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The purpose of this paper is to introduce an efficient algorithm based on a non-linear accepting threshold to solve the redundancy allocation problem (RAP) considering multiple redundancy strategies. In addition to the components reliability, multiple redundancy strategies are simultaneously considered to vary the reliability of the system. The goal is to determine the optimal selection of elements, redundancy levels and redundancy strategy, which maximizes the system reliability under various system-level constraints.

The mixed RAP considering the use of active and standby components at the subsystem level belongs to the class of NP-hard problems involving selection of elements and redundancy levels, to maximize a specific system performance under a given set of physical and budget constraints. Generally, the authors recourse to meta-heuristic algorithms to solve this type of optimization problem in a reasonable computational time, especially for large-size problems. A non-linear threshold accepting algorithm (NTAA) is developed to solve the tackled optimization problem. Numerical results for test problems from previous research are reported and analyzed to assess the efficiency of the proposed algorithm.

The comparison with the best solutions obtained in previous studies, namely: genetic algorithm, simulated annealing, memetic algorithm and the particle swarm optimization for 33 different instances of the problem, demonstrated the superiority of the proposed algorithm in finding for all considered instances, a high-quality solution in a minimum computational time.

Considering multiple redundancy strategies helps to achieve higher reliability levels but increases the complexity of the obtained solution leading to infeasible systems in term of physical design. Technological constraints must be integrated into the model to provide a more comprehensive and realistic approach.

Designing high performant systems which meet customer requirements, under different economic and functional constraints is the main challenge faced by the manufacturers. The proposed algorithm aims to provide a superior solution of the reliability optimization problem by considering the possibility to adopt multiple redundancy strategies at the subsystem level in a minimum computational time.

A NTAA is expanded to the RAP considering multiple redundancy strategies at the subsystem level subject to weight and cost constraints. A procedure based on a penalized objective function is developed to encourage the algorithm to explore toward the feasible solutions area. By outperforming well-known solving technique, the NTAA provides a powerful tool to reliability designers of complex systems where different varieties of redundancies can be considered to achieve high-reliability systems.

The purpose of this paper is to extend the optimal design problem of series manufacturing production lines to series‐parallel lines, where redundant machines and in‐process buffers are both included to achieve a greater production rate. The objective is to maximize production rate subject to a total cost constraint.

An analytical method is proposed to evaluate the production rate, and an ant colony approach is developed to solve the problem. To estimate series‐parallel production line performance, each component (i.e. each set of parallel machines) of the original production line is approximated as a single unreliable machine. To determine the steady state behaviour of the resulting non‐homogeneous production line, it is first transformed into an approximately equivalent homogeneous line. Then, the well‐known Dallery‐David‐Xie algorithm (DDX) is used to solve the decomposition equations of the resulting (homogenous) line. The optimal design problem is formulated as a combinatorial optimisation one where the decision variables are buffers and types of machines, as well as the number of redundant machines. The effectiveness of the ant colony system approach is illustrated through numerical examples.

Simulation results show that the analytical approximation used to estimate series‐parallel production lines is very accurate. It has been found also that ant colonies can be extended to deal with the series‐parallel extension to determine near‐optimal or optimal solutions in a reasonable amount of time.

The model and the solution approach developed can be applied for optimal design of several industrial systems such as manufacturing lines and power production systems.

The paper presents an approach for the optimal design problem of series‐parallel manufacturing production lines.

The purpose of this paper is to apply a recent kind of neural networks in a reliability optimization problem for a series system with multiple‐choice constraints incorporated at each subsystem, to maximize the system reliability subject to the system budget and weight. The problem is formulated as a non‐linear binary integer programming problem and characterized as an NP‐hard problem.

The design of neural network to solve this problem efficiently is based on a quantized Hopfield network (QHN). It has been found that this network allows one to obtain optimal design solutions very frequently and much more quickly than other Hopfield networks.

For systems more complex than series systems considered in this paper, the proposed approach needs to be adapted. The QHN‐based solution approach can be applied in many industrial systems where reliability is considered as an important design measure, e.g. in manufacturing systems, telecommunication systems and power systems.

The paper develops a new efficient method for reliability optimization. The most interesting characteristic of this method is related to its high‐speed computation, since the practical importance lies in the short computation time needed to obtain an optimal or nearly optimal solution for large industrial problems.

The purpose of this paper is to formulate a new problem of the optimal design of a series manufacturing production line system, and to develop an efficient heuristic approach to solve it. The optimal design objective is to maximize the efficiency subject to a total cost constraint.

To estimate series production line efficiency, an analytical decomposition‐type approximation is used. The optimal design problem is formulated as one of combinatorial optimization where the decision variables are buffers and types of machines. This problem is solved by developing and demonstrating a problem‐specific ant system algorithm. Numerical examples illustrate the effectiveness of the algorithm.

It has been found that this algorithm can always find near‐optimal or optimal solutions quickly. The approach developed in this paper for manufacturing lines can be adapted for power systems and telecommunication systems.

The paper presents a new approach for the optimal design of buffered series production lines. This optimization approach aims at selecting both the machines and the levels of buffers. The paper also develops an efficient solution approach based on the ant system meta‐heuristic.