Dual-Objective Optimization Research of Ship Cargo Flow Allocation in Multi-Mode Dam-Crossing System
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摘要:
为解决船舶过坝货流分配不均衡导致的水利枢纽通航拥堵问题，以船舶额外过坝总成本和等待时间为双目标，建立货流分配优化模型；进一步引入面向水运新通道过坝模式的服务收费机制，分析其对船舶货流转移规律的影响；然后，运用非支配排序遗传算法（NSGA-Ⅱ）对模型进行求解，提出过坝船舶货流分配优化方案. 最后，以三峡枢纽为例，验证所提模型和算法的有效性. 试验结果表明：该算法可求得多组Pareto前沿解，提供多样化的船舶货流分配方案，船舶额外过坝总成本与其等待时间呈显著负相关关系；双模式和多模式过坝系统的船舶货流分配方案，均能实现降本增效目标，且多模式系统的优化方案可使额外过坝总成本和等待时间分别降低67.1%和0.5%；与初始调度方案相比，船舶货流分配方案使得至少33.4%的船舶货流出现过坝模式转移，缓解了水利枢纽通航拥堵；且合理的水运新通道服务费率设置，可有效降低船舶过坝成本和提高过坝效率.
Abstract:The navigation congestion problem in water control projects is often caused by the unbalanced allocation of cargo flow for dam-passing ships. To address this issue, a cargo flow distribution optimization model was established to achieve dual objectives of minimizing the total additional cost for dam-crossing ships and waiting time. Furthermore, the service charge mechanism oriented to the dam-crossing mode of the new waterway was further introduced, and its influence on the transfer law of ship cargo flow was analyzed. Then, a non-dominated sorting genetic algorithm (NSGA)-II was applied to solve the model, and the dam-crossing ship cargo flow allocation optimization scheme was proposed. Finally, by taking the Three Gorges water control project as an example, the effectiveness of the proposed model and algorithm was verified. The results demonstrate that the algorithm successfully obtains multiple sets of Pareto frontier solutions and provides diversified ship cargo flow allocation schemes. The total additional cost of dam-crossing ships is significantly negatively correlated with their waiting time. The cargo flow allocation schemes of the dam-crossing system with dual and multiple modes can achieve the objectives of effectively reducing costs and improving efficiency. The optimized scheme with a multi-mode system reduces the total additional cost for dam-crossing ships and waiting time by 67.1% and 0.5%, respectively. Compared with the initial scheduling scheme, the proposed ship cargo flow allocation scheme results in a mode shift of at least 33.4% of the ship cargo flow, which alleviates navigation congestion in water control projects. Moreover, a reasonable service charge rate for the new waterway can effectively reduce the cost and improve the efficiency of dam-crossing ships.
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图 1 多模式过坝系统中船舶货流分配流程图
Figure 1. Ship cargo flow allocation in multi-mode dam-crossing system
图 3 NSGA-Ⅱ和SPEA-Ⅱ算法的帕累托前沿解
Figure 3. Pareto frontier solution of NSGA-Ⅱ and SPEA-Ⅱ algorithms
表 1 模型符号说明
Table 1. Notation description of model
类型 符号 说明 符号 说明 模型
参数$ I $ 决策期天数集合，$ I=\{1,2,\cdot \cdot \cdot ,i\} $ $ J $ 每日决策时段集合，$ J=\{1,2,\cdot \cdot \cdot ,j\} $ $ {Q}_{ij} $ 第 $i $ 天第 $j $ 时段船舶到达数量 $ q_{{\mathrm{L}},i} $ 第 $i $ 天通航建筑物船舶数量限制 $ q_{{\mathrm{F}},i} $ 第 $i $ 天货物翻坝船舶数量限制 $ q_{N,i} $ 第$ i $天水运新通道船舶数量限制 $ \alpha $ 货物翻坝转运单位装卸成本，元/t $ \beta $ 货物转运单位运输成本，元/(t•km) $ \omega $ 船舶的载货量，t $ \sigma $ 船舶的自重 $ D $ 锚地到通航建筑物的距离，km $ v $ 船舶平均航行速度，km/h $ T $ 平均过坝时间，h $ P $ 燃油价格，元/kg $ A $ 调整低船速油耗常数项 $ B $ 船舶通航耗油量模型速度项 $ L $ 船舶货物翻坝转运的运输距离 $ {t}_{\max } $ 船舶最大等待时间限制 $ d_{{\mathrm{L}},i,j} $ 第 $i $ 天第 $j $ 时段通航建筑物过坝服务量 $ A_{{\mathrm{L}},\max },A_{{\mathrm{L}},\min } $ 通航建筑物的船舶货流分配限制 $ {l}_{\max } $ 船舶最大队长限制 $ B_{{\mathrm{F}},\max },B_{{\mathrm{F}},\min } $ 翻坝转运的船舶货流分配限制 $ {\theta }_{\max } $ 新通道最大服务费率 $ C_{{\mathrm{N}},\max },C_{{\mathrm{N}},\min } $ 新通道的船舶货流分配限制 $ t_{{\mathrm{L}},i,j} $ 平均排队时间 $ l_{{\mathrm{L}},i,j} $ 船舶排队队长 模型变量 $ \tau $ 船舶新通道过坝的单位费率，元/t $ x_{{\mathrm{L}},i,j} $ 该时段选择通航建筑物的船舶货流量 $ x_{{\mathrm{F}},i,j} $ 该时段选择翻坝转运的船舶货流量 $ x_{{\mathrm{N}},i,j} $ 该时段选择水运新通道的船舶货流量 
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表 5 不同服务费率下的额外总成本和总等待时间均值比较
Table 5. Comparison of mean value of total additional cost and waiting time under different service charge rates
目标值 服务费率τ/（元·t−1） 0 （新通道未开通） 2 4 6 8 10 额外过坝总成本/万元 1924.7 346.2 632.4 868.2 1061.6 1250.2 总等待时间/h 7555.5 7275.4 7518.8 8277.1 9466.0 9782.1
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