基于分组策略的多目标三维装箱算法

目的 针对现有三维装箱算法优化目标单一、优化效率低的问题,提出适用于求解大规模货物装载问题的多目标装箱算法,以提高装箱规划效率,确保货物运输安全。方法 考虑5种现实约束条件,以体积利用率和装载垛型重心偏移量为优化目标,建立多目标货物装载优化模型。采用拟人式装箱对货物进行预分组,减小决策空间,然后结合分组信息与装箱算法生成初始解;引入数据驱动的装箱交叉算子提高算法收敛性;设计多策略变异算子提高算法结果的多样性。结果 以公共数据集和真实航空货物数据作为实验数据进行实验。实验结果表明,在满足多种约束条件下,集装箱装载强异构货物平均体积利用率达到92.0%,重心位置空间偏移从20 cm减少到7.5 cm,并且算法运行时间减少了73.5%。结论 本文所提算法应用于求解大规模多目标三维装箱问题,提高了装箱质量和效率,可为三维装箱算法的工程应用提供参考。     

不确定条件下集装箱堆场出口箱具体箱位优选

集装箱码头堆场出口箱箱位分配是翻箱率和装船效率的关键。为合理分配堆场出口箱箱位,考虑集装箱进出场时间的随机不确定性,建立了出口箱位随机双层规划模型,分别优化堆场预期翻箱量和龙门吊取箱时的行车成本。根据双层规划模型分别优选堆场贝和栈的特点及较优解特征,设计了求解模型的启发式算法。实验结果表明,上述方法能有效地利用集装箱不确定进出场信息改善堆场箱位分配的合理性,提高作业效率。     

热轧圆钢的轧制批量计划优化模型与算法

针对热轧圆钢的轧制批量计划编制问题,以热轧圆钢的需求为导向,综合考虑热轧和加热炉阶段的工艺要求,建立了以最小化钢坯余料浪费惩罚和相邻钢坯间跳跃惩罚为目标的数学模型,并基于约束满足技术设计求解算法.算法通过变量选择和值选择规则对待轧制钢坯进行选择、分组和序列生成操作;通过约束传播技术缩减搜索空间,并划分轧制单元;同时,将装箱启发式Best Fit Decreasing (BFD)嵌入到算法中,以优化钢坯余料浪费惩罚和钢坯属性跳跃惩罚.基于实际生产数据的仿真实验表明了模型和算法的可行性和有效性.     

路径优化算法求解集装箱码头堆场翻箱问题北大核心CSSCI

集装箱翻箱问题(CRP)可描述为在集装箱堆场现有堆垛状态和提箱序列确定情况下,以最少的翻箱数量提取出堆场箱区内所有集装箱;CRP是一个NP-hard问题。为此构建双层目标规划模型,提出嵌套翻箱规则的路径规划算法(POA),以期减少解空间大小,从而在更短的CPU运行时间内得到CRP的最优解。数值实验结果表明,POA在翻箱数量及运行时间上均优于多数算法,有效提高集装箱码头堆场作业效率,更适用于求解集装箱码头翻箱作业优化问题。     

一刀切约束下的二维装箱问题高效求解算法

目的 为实现大规模物料的快速剪裁切割,对考虑一刀切约束的二维装箱问题进行研究,并构建相应的改进优先度算法IPH(Improved Priority Algorithm,IPH).方法 IPH能够在不需要任何迭代搜索下,直接进行剩余空间分割与填充.为此,发展PH算法中的优先度放置规则,并以最大化生成大空间面积和最小化生成小空间面积为基础,设计改进砌砖式空间分割策略.结果 针对标准数据集的对比实验表明,IPH能够在较短时间内完成大规模算例的高效求解,并首次获得了多个算例的最优填装效果.结论 基于概率较优的启发式求解方法,能够实现无迭代优选下的一刀切二维装箱问题直接求解,且运算效果令人满意.     

基于实际约束的三维装箱问题优化算法

针对考虑了8种实际约束的多箱异构装箱优化问题,构建了一个三维装箱问题的多目标混合整数规划模型,给出了求解该模型的一种启发式搜索算法。该算法的核心是在满足实际约束条件下,通过空间切割法确定目标空间,在目标空间内通过生成"垂直条","水平带"搜索最佳"货物块",实现装箱体积利用率尽可能大,进而达到装箱数最小优化目标。通过随机算例和实际算例的计算分析及3D结果显示,说明该算法能有效满足所有现实约束,且稳定性及空间利用率较高,验证了算法有效性和实用性。     

武器维修器材分层装箱算法研究

武器维修器材装箱问题是一个复杂的多约束组合优化问题。在考虑实际约束条件下,分析了武器维修器材装箱问题,采用空间分割、分层装载和最优选择等策略,提出了一种基于启发式的武器维修器材装箱算法,较好地解决了武器维修器材的优化装载问题。     

电商物流背景下基于空间矩阵的三维装箱算法

针对电子商务领域中普遍存在的具有高度个性化和强异构性的三维装箱问题,提出一种电商物流领域适用性极强的组合启发式算法。根据问题特点,首先提出三维装箱的空间矩阵表征方式,基于该表征方式设计优化装箱检验算法,其次优化设计启发式算法的编码译码规则,并引入大规模邻域搜索算法进一步优化装箱序列路径搜索过程,从而共同构成组合启发式算法。结果表明,该算法在电商物流领域装箱问题中性能较好,求解结果接近理论最优解,同时求解质量优于其他装箱算法和商用软件,尤其是在复杂程度较高的装箱问题中更为明显。该算法能有效解决当前研究较少、需求较高的电商物流领域装箱问题,从而极大地降低电商物流企业的装箱成本。     

基于K-means与关键点的组合行李码放算法

目的为了解决当前航空行李码放流程中存在的劳动密集、效率低下的问题,开展行李码放算法研究。方法搭建含有重量、体积和货舱空间约束的航空行李码放数学模型,采用聚类、排序、关键点构建策略,设计一种K-means聚类与"关键点"思想相结合的组合式算法。结果采用100件真实旅客行李数据进行了实验,结果表明算法给出的布局方案规划合理,垛型左右两侧质量之差低于1%,满足了货舱的空间约束与载重平衡约束。结论算法具备在复杂环境下得到优良布局方案的能力,K-means聚类的引入也将机器学习领域的聚类算法引入装箱问题,架起了机器学习算法与传统装箱算法的桥梁,为今后装箱问题算法的设计提供了一条新思路。     

求解集装箱装载问题的混合蚁群模拟退火算法

目的 针对物流行业中存在的大规模、复杂、多规格货物的集装箱装载问题,提出一种基于塔装载启发式算法、二维装载点启发式算法、蚁群模拟退火算法的混合算法。方法 首先,采用塔装载启发式算法将三维待装箱装载成塔集,即将三维装箱问题降为二维装箱问题,有效降低集装箱的装载规模;其次,蚁群算法通过融入信息素选择更新策略,并利用自适应信息素挥发系数来提升算法整体的收敛速度,同时结合模拟退火算法对每代优秀路径集进行局部搜索,避免算法因收敛过快而陷入局部最优;最后,将蚁群模拟退火算法与二维装载点启发式算法相结合,优化每座塔的装载顺序和放置姿态,寻找最优的装载方案。结果 实验证明,在250组算例中,采用混合算法后,集装箱的平均空间利用率为90.92%,优于其他3种对比算法。结论 设计的混合蚁群模拟退火算法适用于解决大规模集装箱装载问题。     

An integrated formulation for hierarchical cast design problems in the steel making industry

Production design is a key decision problem of steel making industry but due to its complexity, solution properties are not well understood. The design problem can be viewed as a multi-stage problem of bin packing, matching and sequencing sub-problems. Traditionally a sequential approach which treats each sub-problem separately has been applied to the simple case where mould width change is not allowed. However, for more general cases where casting with width change and different width is allowed, the sequential approach fails to generate good solutions. In this paper, we propose a mathematical programming formulation which can solve the design problem in an integrative way. By introducing multi-layer network representation of the cast design problem, it is now possible to generate an integrated formulation for the proposed problem. Based on the formulation, we derive a heuristic algorithm. The algorithm is adopted and tested at a large international integrated steel mill. The computational tests with real data-sets show that the proposed algorithm is quite effective and practical.     

Two-staged guillotine cut,two-dimensional bin packing optimisation with flexible bin size for steel mother plate design

This paper looks into the steel mother plate design problem. A slab, which is an intermediate work in process, is subsequently rolled into a mother plate with the specific dimensions of thickness, length, and width. The mother plate is then cut into customer order plates. As a slab is rolled into a mother plate through a series of horizontal and vertical rolling processes, different-sized mother plates can be generated from a single-slab type. This flexibility allows for the size of a mother plate to be determined according to the order plates assigned to it. Furthermore, when the order plates are cut from a mother plate, a guillotine cut is required to reduce the production cost. The steel mother plate design problem involves the placing of order plates on the mother plates in a guillotine cut pattern and determining the sizes of the mother plates with the objective of minimising the number of slabs; thus it may be considered as a two-staged guillotine cut, two-dimensional bin packing problem with flexible bin size. This paper introduces the problem, presents several mathematical models, and proposes an iterative two-phase heuristic method consisting of several algorithms to solve the problem. Computational results for the benchmark problems show the effectiveness of the proposed method.     

Solving non-oriented two dimensional bin packing problem using evolutionary particle swarm optimisation

The non-oriented two-dimensional bin packing problem (NO-2DBPP) deals with a set of integer sized rectangular pieces that are to be packed into identical square bins. The specific problem is to allocate the pieces to a minimum number of bins allowing the pieces to be rotated by 90° but without overlap. In this paper, an evolutionary particle swarm optimisation algorithm (EPSO) is proposed for solving the NO-2DBPP. Computational performance experiments of EPSO, simulating annealing (SA), genetic algorithm (GA) and unified tabu search (UTS) using published benchmark data were studied. Based on the results for packing 3000 rectangles, EPSO outperformed SA and GA. In addition; EPSO results were consistent with the results of UTS indicating that it is a promising algorithm for solving the NO-2DBPP.     

面向批量订单包装的物流箱规格优化问题研究

目的 针对面向仓储物流环境下多型号多批量产品的订单包装问题,提出一种预制物流箱规格优化模型及算法。方法 对产品订单建立订单分包规则,确定分包方案,以订单包装材料总成本最小为优化目标建立物流箱规格优化模型。针对该模型提出一种改进模拟退火算法,通过贪婪策略求解最优分包方案,降低模型计算复杂度,设计一种新型解更新算子,以提高算法寻优能力,设计一种自适应步长策略,以平衡算法前期全局搜索与后期局部搜索的能力。结果 通过实例证明,文中提出的算法相较于其他算法,具有更强的求解能力,与实例企业仓储包装现状相比,同批订单降低了17%的包装材料成本。结论 该方法可用于解决产品种类多、尺寸差异大、动态更新等应用场景下的系列运输包装纸箱规格优化问题,为企业物流运输管理提供了一种有效的包装优化思路和解决方法。     

A two-dimensional bin-packing problem with conflict penalties

In this paper, we address the two-dimensional bin-packing (2BP) problem with variable conflict penalties, which incur if conflicting items are loaded into the same bin. Such a problem is observed in applications such as supermarket chains and automobile components transportation. The problem not only focuses on minimisation of number of bins used, but also deals with the conflict penalties at the same time. We propose a heuristic method based on the IMA algorithm and adapt it to solve this problem. A local search procedure is also designed to further improve the solutions. For instances derived from benchmark test data, the computational results indicate that the adapted IMA heuristic algorithm with local search effectively balances the number of bins used and the conflict penalties. The algorithm outperforms several adapted approaches that are well known for the 2BP problems.     

A batching-move iterated local search algorithm for the bin packing problem with generalized precedence constraints

In this paper, we propose a generalisation of the bin packing problem, obtained by adding precedences between items that can assume heterogeneous non-negative integer values. Such generalisation also models the well-known Simple Assembly Line Balancing Problem of type I. To solve the problem, we propose a simple and effective iterated local search algorithm that integrates in an innovative way of constructive procedures and neighbourhood structures to guide the search to local optimal solutions. Moreover, we apply some preprocessing procedures and adapt classical lower bounds from the literature. Extensive computational experiments on benchmark instances suggest that the developed algorithm is able to generate good quality solutions in a reasonable computational time.     

Computer Simulation of Random Sphere Packing in an Arbitrarily Shaped Container

Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4~0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.     

Optimization Models for Scheduling of Jobs

This work is motivated by a particular scheduling problem that is faced by logistics centers that perform aircraft maintenance and modification. Here we concentrate on a single facility (hangar) which is equipped with several work stations (bays). Specifically, a number of jobs have already been scheduled for processing at the facility; the starting times, durations, and work station assignments for these jobs are assumed to be known. We are interested in how best to schedule a number of new jobs that the facility will be processing in the near future. We first develop a mixed integer quadratic programming model (MIQP) for this problem. Since the exact solution of this MIQP formulation is time consuming, we develop a heuristic procedure, based on existing bin packing techniques. This heuristic is further enhanced by application of certain local optimality conditions.