Sequence based heuristics for two-dimensional bin packing problems

This article addresses several variants of the two-dimensional bin packing problem. In the most basic version of the problem it is intended to pack a given number of rectangular items with given sizes in rectangular bins in such a way that the number of bins used is minimized. Different heuristic approaches (greedy, local search, and variable neighbourhood descent) are proposed for solving four guillotine two-dimensional bin packing problems. The heuristics are based on the definition of a packing sequence for items and in a set of criteria for packing one item in a current partial solution. Several extensions are introduced to deal with issues pointed out by two furniture companies. Extensive computational results on instances from the literature and from the two furniture companies are reported and compared with optimal solutions, solutions from other five (meta)heuristics and, for a small set of instances, with the ones used in the companies.     

基于边界效应理论确定热轧碳素钢的韧度与强度

该文研究确定热轧碳素钢的材料韧度与强度特性,提出一种确定热轧碳素钢材料的断裂韧度与屈服强度的模型及方法。建立了等效裂缝长度、名义应力等具体设计参数的计算表达式。通过相同尺寸而不同初始缝高比的单边拉伸Q235B热轧碳素钢板的系列试验,证明所提模型及方法的合理性与适用性。所提模型及方法只需由小尺寸单边裂缝钢板的拉伸试验测得的屈服荷载,即可同时确定出热轧碳素钢平面应力条件下的断裂韧度K_C及屈服强度σ_Y。采用该文所提方法确定热轧碳素钢的材料特性,试验试样不需要满足现行国内外规范对试验试样尺寸、型式,加载条件等的严格规定,试样不需要预制疲劳裂纹。     

A simplified steel plate stacking problem

This article examines a simplified steel plate stacking problem. Manufactured thick steel plates arrive in series at a storage area, which consists of a certain number of uncapacitated beds. The arriving plates are first stacked on beds, after which the plates are removed in the pre-defined delivery sequence. No more than one plate can be moved simultaneously. When a target plate is not in the top position of a bed, the plates that block the target plate must be relocated. This relocation of a plate is called shift. Depending on the problem situation, it is assumed that the relocated plates must be replaced on to the original beds so they can cause multiple shifts or once they are relocated, they are treated separately in different beds so that they cause no more shifts to the original stacking. The problem is to make a storage plan that requires the minimum number of shifts in the delivery stage. This article shows that the problem is difficult to solve. Several mathematical models are developed to get optimal solutions for small problems and lower bounds for large problems. An iterative randomised approach is also proposed as a solution approach for large problem instances, and its effectiveness is shown by some computational experiments on benchmark problem sets.     

高层建筑用Q345GJC钢板表面裂纹成因分析

采用宏观分析、化学成分分析、金相检验、扫描电镜观察和能谱分析等方法对某批轧制后表面存在纵向裂纹的高层建筑用Q345GJC钢板的裂纹形成原因进行了分析。结果表明:钢板表面裂纹在连铸板坯上就已经存在,裂纹产生的主要原因是在连铸过程中结晶器涂层严重磨损致使铜板外露,从而使铜元素渗入到连铸板坯中,降低了钢的热塑性,导致了裂纹的产生;在随后的轧制过程中,裂纹沿轧制方向进一步扩展形成纵向裂纹。     

A dynamic programming-based heuristic for the variable sized two-dimensional bin packing problem

This paper addresses a variable sized two-dimensional bin packing problem. We propose two heuristics, H1 and H2, stemming from the dynamic programming idea by aggregating states to avoid the explosion in the number of states. These algorithms are elaborated for different purposes: H1 builds a general packing plan for items, while H2 can provide solutions by considering a variety of customer demands, such as guillotine cutting style and rotation of items. The performance of both algorithms is evaluated based on randomly generated instances reported in the literature by comparing them with the lower bounds and optimal solutions for identical bins. Computational results show that the average gaps are 8.97% and 13.41%, respectively, for H1 and H2 compared with lower bounds, and 5.26% and 6.26% compared with optimal solutions for identical bins. We also found that we can save 6.67% of space, on average, by considering variable sized bins instead of a bin packing problem with identical bins.     

A nested column generation algorithm to the meta slab allocation problem in the steel making industry

This paper addresses one of the key operational decision problems in the steel industry which is related to the allocation of orders to stock materials in the surplus inventory. The meta slab allocation problem can be stated as the ‘multi-stage multiple knapsack problem’ where the problem is to design slabs using orders with similar properties (the first stage) and allocating these designed slabs into the existing meta slabs in the inventory yard (the second stage). The objective of the problem is to maximise the allocated order weights in slabs and meta slabs. For the given problem, we propose a column generation algorithm, where a column in the master problem represents meta slabs and the sub problem is to design ‘bins’, here slabs with the given orders. The sub problem itself also becomes a multiple knapsack problem and we proposed a practical set-partitioning heuristic. The proposed algorithm was tested with daily operation data given from an integrated steel company in the Asia Pacific. The computational results showed that the proposed heuristic solved the real instances pretty well. The proposed algorithm was successfully deployed to the integrated steel mill.     

样品取向对轧制钢板拉伸性能的影响

分别对不同厚度、不同取向(α=0°,45°,90°)的SPCC冷轧钢板、SPHC热轧钢板、SUS304冷轧不锈钢板和SUS304热轧不锈钢板进行了拉伸试验,研究了取向因素对轧制钢板拉伸性能的影响,并分别探讨了钢板厚度、轧制状态和钢板材料等因素引起的拉伸性能各向异性程度的差异。结果表明:样品取向对轧制钢板的拉伸性能有明显影响,轧制方向的抗拉强度和断后伸长率较高,而屈服强度的变化规律则较为复杂;钢板厚度、轧制状态、钢板材料等因素对轧制钢板拉伸性能的各向异性都有不同程度的影响。     

Elimination of Surface Defects in High Tensile Steel for Wheel Rim Application

One of the important applications of high tensile steel grades is in wheel rims by the automotive industry. High tensile steel facilitates vehicle weight reduction under the ‘Go Green’ initiative. Along with weight reduction, in recent times, the surface quality requirement of steels for wheel rim applications has also gained a significant focus, and in many cases, it is becoming the cause of rejection at the customers’ processing line. It is known that owing to chemistry requirements such high strength steel grades generally show peritectic behavior during solidification and are prone to surface defects. Tata Steel India produces several wheel rim grades of varying strength levels. In one such high manganese and micro-alloyed peritectic steel grade, the rejection by the customer on account of surface defects was a major concern. The defects consisted of typical longitudinal cracks of varying dimensions along with the unique defects in transverse direction named tear marks on the surface of 100-mm-thick plates rolled from 215-mm-thick slab. In subsequent stages, these plates were processed into rim profiles through hot working by the wheel customer. The paper highlights how systematic study led to arrive at root causes and helped redesign steel chemistry to ensure zero rejection for surface quality without affecting mechanical property requirements.     

Slurry Preparation and Rolling of Semi-solid 60Si2Mn Spring Steel

The nondendritic semi-solid slurry preparation of 60Si2Mn spring steel has been studied in this paper. The experiments have shown that when stirred for 2 min on the test condition, the semi-solid slurry with 50%～60% fraction solid and spherical primary austenitic grains in the size of 100～300μm can be obtained and is easy to be discharged from the bottom little hole of the stirring chamber. The nondendritic slurry of 60Si2Mn spring steel can be rolled into given plate form successfully, but the solid phase and liquid phase is easy to be separated in rolling process so that the solid primary austenite is concentrated in the center and the liquid is near the edge of the rolled plate. The rupture strength and elongation of the plate rolled only once with semi-solid slurry are lower than that of the traditionally repeated hot-rolled plate of 60Si2Mn spring steel.     

轧后冷却速率对14CrMoR钢板热处理后显微组织和力学性能的影响

首先对14CrMoR钢进行了轧制后不同冷却速率的冷却,然后进行了相同工艺的正火+回火热处理,研究了轧后冷却速率对14CrMoR钢板热处理后显微组织和力学性能的影响。结果表明:轧后冷却速率越小,钢板热处理后的各类显微组织越细小,珠光体和回火贝氏体组织的分布越均匀,综合力学性能也越好。     

A recursive algorithm for the rectangular guillotine strip packing problem

This article presents a recursive heuristic algorithm to generate cutting patterns for the rectangular guillotine strip packing problem in which a set of rectangular items must be cut from the strip such that the consumed strip length is minimized. The strip is placed with its length along the horizontal direction, and is divided into several segments with vertical cuts. The length of a segment is determined by the item placed at the bottom. Orthogonal cuts divide the segments into blocks and finished items. For the current block considered, the algorithm selects an item, puts it at the bottom-left corner of the block, and divides the unoccupied region into two smaller blocks with an orthogonal cut. Rotation of the items by 90 is allowed. Both lower and upper bounds are used to prune unpromising branches. The computational results indicate that the algorithm performs better than several recently published algorithms.     

集中荷载作用下四边简支双钢板混凝土组合板的力学性能研究

根据5组33片四边简支双钢板混凝土组合板的试验结果,将组合板的变形模式归纳为弯曲变形模式和冲切变形模式,推导其抗力和刚度的理论计算式,提出能够描述组合板受力全过程的抗力函数模型,并通过现有试验和数值模拟结果验证模型的准确性。基于该模型研究含钢率、材料强度、连接件布置等参数对组合板变形模式和耗能能力的影响,结果表明:含钢率和钢板强度对SC板的极限承载力和耗能能力影响较大,而混凝土强度的影响很小;为了充分利用钢板的力学性能,应合理限制含钢率和钢板强度,或加强连接件布置保证组合作用;不同的设计参数可能导致不同的变形模式和破坏顺序,设计中应针对具体的需求对设计参数加以优化。     

高架钢弹簧浮置板轨道减振特性研究及参数优化

为探讨钢弹簧刚度和浮置板密度对高架钢弹簧浮置板轨道减振特性的影响规律,构建车辆-浮置板轨道-桥梁耦合模型,从时频域的角度对其进行分析,为钢弹簧浮置板轨道的设计参数的合理选择与组合优化提供理论依据。研究结果表明:在2 Hz~20 Hz范围内浮置板的振动水平随钢弹簧刚度的减小而增大。在16 Hz~125 Hz频率范围内,轨道中心线、翼缘、腹板、梁底的振动水平随着钢弹簧刚度的减小而减小,最大减幅达到13 dB。钢弹簧刚度的变化对传递函数的影响比较明显,弹簧刚度越小,浮置板到桥梁结构的竖向传递函数值越小。综合考虑,在设计浮置板轨道结构时建议将钢弹簧的刚度控制在6×106N/m~8×106N/m。浮置板密度的增大会在一定程度上减小系统的振动水平,实际设计中要合理设置浮置板密度,建议控制在2 800 kg/m3~3 200 kg/m3。     

稀土丝喂入位置对连铸板坯质量影响的研究

针对结晶器喂稀土丝生产的连铸板坯热轧后钢板表面出现龟纹缺陷技术难题，在分析该缺陷形成原因的基础上，开展了中间包喂稀土丝工艺试验，结果表明：与结晶器喂稀土的连铸坯相比，中间包喂稀土连铸板坯横断面上的稀土夹杂物大多呈细小颗粒状均匀分布，冲击韧性更高，热轧后钢板未出现表面缺陷，中间包喂稀土工艺彻底解决了结晶器喂稀土存在的质量问题，使稀土使用得以更充分地挥，板坯质量更好。     

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.     

22mm厚Q235B钢板表面裂纹成因

某批规格为22 mm厚的Q235B钢板在表面质量检验过程中发现部分钢板表面存在纵向裂纹缺陷。采用光学显微镜和扫描电镜等手段对钢板表面裂纹的形成原因进行了分析。结果表明:该批钢板表面裂纹主要是由于其原始连铸板坯表面存在较深的裂纹缺陷,在后期轧制过程中被压扁、延伸,未轧合所致。     

Structural limits of FRP-balsa sandwich decks in bridge construction

The span limits of two glass fiber-reinforced polymer (GFRP) bridge concepts involving GFRP-balsa sandwich plates are discussed. The sandwich plates were either used directly as slab bridges or as decks of a hybrid sandwich-steel girder bridges. In the latter case, the potential of the sandwich decks to replace reinforced concrete (RC) decks was also evaluated. Taking the limits of manufacturing into account (800 mm slab thickness), maximum bridge spans of approximately 19 m can be reached with FRP-balsa sandwich slab bridges, if a carbon-FRP (CFRP) arch is integrated into the balsa core. Above this limit, hybrid sandwich-steel girder bridges can be used up to spans of 30 m. RC deck replacement requires timber and steel plate inserts into the balsa core above the steel girders. GFRP-balsa sandwich slabs or decks exhibit full composite action between lower and upper face sheets. Stress concentrations occur at the joints between balsa core and timber inserts which however can effectively be reduced by changing from butt to scarf joints.     

Aktuelle Entwicklungen bei TM‐gewalzten Grobblechen

Topical Developements at TMCP‐rolled Heavy Plates The lecture presents topical developements at TMCP‐rolled heavy plates for shipbuilding application. There are shown requirements for present‐day shipbuilding plates and the subsequently derived different processes of thermomechanical rolling of heavy plates. Based on the plate making process of the rolling mill of Dillinger Hütte the metallurgical design and results of the heavy plate production are presented.     

On the Occurrences of “Frizzle-Type” Surface Defects in a Hot-Rolled Steel Plate

Metallurgical investigations were directed to probe into the genesis of “frizzle” and fissure-type surface defects on 10-mm hot-rolled steel plates meant for application in flat-bed wagons for carrying heavy machinery. The thin hairline fissures on the steel plates were identified as skin laminations associated with long, shallow, and branched cracks, intruding from the plate surfaces to the interior with curved contours, replete with fragmented oxide scale entrapments and debris. The incidence of these superficial defects on the plates was linked to surface damage to the solidifying skin of continuously cast steel slabs, induced by the extensive pitting and cavitation of caster pinch rolls. It is presumed that during hot rolling of the steel slabs, surface blemishes like indentations and folds got rolled over by metal flow, entrapping copious amounts of primary as well as secondary scales underneath the laminated skin. Under the influence of shear forces during rolling, the defects are believed to have ingressed further into the plate interior leading to the formation of long, shallow, and branched cracks with curved contours and entrapped fragmented oxide scales.     

内嵌钢板及边缘框架相互作用对带连梁低屈服点钢板剪力墙结构受力性能的影响

为满足快速发展的高层建筑结构对抗震性能及空间灵活性的要求,将高耗能能力、高延性的低屈服点钢材与带连梁钢板剪力墙组合成新型带连梁低屈服点钢板剪力墙结构体系。采用有限元软件ABAQUS建立带连梁钢板剪力墙结构模型,结合国内外已有的典型试验结果验证数值方法的有效性。在此基础上,设计5个不同耦合度的低屈服点钢板剪力墙结构模型进行单调和循环加载,对比分析其损伤机制、承载性能及滞回耗能能力,探讨内嵌钢板与边缘框架的相互作用对结构及构件受力性能的影响,给出设计建议。结果表明:带连梁低屈服点钢板剪力墙结构内嵌钢板与边缘框架相互作用能够有效提高整体结构承载力、承载效率以及耗能能力。综合考虑材料利用率、承载能力及耗能能力,建议连梁耦合度控制在0.45以内。随着连梁耦合度的提高,边缘框架分担剪力多至60%,内部框架柱的轴力显著减小,连梁转角不断减小。因此,在带连梁低屈服点钢板剪力墙结构设计过程中应充分考虑内嵌钢板与边缘框架的相互作用,适当减小内嵌钢板设计厚度及边缘框架截面尺寸,提高材料利用率及设计经济性。同时,与纯框架抗侧性能相比,内嵌钢板与边缘框架的相互作用有效提高了边缘框架的初始抗侧刚度及承载力。