Optimal tasks assignment policy in multi-task multi-attempt missions

Motivated by real-world applications like unmanned reconnaissance aerial vehicles, this paper considers a multi-task multi-attempt mission system, where each task may be attempted multiple times and each attempt may be performed simultaneously by multiple components to enhance the task completion probability. Such an active redundancy, on the other hand, incurs high cost and high risk associated with the failures of the components. To balance the reward and the risk, this paper formulates and solves a new optimization problem, which determines the number of components performing each uncompleted task in each attempt, referred to as the task assignment policy (TAP), minimizing the expected mission cost (EMC). A recursive algorithm is proposed to evaluate the EMC (aggregating the expected operational cost, cost of lost components, and cost associated with uncompleted tasks) for the considered multi-task multi-attempt system under a given TAP. Based on the suggested EMC evaluation algorithm, the genetic algorithm is implemented to solve the optimal TAP problem. A detailed case study of an unmanned reconnaissance aerial vehicle system performing five independent surveillance tasks is conducted to examine the impacts of several model parameters on the EMC, task successful completion probabilities, and the optimal TAP solutions.