求解长方体Packing问题的纯粹拟人算法

对于具有NP难度的长方体Packing问题,挖掘出了中国古代谚语"金角银边草肚皮"中隐藏的智慧,并进一步发展出新子句"价值最高钻石穴".在利用现代西方的先进数学工具经过确切化、完整化与形式化后,得出了一种纯粹拟人型的求解算法.试算了国际上公开通行的两组有代表性的算例(benchmark).对于100个强异构型的困难算例,所得布局图案达到了87.31%的平均空间利用率,刷新了当今国际上的最好纪录,将它提高了1.83个百分点.对于47个无方向约束的困难算例,得到了92.05%的平均空间利用率,将当今国际上的最好纪录提高了1.05个百分点.     

求解二维矩形Packing面积最小化问题的动态归约算法

二维矩形Packing 面积最小化问题(rectangle packing area minimization problem,简称RPAMP)是具有NP难度的高复杂度的布局优化问题,也是大规模集成电路设计中floorplanning 问题的一个核心问题.通过动态构造矩形框的宽和高,将求解一个RPAMP 转化为求解一组二维矩形Packing 判定问题(rectangle packing decision problem,简称RPDP).在求解RPDP 的最大适配度算法的基础上,进一步考虑了当前动作对全局紧凑性的影响,评估了当前动作对局部空间的损害程度,设计了求解RPDP 的最小损害度算法.然后,结合矩形框宽、高的动态构造方法,设计得到求解RPAMP 的最终算法.对15 个相关的RPAMP 算例(包括著名的MCNC 算例和GSRC 算例)进行了测试.更新了其中9 个算例的最好记录,另有2 个与当前的最好记录持平.得到了98.50%的平均填充率,将国内外文献中已见报道的最高平均填充率提高了0.85%.     

基于粗精调技术的求解带平衡约束圆形Packing问题的拟物算法

带平衡约束的圆形Packing问题是以卫星舱布局为背景的具有NP难度的布局优化问题.文中建立了此问题相应的数学模型,同时提出了两个新的物理模型,并受工艺加工过程中“粗精加工”现象的启发,提出了基于粗精调技术的拟物算法QPCFA.该算法既兼顾了搜索空间的多样性以利于全局搜索,又能对有前途的局部区域进行精细搜索以找到相应的局部最优解.同时,在计算过程中引入禁忌技术和跳坑策略,以提高算法的求解质量.对国际上11个代表性的算例进行了计算,QPCFA更新了其中7个算例的最好记录,其余4个与目前的最好记录基本持平,且与目前的最好结果相比在计算精度上均有较大的提高.     

基于动作空间的求解三维矩形装箱问题的穴度算法

基于拟人途径求解三维矩形装箱问题。在穴度算法的基础之上,通过定义当前格局下的极大空闲矩形空间即动作空间,使得穴度的定义既能反映其本质,同时又大能幅度地缩减计算量,从而使算法能在较短的时间内得出空间利用率较高的布局图案。试算了OR-Library中无方向约束的全部47个算例。实验结果表明,改进后的穴度算法得到的平均空间利用率为95. 24 %,将目前的最好结果提高了0.32%,且花费了更少的计算时间。     

求解VLSI布局问题的启发式算法

在人们现实布局实践经验的启发下。对 VLSI 布局问题提出了一个启发式算法。该算法由定序规则和定位规则组成,定序规则用来确定布局物体放入布局空间的先后顺序,定位规则规定每一布局物体都被当前最优的占角动作放入布局空间。对5个 MCNC 算例的测试结果表明,本文算法与基于 O-tree 表示的算法相比,速度提高15～56倍;对于其中4个算例,面积利用率提高0.95%～5.31%。     

求解长方体Packing问题的高效算法

对典型的NP难度问题--著名的长方体Packing问题,通过观察体会人类几千年来在砌石头下围棋等活动中形成的经验和智慧,受到谚语"金角银边草肚皮"的启发,并将它发展提高到"价值最高钻石穴",提出了一种最大穴度的占角动作优先处理的拟人算法.计算了Loh和Nee提出的15个代表性的算例,算法在合理的时间内得出了高空间利用率的布局,其精度达到了国际先进的纪录.     

偶发实时系统可调度性分析问题的整数规划方法

偶发实时任务最早截止期优先（earliest deadline first,简称EDF）可调度分析是实时系统领域经典的NP困难问题.现有的伪多项式时间判定算法（pseudo-polynomail time decision algorithm,简称PTDA）均局限于利用率U严格小于1的同步任务系统.对于U≤1的同步系统或更加困难的异步系统,现有PTDA则不再适用.针对以上问题,为同步和异步两类实时系统建立了统一的整数规划模型,其规模并不依赖于利用率U的取值.基于多面体理论证明了模型维数和极大诱导不等式,进而提出了同/异步系统上EDF可调度性分析问题统一的多项式时间线性松弛求解方法.实验结果表明,该方法能够获得较紧的问题解下界,在异步和同步系统中,线性松弛解与最优解之间的平均百分界差gap分别为0.78%和1.27%.另外,随机生成了大量同步和异步系统的算例,用于该算法和传统算法进行性能比较.对于同步算例,实验结果表明,在U>0.99时,该算法能够对70%的算例给出判定结果,算法性能与QPA算法相比有指数级提升.对于异步算例,实验结果表明,该算法能够对近96%的算例给出可调度性判定.与传统算法相比,该方法将不能判定可调度性的算例比例平均降低了29.27%.对于剩余的4%的算例,该算法将可调度上界的值平均降低了近10⁴倍.     

基于禁忌搜索的启发式算法求解带平衡约束的圆形装填问题

带平衡约束的圆形装填(Packing)问题是一类简化的卫星舱布局优化问题.现提出一个基于禁忌搜索的启发式(TSH)算法对该问题进行求解.算法从任一初始格局出发,应用基于自适应步长的梯度法进行能量极小化.为了使计算能有效地逃离局部极小点的陷阱且避免迂回搜索,算法采用了禁忌搜索的策略.在禁忌搜索的过程中,我们对传统的邻域解、禁忌对象以及当前解接受原则进行了有效的改进.对两组共11个有代表性的算例进行了实算.计算结果表明,TSH算法刷新了其中7个算例的当今国际上的最好纪录,对于其余4个算例,该算法均达到问题的最优解.     

求解卸装一体化的车辆路径问题的混合启发式算法

提出一种结合蚁群系统(Ant Colony System,ACS)和变邻域下降搜索(Variable Neighborhood Descent,VND)的混合启发式算法ACS_VND,求解卸装一体化车辆路径问题.利用基于插入的ACS解构造方法产生多个弱可行解,再逐个转换成强可行解,并选择其中最好的作为VND的初始解.在VND过程中使用三种不同的邻域结构:插入、交换和2-opt依次对解进行迭代优化.对55个规模为22~199的benchmark算例的求解结果表明,算法ACS_VND能在较短时间内获得52个算例的已知最好解,并且更新了其中44个算例的已知最好解,求解性能优于现有算法.     

车辆路径问题的水波算法

水波算法(Water Wave Optimization WWO)是郑宇军于2014年基于浅水波理论提出的一种新颖的元启发式算法,用于全局优化问题.通过水波的传播、折射和碎浪操作,可以用来导出在高维解决方案空间中搜索的有效机制.算法WWO的框架简单,易于实现,并且只需要少量的控制参数.本文应用WWO求解车辆路径问题(the Capacitated Vehicle Routing Problem CVRP),算法采用0-1矩阵编码方式,通过传播操作进行全局搜索,反射操作实现进化,碎浪操作防止陷入局部最优.利用构建的算法求解64个benchmark算例,求解的结果中有65%的算例获得已知最优解,有6个算例更新了已知最好解,验证水波算法求解车辆路径问题的可行性,为水波算法应用于其他优化问题提供参考.     

A caving degree based flake arrangement approach for the container loading problem

A caving degree based flake arrangement (CDFA) approach for the NP-hard container loading problem is presented in this paper. Based on the caving degree approach, CDFA binds items in the same size into a larger flake whose binding number is 1 in one of its three dimensions, and then it tries to pack the flake into a corner nearest to the eight vertices of the container. Then, caving degree is redefined to evaluate different placements of flakes, such that an action is selected whose packing flake is as compact and close as possible with other flakes already in (the six surfaces of the container can be regarded as six special flakes). CDFA is extensively tested over two sets of famous benchmarks: 15 LN instances and 1500 BR instances. Experimental results show the high performance of this new approach. Especially for the LN set, CDFA improved current highest volume utilization by 1.3% and 0.5% for two difficult instances LN2 and LN6 respectively; at the same time it got optimal layouts for the other 13 instances, equalling current best records. This breaks current best record created and held by Bortfeldt and Gehring since 1998. Besides, CDFA achieved the second highest average volume utilization among several top efficient algorithms for the BR set.     

A pure quasi-human algorithm for solving the cuboid packing problem

We excavate the wisdom from an old Chinese proverb “gold corner, silver side and strawy void”, and further improve it into “maximum value in diamond cave” for solving the NP-hard cuboid packing problem. We extract, integrate and formalize the idea by west modern mathematical tools, and propose a pure quasi-human algorithm. The performance of the algorithm is evaluated on two sets of public benchmarks. For 100 strongly heterogeneous difficult benchmarks, experiments show an average packing utilization of 87.31%, which surpasses current best record reported in the literature by 1.83%. For 47 difficult benchmarks without orientation constraint, experiments show an average volume utilization of 92.05%, which improves current best record reported in the literature by 1.05%. Supported by the National Natural Science Foundation of China (Grant No. 60773194), the National Basic Research Program of China (Grant No. 2004CB318000), and Postdoctoral Science Foundation of China (Grant No. 20070420174)     

A new heuristic algorithm for cuboids packing with no orientation constraints

The three-dimensional cuboids packing is NP-hard and finds many applications in the transportation industry. The problem is to pack a subset of cuboid boxes into a big cuboid container such that the total volume of the packed boxes is maximized. The boxes have no orientation constraints, i.e. they can be rotated by 90^°${90}^{°}$ in any direction. A new heuristic algorithm is presented that defines a conception of caving degree to judge how close a packing box is to those boxes already packed into the container, and always chooses a packing with the largest caving degree to do. The performance is evaluated on all the 47 related benchmarks from the OR-Library. Experiments on a personal computer show a high average volume utilization of 94.6% with an average computation time of 23 min for the strengthened A1 algorithm, which improves current best records by 3.6%. In addition, the top-10 A2 algorithm achieved an average volume utilization of 91.9% with an average computation time of 55 s, which also got higher utilization than current best records reported in the literature.     

基于图形处理器的Cuboid算法

近年来,基于图形处理器的通用计算获得了广泛关注,并在多个领域取得了进展.内存OLAP减少了磁盘I/O,但基于单核或多核CPU的计算能力及cache miss成为新的性能瓶颈,从而无法保证好的效率.而图形处理器由于其众多核和高带宽能够很好地适应OLAP计算特性.通过图形处理器来加速任一cuboid的计算,从而提高整个内存OLAP系统的性能.提出了基于图形处理器的分块并行算法,并对算法进行了优化及讨论了数据稀疏和数据分布倾斜等不同条件下的算法.算法通过扩展可以突破内存限制,组成磁盘、内存、显存三级流水线,适应海量数据计算;同时算法也可以作为计算整个cube的基础.通过实验比较,基于图形处理器的算法明显优于四核CPU算法.     

An efficient placement heuristic for three-dimensional rectangular packing

By embodying the spirit of “gold corner, silver side and strawy void” directly on the candidate packing place such that the searching space is reduced considerably, and by utilizing the characteristic of weakly heterogeneous problems that many items are in the same size, a fit degree algorithm (FDA) is proposed for solving a classical 3D rectangular packing problem, container loading problem. Experiments show that FDA works well on the complete set of 1500 instances proposed by Bischoff, Ratcliff and Davies. Especially for the 800 difficult strongly heterogeneous instances among them, FDA outperforms other algorithms with an average volume utilization of 91.91%, which to our knowledge is 0.45% higher than current best result just reported in 2010.     

基于马氏距离的方体模型及其在病毒预警中的应用

从几何学的角度探讨了人工免疫系统搜索空间的表示方法以及识别器的构造模型。重点讨论了超球体模型和方体模型的缺陷。提出了一个具有空间自适应能力的方体模型,运用贪婪策略,通过膨胀,收缩自适应地调节识别器的体积。实验表明,方体模型能较好地适应不规则的SELF点集分布,然而贪婪策略却导致该模型具有较高的误报率。借鉴方体模型空间自适应优势,提出了一个基于马氏距离的方体模型(CMMD)。     

Local search with edge weighting and configuration checking heuristics for minimum vertex cover

The Minimum Vertex Cover (MVC) problem is a well-known combinatorial optimization problem of great importance in theory and applications. In recent years, local search has been shown to be an effective and promising approach to solve hard problems, such as MVC. In this paper, we introduce two new local search algorithms for MVC, called EWLS (Edge Weighting Local Search) and EWCC (Edge Weighting Configuration Checking). The first algorithm EWLS is an iterated local search algorithm that works with a partial vertex cover, and utilizes an edge weighting scheme which updates edge weights when getting stuck in local optima. Nevertheless, EWLS has an instance-dependent parameter. Further, we propose a strategy called Configuration Checking for handling the cycling problem in local search. This is used in designing a more efficient algorithm that has no instance-dependent parameters, which is referred to as EWCC. Unlike previous vertex-based heuristics, the configuration checking strategy considers the induced subgraph configurations when selecting a vertex to add into the current candidate solution.A detailed experimental study is carried out using the well-known DIMACS and BHOSLIB benchmarks. The experimental results conclude that EWLS and EWCC are largely competitive on DIMACS benchmarks, where they outperform other current best heuristic algorithms on most hard instances, and dominate on the hard random BHOSLIB benchmarks. Moreover, EWCC makes a significant improvement over EWLS, while both EWLS and EWCC set a new record on a twenty-year challenge instance. Further, EWCC performs quite well even on structured instances in comparison to the best exact algorithm we know. We also study the run-time behavior of EWLS and EWCC which shows interesting properties of both algorithms.     

用遗传算法求多面体的最小包容长方体

建立了求多面体包容长方体的数学模型,将求最小包容长方体问题转化为函数优化问题,并用遗传算法解决了函数最优解的求解问题。     

An augmented large neighborhood search method for solving the team orienteering problem

In the Team Orienteering Problem (TOP), a team of vehicles attempts to collect rewards at a given number of stops within a specified time frame. Once a vehicle visits a stop and collects its reward, no other vehicles can collect the reward again. Typically, a team cannot visit all stops and therefore has to identify the “best” set of stops to visit in order to maximize total rewards. We propose a large neighborhood search method with three improvement algorithms: a local search improvement, a shift and insertion improvement, and replacement improvement. Our proposed approach can find the best known solutions for 386 of the 387 benchmark instances, for the one instance which our solution is not the current best it is only varies by one from the best. Our approach outperforms all the previous approaches in terms of solution quality and computation time.