二型模糊可靠性冗余分配问题及其粒子群算法求解
Type-2 fuzzy reliability redundancy allocation problem and its solution using particle swarm optimization algorithm
摘要：
提出了一类模糊多目标可靠性冗余分配问题（FMORRAP），该问题在第2类模糊不确定性下，使系统可靠性最大化，同时使系统费用最小化.在建议的配方，高阶不确定性（如参数，制造，环境和设计师的不确定性）与系统建模与区间2型模糊集（IT 2 FS）。区间2型隶属函数（IT 2 MF）的不确定性足迹通过捕获来自多个系统专家的多个意见来容纳这些不确定性。我们考虑IT 2 MF来表示子系统的可靠性和成本，根据其配置，使用可拓原理进一步聚合以评估总系统可靠性和成本，即，串联并联和并联串联。我们提出了一种基于粒子群优化（PSO）的新的解决方法来解决FMORRAP。为了证明两个配方，即，串联并联FMORRAP和并联串联FMORRAP的适用性，我们进行了实验模拟各种数值数据集。决策者/系统专家为目标（系统可靠性和成本）分配不同的重要性，这些偏好由权重集表示。最优结果从我们的解决方案的方法，和帕累托最优前沿建立使用这些不同的权重集。实施遗传算法（GA），比较我们提出的解决方案所获得的结果。对粒子群算法和遗传算法进行了统计分析，发现基于粒子群算法的Pareto解优于遗传算法。
英文摘要：
In this paper, the fuzzy multi-objective reliability redundancy allocation problem (FMORRAP) is proposed, which maximizes the system reliability while simultaneously minimizing the system cost under the type 2 fuzzy uncertainty. In the proposed formulation, the higher order uncertainties (such as parametric, manufacturing, environmental, and designers uncertainty) associated with the system are modeled with interval type 2 fuzzy sets (IT2 FS). The footprint of uncertainty of the interval type 2 membership functions (IT2 MFs) accommodates these uncertainties by capturing the multiple opinions from several system experts. We consider IT2 MFs to represent the subsystem reliability and cost, which are to be further aggregated using extension principle to evaluate the total system reliability and cost according to their configurations, i.e., series parallel and parallel series. We proposed a particle swarm optimization (PSO) based novel solution approach to solve the FMORRAP. To demonstrate the applicability of two formulations, namely, series parallel FMORRAP and parallel series FMORRAP, we performed experimental simulations on various numerical data sets. The decision makers/system experts assign different importance to the objectives (system reliability and cost), and these preferences are represented by sets of weights. The optimal results are obtained from our solution approach, and the Pareto optimal front is established using these different weight sets. The genetic algorithm (GA) was implemented to compare the results obtained from our proposed solution approach. A statistical analysis was conducted between PSO and GA, and it was found that the PSO based Pareto solution outperforms the GA.
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