بهبود بهینه سازی ازدحام ذرات برای به حداقل رساندن هزینه های تعمیر و نگهداری پیشگیرانه دوره ای برای سیستم های سری و موازی

This study minimizes the periodic preventive maintenance cost for a series-parallel system using an improved particle swam optimization (IPSO). The optimal maintenance periods for all components in the system are determined efficiently. Though having advantages such as simple understanding and easy operation, a typical particle swam optimization (PSO) is easily trapped in local solutions when optimizing complex problems and yields inferior solutions. The proposed IPSO considers maintainable properties of a series-parallel system. The importance measure of components is utilized to evaluate the effects of components on system reliability when maintaining a component. Accordingly, the important components form superior initial particles. Furthermore, an adjustment mechanism is developed to deal with the problem in which particles move into an infeasible area. A replacement mechanism is implemented that replaces the first n particles ranked in descending order of total maintenance cost with randomly generated particles in the feasible area. The purpose of doing so is overcome the weakness in that a typical PSO is easily trapped in local solutions when optimizing a complex problem. An elitist strategy is also applied within the IPSO. Additionally, this study employs response surface methodology (RSM) via systematic parameters experiments to determine the optimal settings of IPSO parameters. Finally, a case demonstrates the effectiveness of the proposed IPSO in optimizing the periodic preventive maintenance model for series-parallel systems.

All equipment ages and deteriorates with usage and age. Preventive maintenance (PM) must be performed on a repairable series-parallel system to reduce failure rates and improve reliability. Notably, PM consumes human resources and time and has associated costs. However, nonessential services or an inadequate maintenance schedule wastes limited maintenance resources. The structure of a repairable series-parallel system markedly impacts system reliability. Establishing an appropriate maintenance strategy for a complex repairable system requires that maintenance priority of subsystems or components and their maintenance periods given limited maintenance resources be determined simultaneously. Maintenance quality is typically categorized into five classes – perfect maintenance, minimal maintenance, imperfect maintenance, worse maintenance and worst maintenance – according to degree of equipment restoration (Pham & Wang, 1996). Furthermore, to meet practical requirements, numerous studies have constructed maintenance models and optimization algorithms (Leou, 2006). However, the complexity of optimizing a maintenance model in a series-parallel system increases significantly as the number of components in a system increases. In such situations, obtaining the exact global optimum using analytical approaches via mathematical inference is impractical. Therefore, meta-heuristic algorithms, such as a genetic algorithm (GA) (Bris et al., 2003 and Marseguerra and Zio, 2000), ant colony optimization (Samrout, Yalaoui, Chatelet, & Chebbo, 2005) and simulated annealing (Leou, 2006), are commonly employed to optimize these models and approach the global optimum. Meta-heuristic algorithms commonly have three impediments to efficiently solving complex optimization problems (Battiti & Tecchiolli, 1994) – becoming trapped in local optimum, a limited cycle, and an inability to escape from a specific search region. These hindrances must be overcome when solving complex problems. Furthermore, when solving a constrained optimization problem using the particle swam optimization (PSO), an adjustment mechanism that moves particles back to a feasible area from an infeasible area is beneficial to optimized solutions (El-Gallad et al., 2001, Hu and Eberhart, 2002 and Parsopoulos and Vrahatis, 2002). Past studies (Baker & Ayechew, 2003) demonstrated that a superior initial population structure can significantly benefit the ability of meta-heuristic algorithm to approach the global optimum. Hence, numerous studies (Chen et al., 2008 and Shieh and May, 2001) have attempted to establish a superior initial population to enhance solving ability of current algorithms, particularly for solving complex problems. However, the idea regarding the establishment of the superior initial population in optimizing the preventive maintenance model for series-parallel systems has seldom been seen. Kennedy and Eberhart (1995) developed the PSO in 1995. The PSO retains the advantages of easy understanding, simple operation, and rapid searching. However, when solving a large complex problem, PSO easily becomes trapped in local optimum. This weakness must be overcome to extend its practicability. Therefore, this study proposes an improved particle swarm optimization (IPSO) to overcome this weakness and thereby optimize the periodic preventive maintenance model for the series-parallel system. The maintenance period for each component in a system can thus be obtained. The properties of a preventive maintenance model for series-parallel systems, a constrained optimization model, are considered to create the improved mechanisms. Since the failure of any component can adversely affect the reliability of a series-parallel system, this study revises Birnbaum’s importance measures of components (Elsayed, 1996) to appropriately adopt in assessing components importance form the aspect of preventive maintenance. This is because the calculation of Birnbaum’s importance measures is based on a specific time. The values of importance measures vary with time given. The revised importance measures of components account for the adverse effect of components on system reliability given a component is failed during the time period from the start of system operating until the time system reliability reaching the allowable worst value. Additionally, the search mechanisms within the IPSO overcoming typical PSO weaknesses include: (1) An adjustment mechanism moves particles back into an feasible area from infeasible area by shortening maintenance periods for components scheduled to be maintained at the point of lowest reliability. (2) Replacement mechanism can enhance the search ability of particles in terms of exploration. The first n particles, which are ranked in a descending order for total maintenance cost, are replaced with randomly generated particles in the feasible area. (3) The elitist conservative strategy is employed, such that the best particle that with the lowest total maintenance cost through previous iterations is conserved to guide the other particles toward the superior positions. Additionally, this study employs response surface methodology (RSM) ( Montgomery, 2005), a systematic parameter experiments from design of experiments to determine the optimal parameter settings for IPSO. Because the proposed IPSO is designed specifically for a preventive maintenance model for a series-parallel system, a related case from Bris et al. (2003) is used to demonstrate the effectiveness of the proposed improved search mechanisms for overcoming the typical PSO weakness. The proposed IPSO also compared with two approaches, one based on a genetic algorithm ( Bris et al., 2003) and the other on ant colony optimization ( Samrout et al., 2005), for the same case. Comparison results demonstrate the IPSO outperforms these two approaches.

Some superior meta-heuristic algorithms and improved algorithms have been proposed to resolve large complex problems in recent years. However, due to the diversity in solving problems, a tailor-made improved algorithm typically outperforms a general algorithm for solving the specific type of problem. Via an easy understanding, simple operation, and rapid searching, a typical PSO is trapped easily in local solutions when optimizing complex problems. This study proposes a novel IPSO in which improvement mechanisms are established to overcome the weakness in a typical PSO. Furthermore, the properties of a repairable series-parallel system are considered by the IPSO to minimize total periodic PM cost. Finally, a case adopted from a previous study demonstrates the solving efficiency of the proposed IPSO. Although the proposed algorithm can overcome the weakness of a typical PSO in optimizing a periodic preventive maintenance model efficiently, this algorithm can be extended to solve large problems with complex series-parallel systems consisting of numerous subsystems or components. Moreover, with appropriate modifications, the proposed IPSO could be applicable to non-periodic maintenance and imperfect maintenance models.