Experimental Results.xlsx

In this section, we will evaluate the performance of the algorithm A-ABC. CPLEX is employed to directlysolve the relaxation model [OP2]. The A-ABC heuristic algorithm is configured with <i>t </i>= 100 iterations and thesolver is set to solve within 3600 seconds. Table 3 illustrates the average outcomes achieved by both CPLEXand A-ABC across instances involving 6, 9, and 25 clients. The table outlines specifics such as the number ofregions (<i>N</i>), instance count (#), instances optimally solved (#O), lower bound (<i>lb</i>, which represents the best?found target value), upper bound (<i>ub</i>), percentage gap calculated as (<i>ub</i>−<i>lb</i>)/<i>lb</i>×100%, and the Time (<i>s</i>) column,indicating the solver’s duration to establish the lower bound. Additionally, for A-ABC, we present the averagebest target value, average worst target value, average target value, standard deviation from 10 runs, average totalcomputation time (in seconds), and the Gap value derived from CPLEX. Table 4 distinctly emphasizes superiorvalues among diverse heuristic methods alongside their shortest computation times. Detailed solutions for eachinstance can be found in the online supplement.

本节将对算法A-ABC的性能进行评估。本研究采用CPLEX直接求解松弛模型[OP2]。A-ABC启发式算法的迭代次数配置为100次，求解器的单次求解时长上限设置为3600秒。表3展示了CPLEX与A-ABC在包含6、9、25个客户的测试实例上得到的平均结果。该表列出了各项具体指标：区域数量（N）、测试实例总数（#）、最优求解实例数（#O）、下界（lb，即已找到的最优目标值）、上界（ub）、以(ub−lb)/lb×100%计算的间隙百分比，以及标注为Time(s)的列，该列表示求解器求解得到下界所需的时长。此外，针对A-ABC，本研究还给出了其10次运行的平均最优目标值、平均最差目标值、平均目标值、标准差、平均总计算时长（单位：秒），以及基于CPLEX求解结果得到的间隙值。表4重点突出了各类启发式算法中的最优指标值及其最短计算时长。所有测试实例的详细求解结果可查阅在线补充材料。