Constrained Redundancy Optimization Research Articles

Minimal path set importance in complex systems

To find the best mode for system design in reliability optimization, risk engineers around the world use the importance measure as a basic tool. This paper introduces a new importance measure taking into account minimal path sets of the system. It helps to optimize the system designs that occur in many situations. For instance, this importance measure can be used (a) in identifying important components of any complex system and (b) solving constrained redundancy optimization problems. This is illustrated by providing two heuristic algorithms. In the first algorithm, this measure is used to find important components of any complex system ensuring improved system reliability. The second algorithm is used to solve a constrained redundancy optimization problem for any general coherent system giving (near) optimal solutions in 1-neighborhood. The results show that the new importance measure is easily applicable, unlike the classical ones. Hence, it serves as a very useful tool in measuring the important component(s) and solving constrained redundancy optimization problems of complex systems. Thus, it can be considered as a good alternative to the existing importance measures.

Balancing mission success probability and risk of system loss by allocating redundancy in systems operating with a rescue option

In many real-world safety-critical applications, a rescue procedure aimed at saving a system can be activated after its failure to execute a primary mission. For such systems, it is essential to keep the balance between the mission success probability and the system survival probability, as both of these contradicting metrics are extremely important in practice. This balance is achieved in the paper by solving the corresponding constrained redundancy optimization problem utilizing the innovative algorithmic approach. The developed methodology is applied to multicomponent systems with overlapping sets of components involved in primary and rescue phases of a mission, respectively. Each component is a subsystem that consists of parallel heterogeneous elements. The random environment in which the system operates is modeled by the Poisson shock process, whereas each shock can result in failures with given probabilities. The detailed numerical example illustrating optimal redundancy solutions is presented. Further directions for generalizations and applications of the obtained results are discussed.

The Robust Deviation Redundancy Allocation Problem With Interval Component Reliabilities

We propose a robust deviation framework to deal with uncertain component reliabilities in the constrained redundancy optimization problem (CROP) in series-parallel reliability systems. The proposed model is based on a linearized binary version of standard nonlinear integer programming formulations of this problem. We extend the linearized model to address uncertainty by assuming that the component reliabilities belong to an interval uncertainty set, where only upper and lower bounds are known for each component reliability, and develop a Min-Max regret model to handle data uncertainty. A key challenge is that, because the deterministic model involves nonlinear functions of the uncertain data, classical robust deviation approaches cannot be applied directly to find robust solutions. We exploit problem structures to develop four exact solution methods, and present computational results demonstrating their performance.

Optimal redundancy allocation in complex systems

PurposeThis paper aims to focus on solving highly constrained redundancy optimization problems in binary complex systems.Design/methodology/approachThe proposed algorithm searches a possibly improved solution in the k‐neighborhood (k≥2) of the current best feasible solution, by adding one unit in a selected subsystem and eliminating one from some other subsystem(s).FindingsThe algorithm is tested on complex system structures from the literature by solving a set of problems (with both linear and non‐linear constraints), with given and randomly generated data. It is observed that, compared with the other existing heuristics, there is much overall improvement in various performance measures.Practical implicationsThe proposed algorithm is a better alternative and can be easily and efficiently applied to numerous real life systems such as computer and communication systems, telecommunication networks, automobile, nuclear and defense systems etc., giving optimal/near‐optimal solutions.Originality/valueResearchers in reliability optimization have placed emphasis on heuristic approaches. The paper presents a new heuristic algorithm for solving the constrained redundancy optimization problems in complex binary systems.

Ant colony approach to constrained redundancy optimization in binary systems

This paper presents an ant colony optimization algorithm to address the constrained redundancy allocation problem in order to maximize system reliability for complex binary systems. The constraints involved, though separable, are both linear and non-linear. We couple an adaptive penalty function with the basic ant colony approach to handle highly constrained problems and embed a local search technique to find still better locally optimal solutions. The proposed algorithm has been tested on a large number of problems, containing even up to 500 subsystems, with both fixed and randomly generated parameters. Experimental results demonstrate the advantage of the proposed algorithm to solve similar types of problems.

A Heuristic Approach for Constrained Redundancy Optimization in Multi-state Systems

This paper proposes an efficient heuristic approach to solving the constrained redundancy optimization problem in multi-state systems (MSS) with multi-state components using minimal path vectors. A discrete multi-state model is considered, where the system state depends on the discipline of the elements' interaction in the system. When the multi-state nature of the system is considered, exact solution methodologies e.g. Dynamic, Integer Programming are no longer valid. The proposed heuristic offers an efficient and straightforward analysis. To illustrate the simplicity and ease of the application of the algorithm, solutions of a flow network problem with linear constraint and, bridge structure with linear as well as nonlinear constraints are obtained. The results would be applicable to multi-state design problems in real life.

Genetic search for redundancy optimization in complex systems

PurposeConceiving reliable systems is a strategic issue for any industrial society for its economical and technical development. This paper aims to focus on solving highly constrained redundancy optimization problems in complex systems.Design/methodology/approachGenetic algorithms (GAs), one of the metaheuristic techniques, have been used and a dynamic adaptive penalty strategy is proposed, which makes use of feedback obtained during the search along with a dynamic distance metric and helps the algorithm to search efficiently for final, optimal or near optimal solution.FindingsThe effectiveness of the adaptive penalty function is studied and shown graphically on the solution quality as well as the speed of evolution convergence for several highly constrained problems. The investigations show that this approach can be powerful and robust for problems with large search space, even of size 1017, and difficult‐to‐satisfy constraints.Practical implicationsThe results obtained in this paper would be applicable on designing highly reliable systems meeting the requirement of today's society. Moreover, an important advantage of applying GA is that it generates several good solutions (mostly optimal or near optimal) providing a lot of flexibility to decision makers. As such, the paper would be of interest and importance to the system designers, reliability practitioners, as well as to the researchers in academia, business and industry. The paper would have wide applications in the fields of electronics design, telecommunications, computer systems, power systems etc.Originality/valueGenetic algorithms have been recently used in combinatorial optimization approaches to reliable design, mainly for series‐parallel systems. This paper presents a GA for parallel redundancy optimization problem in complex systems.

Heuristic Algorithms for Constrained Redundancy Optimization in Complex Systems Based on New Measures of Importance

In this paper, new measures of importance in respect of minimal path sets and minimal cut sets, respectively, are defined and used to develop efficient heuristic algorithms for solving the problem of constrained redundancy optimization in complex systems. These measures take into account design reliability analysis of a system. With some examples, the effect of the proposed algorithms over other heuristic algorithms existing in literature is discussed. Computational results show that our algorithms can be used as attractive alternatives to other heuristic algorithms keeping in view, both, the solution quality and computational effort.

Penalty Function Approach in Heuristic Algorithms for Constrained Redundancy Reliability Optimization

To solve the problem of constrained redundancy reliability optimization, several heuristic algorithms have been developed in the literature. Most of these algorithms search for the solutions remaining within the feasible boundary e.g. [15], [20]. Perhaps the most interesting & efficient heuristic algorithm in terms of solution quality is that given by KYA, in which the search is made not only in the feasible region but also into the bounded infeasible region by making an excursion, which returns to the feasible region with a possibly improved solution. In this paper, a heuristic algorithm based on the penalty function approach is proposed to solve the constrained redundancy optimization problem for complex systems. An excursion is made into the infeasible region, but an adaptive penalty function helps the search not to go too far into the infeasible region. Thus, promising feasible & infeasible regions of the search space are explored efficiently & effectively to identify finally an optimal or near optimal solution. Computational experiments are conducted on 11 sets of problems (10 with linear constraints, and 1 with nonlinear constraints); each with 10 different randomly generated initial solutions. Comparison is made between the proposed algorithm P-Alg, N-N algorithm [15], Shi algorithm [20], and KYA [9] . It is observed that P-Alg performs consistently better than others, showing an overall improvement in various measures of performance. Besides, as P-Alg does not require any assumptions on the nature of the objective & constraint functions, it can solve a wide variety of problems.

Optimality Condition and Branch and Bound Algorithm for Constrained Redundancy Optimization in Series Systems

This paper considers the constrained redundancy optimization problem in series systems. This problem can be formulated as a nonlinear integer programming problem of maximizing the overall systems reliability under limited resource constraints. By exploiting special features of the problem, we derive a new necessary condition for optimal redundancy assignments. This condition leads to a new fathoming condition in the branch and bound method that may result in a significant reduction of computational efforts, as evidenced in our numerical calculation for linearly constrained redundancy optimization problems.

Heuristic reliability optimization by tabu search

A new heuristic algorithm, based on the tabu search methodology, is proposed for constrained redundancy optimization in series and in complex systems. It has the advantage of not being blocked as soon as a local optimum is found. Results given by the new method are compared with those of previous heuristics on a series of examples.

A heuristic method for solving redundancy optimization problems in complex systems

The authors present a heuristic method for solving constrained redundancy optimization problems in complex systems. The proposed method allows excursions over a bounded infeasible region, which can alleviate the risks of being trapped at a local optimum. Computational results show that the method performs consistently better than other heuristic methods in terms of solution quality. If solution quality is of more concern and if one is willing to accept a moderate increase in computing time for better solutions, then the authors believe that this method is an attractive alternative to other heuristic methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A New Heuristic Algorithm for Constrained Redundancy-Optimization in Complex Systems

A new heuristic algorithm solves the problem of constrained redundancy optimization in complex systems using minimal path sets. With two examples, the effect of new algorithm and existing methods are compared.

A simple approach for constrained redundancy optimization problem : K. B. Misra. IEEE Trans. Reliab.R-21, No. 1, February (1972), p. 30

A mathematical model of a two-unit cold standby system with critical human errors (CHE) and slow switch is investigated. The CHE leads to complete system failure, and repair and post-repair are needed before the system can be put back into operation. Slow switch means that on failure of the operative unit the switch puts the standby unit into operation after a random time. Failure time and switchover time distributions are negative exponential whereas all the repair and post repair time distributions are general. Using a regenerative point technique, we obtain various reliability characteristics which can be used to carry out the cost-benefit analysis. In a particular case, the behaviour of the cost function is also studied graphically.

A Simple Approach for Constrained Redundancy Optimization Problem

This paper provides a simple algorithm for the solution of the redundancy optimization problem in the presence of multiple linear constraints. Basicaily, the solution to an r-constraint problem is obtained successively from the solution of r-unconstrained problems. At each step, an active constraint is picked out, then the maximum gradient concept is used to find a closer point. The approach requires minimum effort and time for solution.