Underwater radiated noise (URN) emanating from ships can adversely impact the life functions of certain marine mammals that rely on sound to navigate, communicate, and locate prey. This paper formulates an optimal voyage scheduling problem to mitigate the impact of URN on sensitive marine species by choosing amongst different possible paths and specifying the cruising speed along the selected path. We focus on all-electric ships (AESs) owing to their greater flexibility for speed regulation by coordinating an integrated power system. The proposed optimization model schedules generators and energy storage devices toward minimizing the operation cost while satisfying constraints pertinent to URN levels and atmospheric greenhouse gas (GHG) emissions, the electric power network and operational limits, and expected voyage timelines, culminating in a mixed-integer nonlinear programming problem. To promote computational tractability, we approximate the nonlinear relationships for URN, propulsion load, and fuel consumption with piecewise linear functions. This leads to a mixed-integer second-order cone programming problem, which enables convergence to the global optimum and computationally efficient solutions. We illustrate the effectiveness of the proposed model in curbing URN levels and GHG emissions with numerical case studies involving an 18-node ship test system.

船舶发出的水下辐射噪声 (URN) 会对某些依赖声音导航、交流和定位猎物的海洋哺乳动物的生命功能产生不利影响。本文通过在不同的可能路径中进行选择并指定沿所选路径的巡航速度，制定了一个最优航程调度问题，以减轻 URN 对敏感海洋物种的影响。我们专注于全电动船 (AES)，因为它们通过协调集成电力系统在速度调节方面具有更大的灵活性。所提出的优化模型调度发电机和储能设备以最大限度地降低运营成本，同时满足与 URN 水平和大气温室气体 (GHG) 排放、电力网络和运营限制以及预期航程时间表相关的约束，最终导致混合整数非线性规划问题。为了提高计算的易处理性，我们使用分段线性函数来近似 URN、推进负载和燃料消耗的非线性关系。这会导致混合整数二阶锥规划问题，从而能够收敛到全局最优和计算高效的解决方案。我们通过涉及 18 节点船舶测试系统的数值案例研究来说明所提出的模型在抑制 URN 水平和 GHG 排放方面的有效性。这使得能够收敛到全局最优和计算有效的解决方案。我们通过涉及 18 节点船舶测试系统的数值案例研究来说明所提出的模型在抑制 URN 水平和 GHG 排放方面的有效性。这使得能够收敛到全局最优和计算有效的解决方案。我们通过涉及 18 节点船舶测试系统的数值案例研究来说明所提出的模型在抑制 URN 水平和 GHG 排放方面的有效性。