Establish global optimality of reported navigation solutions in turbulent flows

Establish rigorously whether the reported minimal-time optimal-control solutions for turbulent-flow navigation are globally optimal among all admissible vessel steering strategies.

Background

For turbulent flows, the optimal-control boundary-value problem can possess multiple solutions, and the corresponding trajectories may be unstable, making them difficult to identify reliably with shooting methods. The paper compares the genetic-algorithm policies with selected minimal-time optimal-control solutions, but the existence of multiple unstable solutions prevents a rigorous global comparison over all admissible trajectories.

The authors therefore treat the close agreement between the genetic-algorithm results and independently obtained navigation methods as supporting evidence rather than a proof that the reported optimal-control trajectories achieve the global minimum travel time. A rigorous global-optimality result would resolve whether these candidate solutions are truly shortest-time routes in the considered turbulent flows.