Abstract: The Multi-stage Multi-level Fuzzy Flexible Job Shop Scheduling Problem (MMFFJSSP) commonly exists in enterprises with complex product hierarchies,diverse products and high process requirements.Existing methods that use single numerical features for fuzzy number operations and evaluations cause information loss of fuzzy numbers,resulting in significant changes in the ranking results and cannot guarantee the consistency and reliability of the outcomes.To address these issues,a fuzzy number ranking method based on Addition Priority of Fuzzy Preference Relation (APFPR) was proposed.Multidimensional features of the shapes and relative positions of fuzzy numbers were integrated by introducing fuzzy preference relations to avoid information loss and ranking deviations,enhancing the credibility of scheduling.In addition,a Multi-Strategy Adaptive Memetic Algorithm based on Fuzzy Fitness Gradient Selection (MSAMA-FFGS) was designed to solve the MMFFJSSP and minimize the maximum fuzzy completion time.In MSAMA-FFGS,adaptive crossover and mutation strategies based on fuzzy fitness were designed to dynamically adjust the algorithm operations,thus the search capabilities were improved.Critical products and job were identified to optimize components that impact overall completion time,which enhanced solution quality.Finally,the stability of APFPR in handling fuzzy number ranking problems was demonstrated by theoretical analysis and experimental results.The effectiveness of the proposed MSAMA-FFGS for solving the MMFFJSSP was verified by simulation comparison experiments.

Key words: multi-stage, multi-level, fuzzy flexible job shop, addition priority, memetic algorithm, fuzzy preference

摘要： 多阶段多层级模糊柔性作业车间调度问题(MMFFJSSP)普遍存在于一类产品层级结构复杂、种类繁多及工艺特性要求高的企业中。针对现有仅采用单一数值特征进行模糊数运算和评价会导致模糊数信息丢失,从而使排序结果发生显著变化,无法保证结果的一致性和可靠性的问题,提出了一种基于模糊偏好关系加法优先度的模糊数排序方法(APFPR)。该方法进一步融合模糊数的形状特征和相对位置的多维特征,通过引入模糊偏好关系,避免了信息丢失和排序偏差,提高了调度方案的可信度。并设计了基于模糊适应度梯度选择的多策略自适应模因算法(MSAMA-FFGS)求解以最小化最大模糊完工时间为优化目标的MMFFJSSP。该算法中设计了基于模糊适应度的自适应交叉和变异策略,动态调整算法操作,提高全局和局部搜索能力;通过识别关键产品和关键工件,针对性地优化对整体完工时间影响最大的部分以提高求解的质量。理论分析和实验结果验证了基于模糊偏好加法优先度在处理模糊数排序问题时的稳定性。最后,通过仿真对比实验验证了所提MSAMA-FFGS算法在解决MMFFJSSP问题中的有效性。

关键词: 多阶段, 多层级, 模糊柔性作业车间, 加法优先度, 模因算法, 模糊偏好