计算机科学 ›› 2020, Vol. 47 ›› Issue (4): 211-216.doi: 10.11896/jsjkx.190500132
杨婷, 罗飞, 丁炜超, 卢海峰
YANG Ting, LUO Fei, DING Wei-chao, LU Hai-feng
摘要: 装箱问题是物流系统和生产系统中的一个经典而重要的数学优化问题。装箱指把一系列物品按照一定顺序放进具有固定容量的箱子中,并最小化所使用的箱子数量,以最大限度地获取装箱问题的近似最优解。然而,现有的装箱算法存在明显的缺陷。遗传算法计算量过大,甚至无法求出所需解,启发式算法无法处理极端值问题,而现有的改进算法即使在引入松弛量的情况下,也极易陷入局部最小值。文中提出的Adaptive-MBS算法采用自适应权重来改进原有方法,即允许方法有一定的松弛量,并具有捕捉物体样本空间随时间变化的直觉,以使用更好的松弛量策略来装箱。Adaptive-MBS算法首先以当前箱子为中心,使用Adaptive_Search搜索算法迭代找到适合箱子容量的集合中所有物体的子集,Adaptive_Search搜索算法不要求完全装满箱子,而是允许箱子具有一定的松弛量,在训练过程中根据当前状态的变化,实现自动地调整松弛量,在找到完全填满箱子的子集后迭代至下轮搜索直至遍历完成。该方法不易陷入局部最优,具有较强的发现全局最优解的能力。文中使用装箱问题中经典的BINDATA和SCH_WAE数据集进行实验,结果表明,数据集中多达991例问题可以通过Adaptive-MBS算法得到最优解。在没有求解出最优解的实例上,所提算法也在所有对比算法上具有最低的相对偏移量百分比。数值实验结果表明,相较于其他经典的装箱算法,Adaptive-MBS算法有更好的效果,其收敛速度也显著优于其他算法。
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[1]DE ALMEIDA R,STEINER M T A.Resolution of 1-D Bin Packing Problem using Augmented Neural Networks and Minimum Bin Slack[C]//Latin America Congress on Computational Intelligence (LA-CCI).IEEE,2015:1-6. [2]KAAOUACHE M A,BOUAMAMA S.Solving bin packingproblem with a hybrid genetic algorithm for VM placement in cloud[J].Procedia Computer Science,2015,60(1):1061-1069. [3]RODRIGO N P,DAUNDASEKERA W B,PERERA A I.One-dimensional bin-packing problems with branch and bound algorithm[J].International Journal of Discrete Mathematics,2018,3(2):36. [4]HU H,ZHANG X,YAN X,et al.Solving a new 3d bin packing problem with deep reinforcement learning method[J].arXiv:1708.05930,2017. [5]DUAN L,HU H,QIAN Y,et al.A Multi-task Selected Learning Approach for Solving 3D Flexible Bin Packing Problem[J].arXiv:1804.06896,2018. [6]KORF R E.A new algorithm for optimal bin packing[C]//Proceedings of the EighteenthNational Conference on Articial Intelligence.AAAI Press,2002:731-736. [7]VAZIRANI V V.Approximation algorithms[M].Springer Science & Business Media,2013:10-19. [8]GUPTA J N D,HO J C.A new heuristic algorithm for the one-dimensional bin-packing problem[J].Production Planning & Control,1999,10(6):598-603. [9]HARTMANIS J.Computers and intractability:a guide to thetheory of NP-completeness (michael r.garey and david s.johnson)[J].Siam Review,1982,24(1):90. [10]COFFMAN J,GAREY M,JOHNSON D S.Approximation algorithms for NP-hard problems.[M].Boston:PWS Publishing,1997:46-93. [11]DOSA G.Encyclopedia of Algorithms [M].New York:Springer,2014:10-19. [12]NGUYEN-DUC T,QUANG-HUNG N,THOAI N.BFD-NN:best fit decreasing-neural network for online energy-aware virtual machine allocation problems[C]//Proceedings of the Se-venth Symposium on Information and Communication Technology.ACM,2016:243-250. [13]JOHNSON D S.Near-optimal bin packing algorithms[D].Cambridge:Massachusetts Institute of Technology,1973. [14]FLESZAR K,HINDI K S.New heuristics for one-dimensionalbin-packing[J].Computers & operations research,2002,29(7):821-839. [15]MARTELLO S,TOTH P.Lower bounds and reduction procedures for the bin packing problem[J].Discrete applied mathematics,1990,28(1):59-70. [16]ZHANG J J.Conbinatorial packing probleming:Models and Algorithms[D].Shanghai:Shanghai Jiao Tong University,2012. [17]SRIDHAR R,CHANDRASEKARAN M,SRIRAMYA C,et al.Optimization of heterogeneous Bin packing using adaptivegene-tic algorithm[C]//IOP Conference Series:Materials Science and Engineering.IOP Publishing,2017. [18]QUIROZ-CASTELLANOS M,CRUZ-REYES L,TORRESJIMENEZ J,et al.A grouping genetic algorithm with controlled gene transmission for the bin packing problem[J].Computers & Operations Research,2015,55:52-64. [19]DOKEROGLU T,COSAR A.Optimization of one-dimensionalbin packing problem with island parallel grouping genetic algorithms[J].Computers & Industrial Engineering,2014,75:176-186. [20]LOH K H,GOLDEN B,WASIL E.Solving the one-dimensional bin packing problem with a weight annealing heuristic[J].Computers & Operations Research,2008,35(7):2283-2291. [21]HIFI M,NEGRE S,WU L.Hybrid greedy heuristics based onlinear programming for the three-dimensional single bin-size bin packing problem[J].International Transactions in Operational Research,2014,21(1):59-79. [22]BALOGH J,BÉKÉSI J,DÒSA G,et al.The optimal absolute ratio for online bin packing[C]//Proceedings of the twenty-sixth Annual ACM-SIAM Symposium on Discrete Algorithms.Philadelphia:Society for Industrial and Applied Mathematics,2014:1425-1438. [23]KHANAFER A,CLAUTIAUX F,TALBI E G.New lowerbounds for bin packing problems with conflicts[J].European Journal of Operational Research,2010,206(2):281-288. [24]CLAUTIAUX F,DELL’AMICO M,IORI M,et al.Lower and upper bounds for the Bin Packing Problem with Fragile Objects[J].Discrete Applied Mathematics,2014,163:73-86. [25]BALOGH J,BÉKÉSI J,GALAMBOS G,et al.Lower bound for 3-batched bin packing[J].Discrete Optimization,2016,21:14-24. [26]BALOGH J,BÉKÉSI J.Semi-on-line bin packing:a short overview and a new lower bound[J].Central European Journal of Operations Research,2013,21(4):685-698. [27]SCHOLL A,KLEIN R,JÜRGENS C.Bison:A fast hybrid procedure for exactly solving the one-dimensional bin packing problem[J].Computers & Operations Research,1997,24(7):627-645. [28]SCHWERIN P,WÄSCHER G.The bin-packing problem:Aproblem generator and some numerical experiments with FFD packing and MTP[J].International Transactions in Operational Research,1997,4(5/6):377-389. [29]LÒPEZ-CAMACHO E,TERASHIMA-MARÍN H,ROSS P.Ahyper-heuristic for solving one and two-dimensional bin packing problems[C]//Proceedings of the 13th Annual Conference Companion on Genetic and Evolutionary Computation.Dublin:ACM,2011:257-258. |
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