A new approach to solving problems of multi-state system reliability optimization

Usually engineers try to achieve the required reliability level with minimal cost. The problem of total investment cost minimization, subject to reliability constraints, is well known as the reliability optimization problem. When applied to multi-state systems (MSS), the system has many performance levels, and reliability is considered as a measure of the ability of the system to meet the demand (required performance). In this case, the outage effect will be essentially different for units with different performance rate. Therefore, the performance of system components, as well as demand, should be taken into account. In this paper, we present a technique for solving a family of MSS reliability optimization problems, such as structure optimization, optimal expansion, maintenance optimization and optimal multistage modernization. This technique combines a universal generating function (UGF) method used for fast reliability estimation of MSS and a genetic algorithm (GA) used as an optimization engine. The UGF method provides the ability to estimate relatively quickly different MSS reliability indices for series-parallel and bridge structures. It can be applied to MSS with different physical nature of system performance measure. The GA is a robust, universal optimization tool that uses only estimates of solution quality to determine the direction of search.