Optimization Methods for Redundancy Allocation in Large Systems

This paper addresses the issue of optimal allocation of spare modules in large series-redundant systems in order to obtain a required reliability under cost constraints. Both cases of active and standby redundancy are considered. Moreover, for a subsystem with standby redundancy, two cases are examined: in the first case, all the spares are maintained in cold state (cold standby redundancy) and, in the second one, to reduce the time needed to put a spare into operation when the active one fails, one of the spares is maintained in warm conditions. To solve this optimization problem, for the simpler case of active redundancy an analytical method based on the Lagrange multipliers technique is first applied. Then the results are improved by using Pairwise Hill Climbing, an original fine-tuning algorithm. An alternative approach is an innovative evolutionary algorithm, RELIVE, in which an individual lives for several generations and improves its fitness based on local search. These methods are especially needed in case of very large systems.