Dual-objective speed optimization of battery-electric ships under lock-transit constraints for energy use and voyage time

Abstract

In inland waterways with dense lock systems, stochastic lock waiting makes voyage time jointly determined by sailing and waiting, while hotel-load consumption during waiting exacerbates SOC-related safety risks for battery-electric ships. To address this issue, a coupled time-energy-SOC model is developed by incorporating cumulative lock-wait energy use and current-induced speed perturbations. A bilevel hybrid optimization framework is proposed to jointly optimize battery-swap node sequences and segmented inter-lock speeds, combining discrete scheme screening with CMA-ES-based continuous search. A 𝛽𝛽-scanning procedure is further employed to generate the energy-time Pareto set and construct an offline library of economic speed policies for multiple scenarios. A case study is conducted for a 120-TEU battery-electric container ship operating on the 471 km Shiqiao-Linjiaba route in the northern Jiangsu section of the Beijing-Hangzhou Grand Canal, which includes 11 cascade locks. Both favorable and adverse current conditions are considered, and lock waiting times are discretized into low-, medium-, and highcongestion scenarios. Results show that candidate solutions form a stable non-dominated structure in the energy-time plane. Under high-wait scenarios, total voyage time becomes markedly less sensitive to speed, and differences among strategies are mainly reflected in energy use and SOC margin. SOC constraints are more likely than power constraints to define the feasibility boundary, while battery-swap siting and swap limits play a decisive role in multi-scenario feasibility coverage.