Redundancy optimization for multi-state series-parallel systems using ordinal optimization-based-genetic algorithm

Multi-state series-parallel systems (MSSPSs) are widely-used for representing engineering systems. In real-life cases, engineers need to design an optimal MSSPS structure by combining different versions and number of redundant components. The objective of the design is to ensure reliability requirements using the least costs, which could be formulated as a redundancy optimization problem under reliability constraints. The genetic algorithm is one of the most frequently used method for solving redundancy optimization problems. In traditional genetic algorithms, the population size needs to be determined based on the experience of the modeler. Often, this ends up creating a large number of unnecessary samples. As a result, the computational burden can be huge, especially for large-scale MSSPS structures. To solve these problems, this paper proposes an optimal structure designing method named as redundancy ordinal optimization. The universal generating function technique is applied to evaluate the reliabilities of the MSSPSs. Based on the reliabilities, an ordinal optimization algorithm is adapted to update the parent populations and the stopping criterion of genetic algorithm, so that the unnecessary structure designs can be eliminated. Numerical examples show that the proposed method improves the computational efficiency while remaining satisfactorily accurate.

Non-Linear Threshold Algorithm for the Redundancy Optimization of Multi-State Systems

To improve system performance, redundancy is widely used in different kinds of industrial applications such as power systems, aerospace, electronic, telecommunications and manufacturing systems. Designing high performant systems which meet customer requirements with a minimum cost is a challenging task in these industries. This paper develops an efficient approach for the redundancy optimization problem of series-parallel structures modeled as multi-state systems. To reach the target system availability, redundancies are used for components among a list of products available in the market. Each component is characterized by its own availability, cost and performance. The goal is to minimize the total cost under a system availability constraint. Discrete levels of performance are considered for the system and its components. The extreme values of such performance levels correspond to perfect functioning and complete failure. A piecewise cumulative load curve represents consumer demand. System availability corresponds to the aptitude to fulfill this demand. The multi-state system availability evaluation uses the universal moment generating function technique. The proposed optimization algorithm is based on the non-linear threshold accepting metaheuristic, while using a self-adjusting penalty guided strategy. The obtained results demonstrate the approach efficiency for solving the redundancy optimization problem of multi-state systems. Its effectiveness is also tested using the classical redundancy optimization problem of binary-state systems. The algorithm is evaluated by comparison to the best known methods. For multi-state systems, it is compared to genetic algorithm and tabu search. For binary-state systems, it is compared to genetic algorithm, tabu search, ant colony optimization and harmony search. The obtained results demonstrate that the proposed approach outperforms these state-of-the-art benchmark methods in finding, for all considered instances, a high-quality solution in a minimum computational time.

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.