Optimizing partial component activation policy in multi-attempt missions

Active redundancy is an effective technique for improving the mission success probability. However, more components simultaneously performing the mission implies higher cost and higher risk associated with components’ failures. This paper formulates and solves a new optimization problem for an active redundancy system performing a multi-attempt mission, which finds the set/number of components activated in each attempt, referred to as the component activation policy (CAP) to minimize the expected mission cost (EMC). The EMC encompasses the expected operational cost, the expected cost of component losses, and the expected cost associated with damage caused by the mission failure. An analytical solution is first suggested for evaluating the EMC and determining the optimal CAP for a special case of a two-component two-attempt system. A recursive method is then proposed to derive the EMC for the general case of multi-component multi-attempt systems under a given CAP. Based on the suggested string representation of the CAP solution, the genetic algorithm is implemented to solve the EMC minimization problem. Impacts of several model parameters and their interactions on EMC and optimal CAP are examined through a detailed case study of unmanned aerial vehicles performing a multi-attempt reconnaissance mission.