Optimal control of container cranes

A dynamical model of container cranes is derived by using Lagrange's equation. When a ship is loaded or unloaded with containers, the total motion of the container load is divided into five fundamental sections. For each fundamental type of motion, the optimal control is calculated such that the corresponding trajectory satisfies the specified boundary conditions and that the swing of the container load during the transfer is minimized. A new algorithm which is employed for computing the optimal control is explained in detail. Some results of numerical computation are also shown.     

An optimization methodology for intermodal terminal management

A solution to the problems of resource allocation and scheduling of loading and unloading operations in a container terminal is presented. The two problems are formulated and solved hierarchically. First, the solution of the resource allocation problem returns, over a number of work shifts, a set of quay cranes used to load and unload containers from the moored ships and the set of yard cranes to store those containers on the yard. Then, a scheduling problem is formulated to compute the loading and unloading lists of containers for each allocated crane. The feasibility of the solution is verified against a detailed, discrete-event based, simulation model of the terminal. The simulation results show that the optimized resource allocation, which reduces the costs by [frac13], can be effectively adopted in combination with the optimized loading and unloading list. Moreover, the simulation shows that the optimized lists reduce the number of crane conflicts on the yard and the average length of the truck queues in the terminal.     

A fast heuristic for quay crane scheduling with interference constraints

This paper considers the problem of scheduling quay cranes which are used at sea port container terminals to load and unload containers. This problem is studied intensively in a recent stream of research but still lacks a correct treatment of crane interference constraints. We present a revised optimization model for the scheduling of quay cranes and propose a heuristic solution procedure. At its core a Branch-and-Bound algorithm is applied for searching a subset of above average quality schedules. The heuristic takes advantage from efficient criteria for branching and bounding the search with respect to the impact of crane interference. Although the used techniques are quite standard, the new heuristic produces much better solutions in considerably shorter run times than all algorithms known from the literature.     

Design of steady-state minimum variance controllers

A new technique to design optimal controllers is presented for plants described by rational transfer functions and additive disturbances with rational spectral densities. The objective is to minimize a weighted sum of the plant input and output steady-state variances subject to asymptotic stability of the closed-loop system.The technique is based on polynomial algebra. In fact, the design procedure is reduced to solving two linear polynomial equations whose unique solution directly yields the optimal controller transfer function as well as the minimized cost. This approach is simple, computationally attractive, and can handle unstable and/or nonminimum-phase plants with improper transfer functions.An integral part of the paper are effective computational algorithms, which include the spectral factorization, the solution of polynomial equations, and the evaluation of minimum cost.     

A multi-objective genetic algorithm for yard crane scheduling problem with multiple work lines

Due to increasing ships and quay cranes, container terminals operations become more and more busy. The traditional handling based on work line is converted into pool strategy, namely loading and unloading containers with multiple work lines are operating simultaneously. In the paper we discuss the yard crane scheduling problem with multiple work lines in container terminals. We develop a multi-objective 0-1 integer programming model considering the minimum total completion time of all yard cranes and the maximization balanced distribution of the completion time at the same time. With the application of adaptive weight GA approach, the problem can be solved by a multi-objective hybrid genetic algorithm and the Pareto solutions can be finally got. Using the compromised approach, the nearest feasible solution to ideal solution is chosen to be the best compromised Pareto optimal solution of the multi-objective model. The numerical example proves the applicability and effectiveness of the proposed method to the multi-objective yard crane scheduling problem.     

铁路集装箱中心站内部集卡调度和箱位配置

针对铁路集装箱中心站集装箱专列卸箱作业的效率问题,将内部集卡的任务调度和集装箱箱位分配进行集成,建立集装箱列车卸车作业的多目标优化模型,包括内卡在轨道门吊和辅助箱场等待时间,以及走行时间对作业效率的影响。采用混合遗传算法进行求解。将模拟结果与实际操作数据作比较,并对20次计算模拟进行平均时间和方差分析,验证了该方法的有效性。     

Generating a rehandling-free intra-block remarshaling plan for an automated container yard

Intra-block remarshaling in a container terminal refers to the task of rearranging the export containers, which are usually scattered around within a block, into designated target bays within the same block. Since the containers must be loaded onto a ship following a predetermined order, the rearrangement should be performed in such a way that the containers to be loaded first are placed on top of those to be loaded later in order to avoid rehandling. To minimize the time required to complete a remarshaling task, rehandling should also be avoided during the remarshaling operations. Moreover, when multiple stacking cranes are used for the remarshaling, the interference between cranes should be minimized. This paper presents a method to efficiently search for an intra-block remarshaling plan which is free from rehandling during both the loading operation and remarshaling, and which minimizes the interference between the stacking cranes.     

基于滚动窗策略的港口海铁联运集装箱转运优化

为了解决港口海铁联运转运集装箱作业规模过大的问题,采用滚动窗策略方法研究港口船舶与列车之间转运进口集装箱作业问题,在每个窗口内建立以列车在港停留时间和集装箱在堆场的堆存时间总时间最小为目标的整数规划模型,设计双层遗传算法进行求解。在此基础上,分别讨论了以固定任务数量和固定时间长度为滚动窗口的情况,对比发现以固定时间长度为窗口的滚动窗策略更适用,并将其与已有的调度策略研究成果作比较分析。最后,设置实验比较双层遗传算法和单层遗传算法,并对设备的工作能力进行灵敏度分析。结果表明,滚动调度策略可以灵活解决大规模集装箱转运问题,双层遗传算法的解优于单层遗传算法的解,增加装卸线数和轨道起重机工作能力可以提高集装箱转运效率。     

Choice of loading clusters in container terminals

The storage allocation in the export yard of a container terminal determines the efficiency of container loading. Even if the yard manager has optimised the allocation of export containers to avoid rehandling, conflicts among loading quay cranes can still occur. Thus, all the possible handlings during loading must be considered when organising the yard space. In previous studies, the yard storage allocation has been assessed based on the subblock, which consists of several adjacent bays. However, to minimise all possible handlings in the loading process at the terminal, optimising more flexible storage clusters is also important. Thus, our aim in this research is to model the choice of loading clusters and derive a more flexible allocation strategy for organising the space in the export yard. A bi-objective model is built, which considers both the transportation distance and handling balance between blocks. A model aimed at minimising all possible handlings in the export yard for the loading process is also developed, and several of the insights derived can inform yard management in real-life operations. It is proven that the handling requirements have a significant effect on the choice of loading clusters, and yard managers should consider the various features of liner and loading processes when organising their storage space.     

Computerized container-ship load planning: A methodology and evaluation

A heuristic is developed to plan loads for containerized cargo ships. It is designed to serve a port which uses gantry cranes (transtainers) and trucks to handle containers. The model recognizes constraints on ship stability, placing containers in a bay with the proper length, limits on stack height in under-deck bays, limits on stack weight in on-deck bays, refrigerated containers, and the need for support under a container. Provisions are made for the operator to handle overstowage of cargo for different ports and placement of oversize cargo. The model uses minimization of transtainer movement time and minimization of rehandles in the yard as an objective. The heuristic uses strategies for container placement similar to those used in manual load planning. A test of two ships and four voyages at the Port of Portland produced feasible load plans for each voyage. Transtainer movement and rehandling time varied for the four voyages; but on the average, the heuristic reduced a composite material handling measure by 4.8%.     

Solving the uncapacitated facility location problem using tabu search

A tabu search heuristic procedure is developed to solve the uncapacitated facility location problem. Tabu search is used to guide the solution process when evolving from one solution to another. A move is defined to be the opening or closing of a facility. The net cost change resulting from a candidate move is used to measure the attractiveness of the move. After a move is made, the net cost change of a candidate move is updated from its old value. Updating, rather than re-computing, the net cost changes substantially reduces computation time needed to solve a problem when the problem is not excessively large. Searching only a small subset of the feasible solutions that contains the optimal solution, the procedure is computationally very efficient. A computational experiment is conducted to test the performance of the procedure and computational results are reported. The procedure can easily find optimal or near optimal solutions for benchmark test problems from the literature. For randomly generated test problems, this tabu search procedure not only obtained solutions completely dominating those obtained with other heuristic methods recently published in the literature but also used substantially less computation time. Therefore, this tabu search procedure has advantage over other heuristic methods in both solution quality and computation speed.     

An integrated model for the transshipment yard scheduling problem

A hub-and-spoke railway system is an efficient way of handling freight transport by land. A modern rail–rail train yard consists of huge gantry cranes that move the containers between the trains. In this context, we consider a rail–rail transshipment yard scheduling problem (TYSP) where the containers arrive to the hub and need to be placed on a train that will deliver them to their destination. In the literature, the problem is decomposed hierarchically into five subproblems, which are solved separately. First, the trains have to be grouped into bundles in which they visit the yard. Next, the trains have to be assigned to tracks within these bundles, namely parking positions. Then the final positions for the containers on trains have to be determined. Next, the container moves that need to be performed are assigned to the cranes. Finally, these moves have to be sequenced for each crane for processing. In this paper, an integrated MILP model is proposed, which aims to solve the TYSP as a single optimization problem. The proposed formulation also enables us to define more robust and complex objective functions that include key characteristics from each of the above-mentioned subproblems. The strength of our proposed formulation is demonstrated via computational experiments using the data from the literature. Indeed, the results show that the TYSP can be solved without the use of decomposition techniques and more insight can be obtained from the same input data used to solve particular single decomposed subproblems.     

A＊算法在轨道式龙门起重机提箱作业优化中的应用

集装箱翻箱问题是影响集装箱码头堆场机械操作效率的一个重要的因素。为了解决在堆场中应用不同装卸机械所产生的相关问题,本文选取轨道式龙门起重机作为堆场装卸机械,建立以码头堆场机械作业时间最短为目标．满足堆场实际作业要求的提箱优化数学模型。应用启发式算法A＊算法对问题进行求解,并通过对实例的研究,验证A＊算法的正确性和有效性。     

多目标交会轨迹优化方法综述

多目标交会能有效降低单次任务的成本并提高任务收益,因此是未来小行星探测、在轨服务等任务的首选方案.该类任务的轨迹优化问题涉及的变量众多,解空间巨大,难以直接得到最优解.该问题的求解通常分为两步:首先优化交会序列,然后对于给定的交会序列,优化每段目标-目标转移的轨迹.优化交会序列时需对转移的速度增量或时间等代价进行快速、准确的估计.因此,多目标交会的轨迹优化可拆分为转移代价估计、交会序列优化、转移轨迹优化三个子问题.本文分别对这三个子问题的求解方法进行综述.     

An analytical framework for integrated maritime terminal scheduling problems with time windows

Container transport, an integral part of intercontinental trade, has steadily increased over the past few decades. The productivity of such a system, in part, hinges on the efficient allocation of terminal resources such that the container transit time is minimized. This study provides an analytical framework, which entails efficient scheduling of quay and yard cranes, to minimize the time spent by containers at a terminal. A mixed-integer programming model is developed to capture the two-stage multi-processor characteristic of the problem, where each crane has specific time window availability. A genetic algorithm equipped with a novel decoding procedure is developed. The mixed-integer model is tested on a number of problem instances of varying sizes to gain managerial insights.     

多类型集装箱装船模型及优化

针对集装箱装船问题提出了一个整数规划模型.该模型能够解决多类型、多目的地集装箱的装船问题.在实现了最小化倒箱次数、最大化运输船空间利用率的同时还保证了船只在不同负载分布下的稳定性,并能保证结果是全局最优解.实验中使用COIN-OR(Common Optimization Interface for Operations Research)对建立的模型进行求解.结果表明其有效性,从而为合理进行船只配载提供了一个有效的途径.     

Operator-scheduling using a constraint satisfaction technique in port container terminals

In port container terminals, the efficient scheduling of operators of handling equipment such as container cranes, yard cranes, and yard trucks is important. Because of many complicated constraints, finding a feasible solution, as opposed to the optimal solution, within a reasonable amount of computing time can be considered satisfactory from a practical point of view. The major constraints include the following: restrictions on the minimum workforce assignment to each time slot, the maximum total operating time per operator per shift, the minimum and maximum consecutive operating times for an operator, types of equipment that can be assigned to each operator, and the available time slots for each operator or piece of equipment. The operator-scheduling problem is defined as a constraint-satisfaction problem, and its solution is obtained by utilizing a commercial software. An actual problem, collected from a container terminal in Pusan, Korea, is solved through the solution procedure proposed in this study.     

Load scheduling for multiple quay cranes in port container terminals

This paper proposes a method to schedule loading operations when multiple yard cranes are operating in the same block. The loading scheduling methods in this paper are based on a genetic algorithm and a simulated annealing method, which consider interferences between adjacent yard cranes. It attempts to minimize the make-span of the yard crane operation. We consider the container handling time, the yard crane travel time, and the waiting time of each yard crane, when evaluating the makespan of the loading operation by yard cranes. An encoding method considering the special properties of the optimal solution of the problem is suggested. Numerical experiment was conducted to compare performances of the algorithms suggested in this study. Received: June 2005 / Accepted: December 2005     

Exact and approximate solutions of the container ship stowage problem

This paper deals with a stowage plan for containers in a container ship. Containers on board a container ship are placed in stacks, located in many bays. Since the access to the containers is only from the top of the stack, a common situation is that contianers designated for port J must be unloaded and reloaded at port I (before J) in order to access containers below them, designated for port I. This operation is called “shifting”. A container ship calling many ports, may encounter a large number of shifting operations, some of which can be avoided by efficient stowage planning. In general, the stowage plan must also take into account stability and strength requirements, as well as several other constraints on the placement of containers. In this paper we deal with stowage planning in order to minimize the number of shiftings, without considering stability constraints. First, a 0–1 binary linear programming formulating is presented that can find the optimal solution for stowage in a single rectangular bay of a vessel calling a given number of ports, assuming that the number of constainers to ship is known in advance. This model was successfully implemented using the GAMS software system. It was found, however, that finding the optimal solution using this model is quite limited, because of the large number of binary variables needed for the formulation. For this reason, several alternative heuristic algorithms were developed. The one presented here is based on a “reduced” transportation matrix. Containers with the same source and destination ports are stowed in full stacks as much as possible, and only the remaining containers are allocated by the binary linear programming model. This approach often allows the stowage planning of a much larger number of containers than using the exact formulation.     

Wiener?Hopf design of optimal decoupling one-degree-of-freedom controllers for plants with rectangular transfer matrices

This paper is a sequel to an earlier one which treated the design of optimal decoupling one-degree-of-freedom stabilizing multivariable controllers for plants with square transfer matrices. Here designs for plants with rectangular transfer matrices are given which allow for feedforward compensation and more generality in the specification of the desired closed-loop transfer matrix. As in the earlier work, all controllers are placed in the forward path of the feedback loop and non-unity feedback is permitted. The criterion for optimality is a quadratic-cost functional that penalizes both tracking error and saturation. Explicit formulas are derived which give the set of all those controllers that yield finite cost, as well as the ones that are optimal. It is shown that these controllers are strictly-proper under conditions usually prevailing in practice. The solution for plants with rectangular transfer matrices is expressed in terms of both Schur and Kronecker matrix products. When the plant transfer matrix is square, the solution reduces to the one obtained in the earlier work and involves only Schur matrix products.