This paper considers a container liner shipping problem with speed optimisation (CLSP-SO) to minimise the total costs of the fleet, which includes operating costs, capital costs and voyage costs. A mixed-integer nonlinear programming model is first formulated to illustrate the problem, in which the oil consumption of ships is treated as a cubic function of speeds. Then, the computational complexity of the problem is analysed and a lower bound is given based on the theoretical optimised speed of ships. To solve the problem, a probabilistic tabu search (PTS)-based algorithm is developed considering the NP-hardness of the problem. Extensive computational experiments on randomly generated data and a real-world case are conducted and the performance of the proposed method is compared with the lower bound and that of the basic tabu search (TS) algorithm. The results show that the proposed PTS-based algorithm obtains satisfactory solutions with respect to lower bounds in reasonable computation time and it outperforms the basic TS-based algorithm.

本文考虑一个具有速度优化（CLSP-SO）的集装箱班轮运输问题，以最小化船队的总成本，包括运营成本、资金成本和航次成本。首先建立混合整数非线性规划模型来说明问题，其中船舶的油耗被视为速度的三次函数。然后，分析了该问题的计算复杂度，并在船舶理论优化航速的基础上给出了一个下界。为了解决这个问题，考虑到问题的NP-hardness，开发了一种基于概率禁忌搜索（PTS）的算法。对随机生成的数据和真实案例进行了广泛的计算实验，并将所提出方法的性能与下限和基本禁忌搜索 (TS) 算法的性能进行了比较。