This paper proposes an efficient algorithm based on memetic algorithm (MA) for a redundancy allocation problem without component mixing (RAPCM) in a series-parallel system when the redundancy strategy can be chosen for individual subsystems. Majority of the solution methods for the general RAPCM assume that the type of a redundancy strategy for each subsystem is pre-determined and known a priori. In general, active redundancy has traditionally received greater attention; however, in practice both active and cold-standby redundancies may be used within a particular system design. The choice of the redundancy strategy then becomes an additional decision variable. Thus, the problem is to select the best redundancy strategy, component and redundancy level for each subsystem in order to maximize the system reliability under system-level constraints. Due to its complexity and NP-hardness, it is so difficult to optimally solve such a problem by using traditional optimization tools. To validate the performance of the proposed MA in terms of solution quality, a number of test problems are examined and the robustness of this algorithm is then discussed. Finally, the related results are reported and it is shown that the proposed MA performs well.

The Redundancy Allocation Problem (RAP) aims to optimize system reliability or cost by selecting redundant components under given constraints. While traditional RAP studies focus on reliability or cost alone, real-world systems, particularly queueing networks, require a balance between redundancy allocation and operational performance. This paper investigates the RAP for a tandem queueing network with repairable subsystems, where queueing costs and repair costs are jointly minimized. Unlike prior works, our model integrates queueing dynamics into redundancy optimization, ensuring both system reliability and operational efficiency. To solve this NP-hard problem, we propose a hybrid simulation-PSO algorithm, combining simulation for performance evaluation and Particle Swarm Optimization (PSO) for efficient solution search. Extensive numerical experiments demonstrate that our approach effectively minimizes total system costs while maintaining reliability. The results validate the applicability of our model in real-world service and manufacturing systems, such as healthcare, assembly lines, and logistics networks.

To increase the reliability of a specific system, using redundant components is a common method which is called redundancy allocation problem (RAP). Some of the RAP studies have focused on k -out-of- n systems. However, all of these studies assumed predetermined active or standby strategies for each subsystem. In this paper, for the first time, we propose a k -out-of-n system with a choice of redundancy strategies. Therefore, a k-out-of- n series–parallel system is considered when the redundancy strategy can be chosen for each subsystem. In other words, in the proposed model, the redundancy strategy is considered as an additional decision variable and an exact method based on integer programming is used to obtain the optimal solution of the problem. As the optimization of RAP belongs to the NP-hard class of problems, a modified version of genetic algorithm (GA) is also developed. The exact method and the proposed GA are implemented on a well-known test problem and the results demonstrate the efficiency of the new approach compared with the previous studies.

In general redundancy allocation problems the redundancy strategy for each subsystem is predetermined. Tavakkoli- Moghaddam presented a series-parallel redundancy allocation problem with mixing components (RAPMC) in which the redundancy strategy can be chosen for individual subsystems. In this paper, we present a bi-objective redundancy allocation when the redundancy strategies for subsystems are considered as a variable of the problem. As the problem belongs to the NP-hard class problems, we will present a new approach for the non-dominated sorting genetic algorithm (NSGAII) and Memtic algorithm (MA) with each one to solve the multi-objective model.

This paper proposes a new mathematical model for multi-objective redundancy allocation problem (RAP) without component mixing in each subsystem when the redundancy strategy can be chosen for individual subsystems. Majority of the mathematical model for the multi-objective redundancy allocation problems (MORAP) assume that the redundancy strategy for each subsystem is predetermined and fixed. In general, active redundancy has received more attention in the past. However, in practice both active and cold-standby redundancies may be used within a particular system design and the choice of the redundancy strategy becomes an additional decision variable. The proposed model for MORAP simultaneously maximizes the reliability and the net profit of the system. And finally, to clarify the proposed mathematical model a numerical example will be solved.

One of the most important steps to design an engineering system is reliability allocation. Often, redundancy is used to achieve a highly reliable system. The redundancy allocation problem (RAP) is increasingly becoming an important tool in the initial stages of or prior to the plan, design, and control of systems. The multi-level redundancy allocation problem (MLRAP) is an extension of the traditional RAP such that all available items for redundancy (system, module, and component) can be simultaneously chosen. Although RAP has been considered by several researchers, MLRAP attracts only a little attention. Ordinarily, reliability uncertainty is ignored too. In this paper, this subject is studied and a new method to solve MLRAP is developed. The total cost is considered the most important constraint. A new meta-heuristic optimization algorithm, called Modified bat algorithm (MBA), to solve the constrained optimization problem (MLRAP) is proposed. This method is based on the Bat behavior to detect a prey. To demonstrate this method's capability, MLRAP for a system is described. The results are comprised with HGA, MA, and two-dimensional arrays encoding and a hybrid genetic algorithm (TDA-HGA). For this system, optimal results are the same as TDA-HGA and better than HGA and MA in all cases. Also, the reliability uncertainty and its influence on reliability allocation are studied. The optimal result is changed when uncertainty is considered. The proposed method is a simple and powerful tool to determine the optimal multi-level redundancy allocation and reliability uncertainty modeling.

Reliability Redundancy Allocation (RRA) is one of the most important problems facing the managers to improve the systems performance. In most RRA models, components’,reliability used to be assumed as an exact value in (0, 1) interval, while various factors might affect components’,reliability and change it over time. Therefore, reliability values should be considered as uncertain parameters. In this paper, by developing a discrete-continuous inference system, an optimization-oriented decision support system is proposed considering the components’,reliability as stochastic variables. Proposed DSS uses stochastic if-then rules to infer optimum or near optimum values for decision variables as well as objective function. Finally, by providing several numerical examples, the efficiency of the proposed DSS is evaluated.

involves the suitable redundancy levels under certain strategies to maximize system reliability under some constraints. However, it has undergone many changes to come closer to the real situations. Selecting the redundancy strategy and using di erent system con guration are some of these changes. In this paper, we studied the e ects of technical and organizational activities on this problem and showed the di erence between the system reliability with and without using these activities. Also, we worked on a system containing s subsystems connected serially. Each subsystem contains ni; i = 1; 2; : : :; s parallel components that can be selected from mi; i = 1; 2; : : :; s di erent component types and all subsystem components must be identical. Because redundancy allocation problem belongs to Np. Hard problems, we used a new metaheuristic algorithm called memetic competition algorithm for solving the presented problem and compared the results of this algorithm with other solving methods.