A neuro-dominance rule (NDR) for single machine total weighted tardiness problem with unequal release date is presented by the author. To obtain the NDR, backpropagation artificial neural network (BPANN) has been trained using 10,000 data and also tested using 10,000 another data. Inputs of the trained BPANN are starting date of the first job (t), processing times (pi and pj), due dates (di and dj), weights of the jobs (wi and wj) and ri and rj release dates of the jobs. Output of the BPANN is a decision of which job should precede. Training set and test set have been obtained using Adjusted Pairwise Interchange method. The proposed NDR provides a sufficient condition for local optimality. It has been proved that if any sequence violates the NDR then violating jobs are switched according to the total weighted tardiness criterion. The proposed NDR is compared to a number of competing heuristics (ATC, COVERT, EDD, SPT, LPT, WDD, WSPT, WPD, CR, FCFS) and meta heuristics (simulated annealing and genetic algorithms) for a set of randomly generated problems. The problem sizes have been taken as 50, 70, 100. NDR is applied 270,000 randomly generated problems. Computational results indicate that the NDR dominates the heuristics and meta heuristics in all runs. Therefore, the NDR can improve the upper and lower bounding schemes.
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机译：作者提出了具有不相等发布日期的单机总加权延误问题的神经主导规则（NDR）。为了获得NDR，已经使用10,000个数据训练了反向传播人工神经网络（BPANN），并使用10,000个其他数据进行了测试。受过训练的BPANN的输入是第一份工作的开始日期（t），处理时间（p i 和p j ），到期日期（d i 和d j ），作业的权重（w i 和w j ）和r i r j 个作业的发布日期。 BPANN的输出决定应先执行哪个作业。训练集和测试集已使用可调整的成对互换方法获得。拟议的NDR为局部最优提供了充分条件。已经证明，如果有任何序列违反NDR，则根据总加权拖延标准切换违反工作。将提议的NDR与许多竞争启发式算法（ATC，COVERT，EDD，SPT，LPT，WDD，WSPT，WPD，CR，FCFS）和元启发式算法（模拟退火和遗传算法）进行比较，以解决一组随机生成的问题。问题大小已定为50、70、100。应用了NDR 270,000个随机生成的问题。计算结果表明，NDR在所有运行中都主导了启发式和元启发式。因此，NDR可以改进上限和下限方案。
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