Optimal abort rules and subtask distribution in missions performed by multiple independent heterogeneous units

In many practical applications, a number of mission subtasks should be completed to make the entire mission successful. Moreover, different subtasks can be executed by different sets of operating units, whereas each subtask can be accomplished by several units to provide the corresponding redundancy. If a failure of a safety critical unit executing a subtask results in substantial losses, the subtask can be aborted to enhance survivability of a unit. It usually happens when a certain malfunction or deterioration condition is met and a risk of losing the unit performing the task in the case of the subtask continuation becomes too high. Usually, a unit rescue or recovery procedure is initiated upon the subtask abort. This paper considers a case when a mission consists of several independent subtasks that can be performed by a heterogeneous set of independent units. The probabilistic model is developed for obtaining the subtask and entire mission success probabilities, as well as the probabilities of units losses. The problem of finding the optimal subtask abort policy for each unit that minimizes the overall losses for the case when the mission failure is associated with a certain penalty is considered. In addition, for the case when the units are interchangeable, the joint problem of optimal subtask distribution among the units and optimal abort policy is formulated and solved. A genetic algorithm is used as an optimization engine. The detailed illustrative example is presented.