In the Two-Bar Charts Packing Problem (2-BCPP), it is required to pack the bar charts (BCs) consisting of two bars into the horizontal unit-height strip of minimal length. The bars may move vertically within the strip, but it is forbidden to change the order and separate the chart's bars. Recently, for this new problem, which is a generalization of the Bin Packing Problem (BPP) and 2-Dimensional Vector Packing Problem (2-DVPP), several approximation algorithms with guaranteed estimates were proposed. However, after a preliminary analysis of the solutions constructed by approximation algorithms, we discerned that the guaranteed estimates are inaccurate. This fact inspired us to conduct a numerical experiment in which the approximate solutions are compared to each other and with the optimal ones. To construct the optimal solutions or lower bounds for optimum, we use the Boolean Linear Programming (BLP) formulation of 2-BCPP proposed earlier and apply the CPLEX package. We also use a database of instances for BPP with known optimal solutions to construct the instances for the 2-BCPP with known minimal packing length. The results of the simulation make up the main content of this paper.

翻译：在双巴图表包装问题(2-BCPPP)中,需要将由两条条条组成的条形图(BCs)打包到最低长度的横向单位-高度条纹内。条形图可能垂直移动,但禁止在条形内移动,但禁止改变顺序和分离图条条。最近,针对这个新问题,即对Bin包装问题(BPP)的一般化和2-二维矢量包装问题(2-DVPPP)的一般化,提出了若干带有有保证估计的近似算法。然而,在对近似算法构建的解决办法进行初步分析后,我们发现有保证的估计数是不准确的。这一事实激励我们进行数字试验,在数字中将大致的解决办法相互比较,并与最佳的解决办法进行比较。为了最佳地构建最佳的解决方案或更低的界限,我们使用早先提出的2-BCPLEX包(2-DPPPPP)的配方。我们还使用一个有已知最佳解决办法的BPPPs实例数据库,以已知的最佳办法为2-BCPPPP2的包装长度最小的包件。模拟的主要内容。