BLEAQ based solution for bilevel reliability-allocation problem

Abstract

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.