Convex modelling for ship speed optimisation

Optimising the ship speed depending on the forecast oceanic and atmospheric conditions is an effective operational measure to reduce both fuel consumption and carbon dioxide emissions. In the literature, this optimal control problem (OCP) has been formulated using different types of mathematical models and solved using various optimisation methods. In this paper, we use convex functions to reformulate the models and cast the OCP as a convex optimisation problem. This type of problem can be solved very efficiently and yields the globally optimal solution. As a first step, we assume that the environ-mental conditions do not vary with time and only depend on the distance along the route. For this case, we show that the convex reformulation of the OCP is accurate and the computation time to solve it is low. Second, we introduce an iterative method to solve the problem under time-varying condi-tions, drawing inspiration from the literature on hybrid electric vehicles. Whilst this method converges quickly, it does not converge to the global optimum, which was calculated using dynamic programming. We present an artificial scenario to explain why convergence to the global optimum is not guaranteed. Finally, we discuss the implications of our findings for potential future research on this topic.