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BLEAQ based solution for Bilevel Reliability-Redundancy Allocation Problem

机译：基于BLEAQ的Bilevel可靠性 - 冗余分配问题解决方案

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摘要

Reliability redundancy allocation problem (RRAP) is an optimization problem with objective to maximize the system reliability considering component reliability and redundancies as decision variables. RRAP was mostly solved as a single level optimization problem. However, the nature of the problem fits quite well in the framework of bilevel optimization. In this paper, we have proposed two novel bilevel formulations for the RRAP and solve them using a latest bilevel optimization algorithm called BLEAQ (bilevel evolutionary algorithm based on quadratic approximations). So far we knew no other research has been reported till date, where RRAP was addressed with bilevel optimization algorithm. Here, optimization is needed at two separate levels, where one problem is encircled within another problem. The inner problem is known as lower-level problem and the external problem is called upper-level problem. Here, we have presented two mixed-integer non-linear bilevel formulations for the RRAP of series-parallel system in a competitive environment. The purpose of the upper-level problem is to determine the component reliability that maximizes the total system reliability; whereas, lower-level problem minimizes the total cost (or weight) needed. We demonstrate the applicability of our approach with a suitable numerical example and show that our proposed approach works quite well than existing single level optimization tools.
机译：可靠性冗余分配问题（RRAP）是一个优化问题，目的是将系统可靠性最大化，以便考虑组件可靠性和冗余作为决策变量。 RRAP大多是解决的单级优化问题。然而，问题的性质在彼得优化框架中非常适合。在本文中，我们提出了用于RRAP的两种新的Bilevel配方，并使用称为BLEAQ的最新的双纤维优化算法来解决它们（基于二次近似的双纤维进化算法）。到目前为止，我们不知道迄今为止报告了其他研究，其中RRAP通过双纤维优化算法解决。在这里，在两个单独的级别中需要优化，其中一个问题在另一个问题中环绕。内部问题被称为较低级别的问题，外部问题称为上层问题。在这里，我们在竞争性环境中介绍了两个混合整数的非线性彼得配方，用于竞争环境中的串联系统的RRAP。上层问题的目的是确定最大化总系统可靠性的组件可靠性;鉴于较低级别的问题最小化所需的总成本（或重量）。我们通过合适的数值示例展示了我们的方法的适用性，并显示我们所提出的方法很远比现有的单层优化工具。

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