Convex Formulation of the Zero Emission Vessel Route Planning Problem

Abstract: This paper focuses on the zero emission vessel route planning problem, which deals with cost-effective planning of battery-electric vessel services for predetermined routes. Vessel characteristics (including battery capacity), fleet size, cyclic schedule frequencies, sailing leg speeds, and shore charging infrastructure are jointly optimized. The problem is nonlinear and nonconvex in its original form, which makes it intractable for most real-world instances. The conventional approach in the literature is to solve a linear approximation by restricting vessel designs and sailing leg speeds to a small finite set. Contrary to the conventional linearization approach, this paper deals with the nonlinearities directly. We show that the problem exhibits a hidden convex structure uncovered by nonlinear changes of variables. By exploiting the favorable convex form of the transformed problem, we solve it in a few seconds using a free off-the-shelf solver that requires no initial guesses, variable bounds, or parameter tuning. We then easily recover the exact solution to the original nonconvex problem by reversing the variable changes. We provide an open-source implementation of our method.