A quay crane dynamic scheduling problem by hybrid evolutionary algorithm for berth allocation planning

A considerable growth in worldwide container transportation needs essential optimization of terminal operations. An operation schedule for berth and quay cranes can significantly affect turnaround time of ships, which is an important objective of all schedules in a port. This paper addresses the problem of determining the berthing position and time of each ship as well as the number of quay cranes assigned to each ship. The objective of the problem is to minimize the sum of the handling time, waiting time and the delay time for every ship. We introduce a formulation for the simultaneous berth and quay crane scheduling problem. Next, we combine genetic algorithm with heuristic to find an approximate solution for the problem. Computational experiments show that the proposed approaches are applicable to solve this difficult but essential terminal operation problem.     

多目标约束处理方法求解泊位岸桥联合分配问题

为了制定合理高效的泊位岸桥联合分配方案,加快船舶周转,本文针对船舶动态到港的连续泊位建立了以船舶总在港时间最短为目标的泊位岸桥联合分配混合整数非线性模型.通过多目标约束处理策略将复杂约束的违反程度转化为另一个目标,从而将原单目标优化模型转化为双目标优化模型,并用基于快速非支配排序的多目标遗传算法(NSGA-II)对其进行求解.同时,针对问题特点,分别设计了基于调整、惩罚函数、可行解优先和综合约束处理策略的单目标遗传算法对原模型进行求解.通过多组不同规模的标准算例对本文的方法进行测试,验证了基于多目标约束处理策略的方法求解效果相较于单目标约束处理策略的方法更加高效和稳定.     

A biased random-key genetic algorithm for the time-invariant berth allocation and quay crane assignment problem

Maritime transportation plays a crucial role in the international economy. Port container terminals around the world compete to attract more traffic and are forced to offer better quality of service. This entails reducing operating costs and vessel service times. In doing so, one of the most important problems they face is the Berth Allocation and quay Crane Assignment Problem (BACAP). This problem consists of assigning a number of cranes and a berthing time and position to each calling vessel, aiming to minimize the total cost. An extension of this problem, known as the BACAP Specific (BACASP), also involves determining which specific cranes are to serve each vessel. In this paper, we address the variant of both BACAP and BACASP consisting of a continuous quay, with dynamic arrivals and time-invariant crane-to-vessel assignments. We propose a metaheuristic approach based on a Biased Random-key Genetic Algorithm with memetic characteristics and several Local Search procedures. The performance of this method, in terms of both time and quality of the solutions obtained, was tested in several computational experiments. The results show that our approach is able to find optimal solutions for some instances of up to 40 vessels and good solutions for instances of up to 100 vessels.     

An enriched model for the integrated berth allocation and quay crane assignment problem

Given the increasing pressure to improve the efficiency of container terminals, a lot of research efforts have been devoted to optimizing container terminal operations. Most papers deal with either the berth allocation problem (BAP) or the (quay) crane assignment problem (CAP). In the literature on the BAP, handling times are often simplified to be berth dependent or proportional to vessel size, so the CAP can be ignored when scheduling vessels. This is unsatisfactory for real-life applications because the handling time primarily depends on the number of containers to be handled and the number of cranes deployed. Only a limited number of papers deals with the combination of berth allocation and crane assignment. In these papers however, authors often have resorted to algorithmic simplifications that limit the practical use of the models. This paper presents a MILP model for the integrated BAP–CAP taking into account vessel priorities, preferred berthing locations and handling time considerations. The model is used in a hybrid heuristic solution procedure that is validated on real-life data illustrating the potential to support operational and tactical decision-making.     

Hybrid rolling-horizon optimization for berth allocation and quay crane assignment with unscheduled vessels

Port operations usually suffer from uncertainties, such as vessels’ arrival time and handling time and unscheduled vessels. To address this, this study presents a dynamic berth allocation and crane assignment specific problem (BACASP) when unscheduled vessels arrive at the port, which is branded the berth allocation and quay crane assignment specific problem with unscheduled vessels (UBACASP). A rolling-horizon based method is proposed to decompose the UBACASP into a multi-stage static decision BACASP, wherein a rescheduling margin-based hybrid rolling-horizon optimization method is developed by incorporating the event-driven and periodical rolling-horizon strategies as the urgency of dynamic events is evaluated. In each rolling horizon, a mixed integer linear programming model (MILP) is presented for the BACASP to minimize the total port stay time of vessels and the penalties of delays associated with the spatial and temporal constraints, such as the length of continuous berth, number of quay cranes (QCs) and non-crossing of QCs. A discretization strategy is designed to divide the continuous berth into discrete segments, and convert the BACASP to a discrete combinatorial optimization problem, which is efficiently solved by the proposed adaptive large neighborhood search algorithm (ALNS). Case studies with different problem characteristics are conducted to prove the effectiveness of the solution methods proposed in this study. Moreover, the performances of the ALNS and the existing methods for solving the BACASP are compared, and the advantages and disadvantages of different rolling strategies under different degrees of uncertainties are deeply analyzed.     

A new continuous berth allocation and quay crane assignment model in container terminal

Over the past decades, Chinese ports throughput grew rapidly, and more and more concerns were shown on the operational efficiency and effectiveness. Many studies have been made for scheduling berth and quay cranes, which are the critical resources in container terminals. In this paper, a two-phase model for berth allocation and quay crane assignment is proposed. In the first phase, according to the relationships of time and space between vessels, a new continuous berth allocation model is established, in which not only the common restricts but the coverage area of quay crane are considered. Then in the quay crane assignment phase, a multi-objective programming model is proposed, in which the first objective is to minimize the range of maximum and minimum quay cranes used for resources saving, and the second one is to minimize the movements of quay cranes so as to improve the efficiency. A particle swarm optimization algorithm for BAP was developed. The results of numerical experiments show that the proposed approach can improve the essential operations in container terminal.     

Modeling berth allocation and quay crane assignment considering QC driver cost and operating efficiency

Due to high labour costs and difference of QC driver’s handling efficiency existing between day and night, factors concerning QC drivers can significantly impact the schedule of berth allocation and quay crane assignment. This paper tackles the berth allocation and quay crane assignment problem considering QC driver cost, difference of the operating efficiency and performance-related pay between day and night. How QC driver-related factors affect the schedules is analyzed, and the objective composition including QC driver cost is given. A mixed integer programming model with model acceleration algorithms is developed for the proposed problem, and a meta-heuristic framework including a three-stage algorithm is proposed for solving the problem. Numerical experiments are conducted to validate the effectiveness of the proposed model and performance of the meta-heuristic approach, leading to a multitude of managerial insights.     

An optimization approach for coupling problem of berth allocation and quay crane assignment in container terminal

This paper addresses an effective approach to solve the issue of berth allocation and quay crane assignment in a multi-user container terminal. First of all, the studied coupling problem is formulated with the interactions between berth allocation and quay crane assignment considered. Then, an evolutionary algorithm with nested loops was developed to obtain optimal solutions. The algorithm is well structured, where two inner loops are used to solve sub-problems of berth allocation and quay crane assignment respectively; an outer loop is then utilized to find an approximate solution based on the results of the two inner loops. The results of numerical experiments show that the proposed approach can improve the essential operations in container terminals.     

基于滚动规划的泊位和岸桥分配集成模型研究

泊位分配（BA）,岸桥配置（QCA）及岸桥调度（QCS）是三个基本的岸边决策问题。提出了一个基于混合整数线性规划的BA和QCA的集成模型,模型综合考虑了货轮优先权,理想泊位及处理时间三个方面的因素。在实际生产数据上的运行结果表明该模型具有决策支持的潜在能力。     

Multi-objective genetic algorithm for berth allocation problem considering daytime preference

Maximization of operational efficiency and minimization of cost are pursued by terminal operators, whereas daytime preference is increasingly emphasized by governments, terminal operators and workers. Daytime preference in berth allocation schedule refers to schedule the workloads in nights as fewer as possible, which improves working comfort, safety, and green and energy-savings degrees, but may decrease the throughput and total operational efficiency. By extending existing dynamic discrete berth allocation model, a bi-objective model considering daytime preference is established to minimize the delayed workloads and the workloads in nights. Based on the well known NSGA-II algorithm, a multi-objective genetic algorithm (moGA) is developed for solving the bi-objective model by using a two-part representation scheme. The sensitivities of the algorithmic parameters and tradeoffs between daytime preference and delayed workloads are analyzed by numerical experiments. The algorithmic aspects of the proposed approach and the effects of daytime preference on solutions are all examined. Finally, the managerial implications are discussed.     

桥吊可动态分配的连续泊位分配问题算法

研究在允许桥吊动态分配的情况下集装箱码头的连续泊位动态分配问题,并建立以船舶在港时间最小为目标的动态泊位分配模型;然后基于兄弟-儿子方法对船舶的位置进行调整以规划桥吊使桥吊不交叉。在相同算例下,比现有方法得到的船舶在港时间更少,从而验证了模型及算法的有效性。     

A modified genetic algorithm for quay crane scheduling operations

The demand for the maritime transportation has significantly increased over the past 20 years due to the rapid pace of globalization. Terminal managers confront the challenge in establishing the appropriate quay crane schedule to achieve the earliest departure time of ship and provide efficient service. In general, quay crane schedule problems include two main issues (1) the allocation of quay cranes to handle the discharging and loading operations, and (2) the service sequence of ship bays in a vessel of each quay crane. Traditionally, the terminal planners determine the quay crane schedule based on their experience and own judgment. In addition, the interference among cranes and the increased in ship size further magnify its difficulty dramatically. Accordingly, this paper proposed a modified genetic algorithm to deal with the problem. To test the optimization reliability of the proposed algorithm, a set of well known benchmarking problem is solved, and the results obtained are being compared with other well known existing algorithms. The comparison demonstrates that the proposed algorithm performs as good as many existing algorithms and obtains better solutions than the best known ones in certain instances. In addition, the computational time(s) required are significantly much lesser, allowing it to be more applicable in practical situation.     

改进Memetic算法求解集装箱码头泊位岸桥调度问题

针对集装箱码头泊位岸桥调度这一NP难题,提出了一种改进的Memetic算法。算法中采用三层染色体结构表示个体,通过改进顺序交叉算子和基于领域搜索的变异算子以避免个体超出可行域,在交叉和变异后采用改进的模拟退火策略进行局部搜索。试验算例表明该算法收敛速度较快,且能获得较好的满意解。     

An efficient genetic algorithm for solving the quay crane scheduling problem

This paper addresses the quay crane scheduling problem (QCSP), which has been shown to be NP-complete. For this reason, a number of studies have proposed the use of genetic algorithm (GA) as the means to obtain the solution in reasonable time. This study extends the research in this area by utilizing the GA that is available in the latest version of Global Optimization Toolbox in MATLAB 7.13 to facilitate development. It aims to improve the efficiency of the GA search by (1) using an initial solution based on the S-LOAD rule developed by Sammarra, Cordeau, Laporte, and Monaco (2007), (2) using a new approach for defining the chromosomes (i.e., solution representation) to reduce the number of decision variables, and (3) using new procedures for calculating tighter lower and upper bounds for the decision variables. The effectiveness of the developed GA is tested using several benchmark instances proposed by Meisel and Bierwirth (2011). Compared to the current best-known solutions, experimental results show that the proposed GA is capable of finding the optimal or near-optimal solution in significantly shorter time for larger problems.     

求解动态停泊计划问题的拉格朗日松弛算法

研究钢铁企业原料码头动态停泊计划问题,其动态特征主要体现在原料船动态到达并有两个或两个以上连续泊位且在停泊计划开始执行时每一泊位上仅有部分泊位长度可利用。针对这个问题,建立了一个数学模型并设计了改进拉格朗日算法在很短的时间内求得了近优解。在改进算法中使用了所提出的四个性质来分别加速求解子问题、乘子更新和获得可行解的过程。通过包含50个实际规模问题的算法性能实验表明改进的拉格朗日松弛算法相比未改进算法减少了80%的运行时间。     

基于滚动策略的集装箱码头连续泊位与桥吊集成调度

针对连续泊位与桥吊集成调度大规模求解困难的问题,提出一种基于滚动策略的优化方法。首先,建立了最小化船舶偏离偏好泊位的成本以及延迟靠泊、延迟离港的惩罚成本的基本的多目标优化模型;然后,采用滚动调度方法根据动态抵泊的船舶抵达顺序将调度过程分成连续的调度窗口,并设计窗口的平移策略、当前窗口对下一窗口的参数更新方式;对每个窗口内船舶进行调度优化,根据每个窗口内的优化结果,更新下一个窗口中数学模型的输入参数;通过选取以船舶数量表示的滚动计划窗口和冻结船舶的数量,持续滚动获得每个窗口的最优解,叠加后获得对所有船舶的靠泊计划。通过算例分析表明,滚动调度能够解决较大规模的调度问题,其效率受滚动窗口大小、冻结船舶数量及滚动次数影响     

不确定环境下集装箱码头泊位与岸桥联合调度

在集装箱码头操作系统中,有效的泊位岸桥调度计划有助于提高码头的运营效率和客户满意度。针对船舶到港时间和装卸作业时间随机的泊位岸桥联合调度问题,综合考虑了连续泊位下船舶偏离偏好泊位产生的惩罚时间,并通过添加延缓时间的方法来吸收不确定性因素带来的影响。为了体现调度计划的鲁棒性,将延缓时间添加在目标函数中,建立了以船舶在港总时间、偏离偏好泊位的惩罚时间、客户满意度和延缓时间之和最小化为目标的混合整数规划模型,提出一种自改变遗传算法和启发式靠泊相结合的改进遗传算法对模型进行求解;通过算例分析,证明了提出的改进遗传算法在计算不确定环境下的泊位岸桥联合调度问题的有效性。     

基于船时效率的岸桥配置优化

在集装箱码头系统中,对船舶进行有效的岸桥配置有助于缓解岸边资源紧张的现状,提高码头的运营效率。针对连续泊位下动态到港船舶的泊位分配和岸桥配置的集成优化问题,对船舶的岸桥配置进行基于船时效率的动态调整,以最小化包括船舶延迟靠泊成本、偏离偏好泊位成本、延迟离港成本和岸桥重新配置成本在内的总成本为目标建立模型,并根据基于船时效率的岸桥配置的调整规则设计了启发式算法,结合遗传算法（GA）对问题进行求解。最终通过算例分析,验证了提出的模型和算法在解决实际港口中泊位分配和岸桥配置问题上的有效性,并通过与未考虑岸桥配置进一步调整的传统GA计算的结果进行比较,证实了提出算法的优化效果。     

货架分配问题的一个有效混合遗传算法

针对货架分配问题提出了一个遗传算法与模拟退火算法及一个局部搜索算法混合的算法。首先,设计了一种比较直观的编码方法,用一个矩阵作为一种货架分配方案。第二,设计了与编码相应的杂交和变异算子,并且杂交、变异都能生成可行解,不需要对解进行修正。第三,为了能够生成好的初始种群,定义了一个阀值,这个阀值不仅反映了解的适应值的信息,而且还反映解的结构的信息。第四,为了增加算法的局部搜索能力,同时又尽量不增加计算的复杂度,让模拟退火算法和一种局部搜索算法并行作用于相应的子群。通过大量的数据模拟实验及与其他的几种算法模拟结果进行比较,实验显示,该算法不论是计算结果还是算法的稳定性都优于其他算法。