution effectively and efficiently. Numerical examples indicate that the proposed approach performs well for the reliability-redundant allocation design problems considered in this paper. As reported, solutions obtained by the proposed approach are as well as or better than the previously best-known solutions.

Multi-Path Approach for Reliability-Redundancy Allocation Using a Scaling Method

The reliability-redundancy allocation problem is an optimization problem that achieves better system reliability by determining levels of component redundancies and reliabilities simultaneously. The problem is classified with the hardest problems in the reliability optimization field because the decision variables are mixed-integer and the system reliability function is nonlinear, non-separable, and non-convex. Thus, iterative heuristics are highly recommended for solving the problem due to their reasonable solution quality and relatively short computation time. At present, most iterative heuristics use sensitivity factors to select an appropriate variable which significantly improves the system reliability. The sensitivity factor represents the impact amount of each variable to the system reliability at a designated iteration. However, these heuristics are inefficient in terms of solution quality and computation time because the sensitivity factor calculations are performed only at integer variables. It results in degradation of the exploration and growth in the number of subsequent continuous nonlinear programming (NLP) subproblems. To overcome the drawbacks of existing iterative heuristics, we propose a new scaling method based on the multi-path iterative heuristics introduced by Ha (2004). The scaling method is able to compute sensitivity factors for all decision variables and results in a decreased number of NLP subproblems. In addition, the approximation heuristic for NLP subproblems helps to avoid redundant computation of NLP subproblems caused by outlined solution candidates. Numerical experimental results show that the proposed heuristic is superior to the best existing heuristic in terms of solution quality and computation time.

Reliability Optimization with the Lagrange-Multiplier and Branch-and-Bound Technique

A method has been developed for constrained reliability optimization problems. This method incorporates the Lagrange multiplier method and the branch-and-bound technique. The Lagrange multiplier method treats the number of redundancies as real numbers. Once a real number solution is obtained, the branch-and-bound technique is used to obtain the integer solution. With our method, a 4-stage series system with two linear constraints is illustrated for the redundancy allocation problem, and a 5-stage series system with three nonlinear constraints is illustrated for the reliability-redundancy allocation problem. The results show that our method is better than previous methods for both the redundancy allocation problem and the mixed integer-type reliability-redundancy allocation problem. Our method also provides more reasonable explanations when solving reliability optimization problems.