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摘要: 梳理了集装箱港口船舶配载计划问题的国内外文献，从配载计划的分类、影响因素与求解方法三方面回顾了其研究现状和成果，探讨了目前研究中存在的不足与后续的研究方向。研究结果表明：在论文题目中直接点明主贝位规划问题或者箱位分配问题的文献越来越少，更多的是直接点明“配载计划问题”；多数文献考虑了船舶稳性、船舶强度、集装箱属性(尺寸、质量、类型等)、岸桥属性等影响配载计划问题中的几个因素，只有极少数文献将配载计划问题的影响因素全部考虑在内，因此，为了使研究更贴近港口实际操作，综合考虑配载计划问题的影响因素将成为未来的研究重点；配载计划还受到港口内其他作业的影响，因此，为了提高港口的作业效率和运营水平，应综合考虑集装箱港口各个区域之间的相互作用；随着铁水联运的发展，铁路集装箱也会堆放在船舶上，因而在配载计划问题中也需要考虑铁路集装箱的影响；多数文献都设计了智能算法，并获得了较多的优化解，但是为了更加直观形象地展示求解结果，应该将仿真优化与算法计算结合在一起。Abstract: Chinese and foreign literatures on the containership stowage planning problem of container terminals was summarized. The research situations and results of stowage planning were reviewed from three aspects, including classification, influencing factors, and solution methods. The shortcomings in current research and future research directions were explored. Analysis results show that there are fewer and fewer literatures those directly point out master bay planning problems and slot allocation problems in the titles, and more of them directly point out stowage planning problem. Most literatures consider several influencing factors of stowage planning problem, such as the containership stability and strength, container properties (size, weight, type, etc.), and quay crane properties. Few literatures consider all the influencing factors of stowage planning problem. Therefore, in order to make the research more closely related to the actual operations in container terminals, comprehensive consideration of the influencing factors of stowage planning problem will be future key research. The stowage planning is also influenced by other operations in container terminals. Hence, in order to improve the operation efficiency and level of the container terminals, the interaction among various regions of container terminals should be comprehensively considered. With the development of rail-water intermodal transportation, railway containers will also be loaded onto the containerships, so the railway containers also need to be considered in the stowage planning problem. Intelligent algorithms are designed in most literatures, and better optimal solutions are gained. However, to display the solution results more intuitively and vividly, simulation optimization and algorithm calculation should be combined.
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表 1 主贝位规划问题的研究汇总
Table 1. Research summary on master bay planning problem
作者 年份 论文特色 不足 Sciomachen等[10] 2003 将主贝位规划问题转换成三维装箱问题，考虑了不同尺寸的集装箱 未给出具体的配载计划模型，同时未考虑不同类型的集装箱 王莉莉等[8] 2008 将稳性、减少翻箱、可操作性等因素作为评估策略，按优先级将各种评估策略划分等级 未考虑不同类型、尺寸的集装箱 卫家骏[9] 2009 将主贝位规划问题转换成装箱问题，并对传统算法进行了改进 未考虑不同类型的集装箱 Zeng等[11] 2010 设计了一个大型集装箱船舶配载计划的原型系统 仅考虑了主贝位规划问题，且仅从稳性的角度考虑了配载计划 Ambrosino等[12] 2010 对主贝位规划问题设计了多种算法 未给出具体的配载计划模型，且仅考虑了一台岸桥 Pacino等[13] 2012 考虑了压载舱和不同尺寸的集装箱、冷藏集装箱(简称冷藏箱) 未考虑危险集装箱(简称危险箱)或其他类型的集装箱 Hernández等[14] 2013 考虑了不同质量、尺寸的集装箱并设计了一个全新的求解配载计划问题的算法 未建立具体的配载计划模型，也未考虑危险箱或其他类型的集装箱 Ambrosino等[15] 2015 考虑了不同尺寸的集装箱，并建立了2个精确混合整数规划模型 未考虑不同类型的集装箱，如冷藏箱和危险箱 Ambrosino等[16] 2015 考虑了不同尺寸、类型(冷藏箱和敞口箱)、质量的集装箱 未考虑危险箱 Ambrosino等[17] 2017 按照集装箱不同的属性对集装箱进行分类，并考虑了不同尺寸的集装箱以及冷藏箱和敞口集装箱 未考虑危险箱 Parthibaraj等[18] 2017 设计了一个多智能体系统求解主贝位规划问题 未建立具体的配载计划模型 张艳伟等[19] 2021 考虑了40 ft岸桥的装卸 未考虑不同类型的集装箱 
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表 2 箱位分配问题的研究汇总
Table 2. Research summary on slot allocation problems
作者 年份 论文特色 不足 段成华等[25] 2004 研究了单贝单港的箱位分配问题，并建立了多阶段决策模型 未考虑不同质量、尺寸和类型的集装箱 孙晓雅等[20] 2011 研究了多港口箱位分配问题，并建立了多目标优化模型 未考虑不同类型、尺寸的集装箱 张维英等[21] 2011 将箱位分配问题转换成指派问题进行研究 未考虑不同类型、尺寸的集装箱 Delgado等[7] 2012 研究了甲板下的箱位分配问题，并建立了约束规划模型 未考虑整个船舶的箱位分配问题以及危险箱或其他类型的集装箱 Pacino等[22] 2012 考虑了不同尺寸的集装箱与冷藏箱 未考虑危险箱或其他类型的集装箱 Parreño等[23] 2016 考虑了不同尺寸和类型的集装箱，并建立了整数规划模型 仅研究了箱位分配问题 Korach等[24] 2020 研究了甲板下的箱位分配问题，并考虑了不同尺寸的集装箱以及冷藏箱 未考虑危险箱或其他类型的集装箱
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表 3 考虑船舶强度的研究汇总
Table 3. Research summary on considering containership strength
作者 年份 船舶强度约束 不足 Imai等[27] 2006 纵倾约束 未考虑集装箱的属性 张维英等[55] 2008 船舶纵向强度 未考虑不同尺寸和类型的集装箱 张维英等[21] 2011 横倾力矩最小 未考虑集装箱的属性 祝慧灵等[56] 2014 最大静水弯矩大于0 未考虑不同尺寸和类型的集装箱 王雅芬[57] 2015 横纵倾约束 未考虑不同尺寸和类型的集装箱 Cohen等[58] 2017 船舶强度约束 未考虑危险箱或其他类型集装箱 徐帅[37] 2018 静水弯矩最优 未考虑集装箱的属性 成保辰[59] 2019 横纵向力矩约束 未考虑危险箱 黄森佳等[60] 2019 纵向受力约束 未考虑特殊集装箱 刘志雄等[61] 2019 横倾力矩约束 未结合堆场取箱和船舶配载作业的协同优化展开 颜家岚[62] 2020 横倾力矩约束 未考虑不同尺寸的集装箱 Zhu[45] 2022 纵倾约束 未考虑不同尺寸和类型的集装箱 姚玗[63] 2022 纵倾约束和力矩约束 未考虑不同尺寸和类型的集装箱 Chang等[46] 2023 横纵倾约束 未考虑其他作业的影响
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表 4 配载计划问题求解算法的文献研究汇总
Table 4. Research summary on solution algorithms of stowage planning problems
作者 年份 求解算法 特点或不足 Ambrosino等[5] 2006 三阶段算法 适合于确定大型集装箱船舶的配载计划，并可以使得船舶各部分的装载作业并行进行 车鉴[117] 2008 模拟退火算法 仅利用50个集装箱验证了算法的可行性，没有与其他不同的求解方法进行比较 史宗耀[118] 2010 混合遗传算法(在传统的遗传算法的基础上引入模拟退火算法和禁忌搜索算法) 以实际问题作为验算对象，解决了传统遗传算法早熟收敛问题，但是设计的案例较为简单 孙晓雅等[20] 2011 离散粒子群算法 算法收敛速度快，能够增加种群的多样性，抑制早熟 张维英等[21] 2011 禁忌搜索算法 仅对30个集装箱的配载计划进行求解，未能证明是否可以求解大规模实际案例 孙俊清等[47] 2012 基于P-1位基因组编码的遗传进化配载算法 与随机配载方法和按照目的港原则的配载方法比较，优化效果更优 孙万宇[111] 2013 自适应并行遗传算法(引入改进的自适应交叉和变异算子，给出可调等比排序的选择操作) 解决了1 459个集装箱的船舶配载计划问题，但是对于集装箱数量的增加，算法是否可以快速求解是未来的研究方向 朱雯[119] 2013 启发式搜索算法 应用实例对算法进行了验证，但是未与其他不同的算法进行对比 Ambrosino等[16] 2015 两阶段渐进随机固定过程 可以在较短时间得出18 000 TEU的集装箱船舶配载方案 Parreño等[23] 2016 贪婪随机自适应搜索过程 与不同的算法进行比较，证明其算法可以获得更好的优化解，未来可以采用元启发式算法进行求解 Shen等[69] 2016 混合遗传算法 求解配载计划问题时具有较好的收敛性和有效性，与标准遗传算法进行比较；但是未给出是否可以有效求解大规模算例 Zhao等[79] 2016 特定的遗传算法(采用自交叉算子和变换变异算子的遗传算法) 可以获得较好的优化解，但是在求解大规模问题时，花费时间较长 余纪胜[120] 2016 人工鱼群算法 未进行案例验证 Shen等[70] 2017 深度强化学习算法 引入深度学习后，在前期训练阶段进行大量的计算与训练后，可以快速求解配载计划问题 李军翼[121] 2017 差分进化算法 利用2 400 TEU的集装箱船舶对算法进行了验证，但是配载计划问题考虑了较多的假设，因而与现实情况有所差距 祝国栋[122] 2017 反馈式启发式算法 求解效率比线性规划算法高，与基本的贪婪算法比，求解质量更高，但是在问题优化上仍存在较大空间 李俊等[49] 2018 混合邻域搜索算法(由蒙特卡罗随机模拟、神经元网络训练以及邻域搜索启发式3个部分组成) 鲁棒性较好，实现配载计划对不确定性的考虑 杨蔚等[123] 2018 改进的自适应遗传算法 与随机配载和启发式配载2种方法比较，当集装箱数量在800~1 600 TEU时，算法开始展现优势；随着集装箱数量增加，优势更加明显 刘志雄等[124] 2019 演化策略算法(采用二维实数编码、基于力矩平衡和逐列装载的装船规则的解码方法以及三点交叉互换的重组算子和两点互换的变异算子) 与粒子群算法和基于力矩平衡和逐列装载的装船规则的启发式算法相比更具优越性 Parreño-Torres等[44] 2021 插入修复启发式算法 可以对5 000 TEU的配载计划问题进行求解 盛进路等[72] 2021 BP神经网络 采用实船数据进行测试，结果与实际配载结果差异率不大 张煜等[84] 2021 带模糊关联熵的启发式算法 结合长江真实运输场景设计多组仿真算例 刘志雄等[90] 2021 结合启发式规则的演化策略算法 通过不同规模算例说明，相比粒子群算法和启发式算法，采用启发式规则的混合演化策略算法具有较好的优化性能 姚玗[63] 2022 二进制人工蜂群算法 可以求解最大载箱量为720 TEU的全集装箱船
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