模糊环境下具有复杂约束的工期设定调度优化理论和算法研究

On the background of how to reduce the cost of enterprises with a lack of cash flow, it is investigated to find an optimal scheduling and set due date to every job in order to minimize the total cost under fuzzy environment and various constraints. Firstly, the due date assignment scheduling problems under fuzzy environment with general precedence constraints、relocation constraints or job-rejection constraints are studied; Some algorithms are proposed for the above problems respectively. Secondly, multi-agent due date assignment scheduling problems are investigated and some algorithms are also given out to solve the problems. Furthermore, the possibilistic mean values and variances of interval-valued fuzzy sets and intuitionistic fuzzy sets are proposed; based on these, interval-valued fuzzy sets and intuitionistic fuzzy sets are employed to model the due date assignment scheduling problems under fuzzy environment and various constraints, where the objective function is to minimize the mean value of the total cost. Compared with stochastic methods, the methods proposed in this project can more effectively solve some cases of due date assignment scheduling problems with various complex constraints under same or similar objectives in stochastic meaning, in which they are bottleneck problems and very hard to model and solve when using stochastic methods. Our work has not only significance in theory, but also important practical applications.

本项目以企业在现金流紧张条件下如何安排生产以降低成本为背景，对模糊环境下工件间具有各种约束的工期设定调度优化问题的理论和方法展开研究.研究内容包括：模糊环境下工件间具有优先加工约束、relocation约束、job-rejection约束,目标函数为极小化总费用均值的工期设定调度问题的建模和算法设计；模糊环境下合理安排多个客户的加工生产顺序和工期，目标函数为极小化总费用均值的多agent系统工期设定调度问题的建模和求解；给出了区间值模糊集、直觉模糊集具有统计意义的数字特征，并分别用直觉模糊集、区间值模糊集刻画调度模型中的不确定变量，对工件间具有复杂约束、目标函数为极小化总费用均值的工期设定调度优化问题进行建模和求解。本项目较好的解决了用随机方法对不确定环境下具有复杂约束工期设定调度问题建模求解难的瓶颈问题，具有很强的理论和现实意义。

本项目研究的背景是现金流等资源有限的情况下如何安排生产以降低生产成本，提高企业竞争力。本项目所获得的模型及算法的相关结果，在理论方面，开拓了模糊调度新的研究方向，特别是引进模糊变量的可能性均值‐方差等工具给出模糊调度的刻画，这些工具的使用，在不确定性调度优化中充分发挥了模糊集合相关理论的优势；在应用方面，丰富了不确定性环境下具有资源约束等生产调度管理策略，能为企业管理降低运营成本提供相关参考。实验结果表明这些算法和模型是非常有效的。该项目围绕模糊环境下工件间具有优先加工顺序约束、relocation资源约束等复杂约束、极小化总费用均值的工期（工期窗口）设定调度优化问题的模型、性质、求解算法设计及分析展开研究。给出了加工时间是非对称模糊变量、工件间具有优先加工顺序约束的工期设定调度优化模型，证明了该问题是NP-难的，并给出了近似算法；构建了加工时间是模糊变量、工件间具有优先加工顺序约束的工期窗口设定调度优化模型，分析了该模型的计算复杂度，基于锥优化技术设计了近似求解算法；完成了工件间具有relocation资源约束、不可中断链状约束、极小化总完工时间的调度优化问题的近似算法；提出了加工时间为对称梯形模糊变量且可控、工件间具有优先加工顺序约束的工期设定调度优化模型，并给出了近似求解算法。针对区间值模糊变量、直觉模糊变量，给出了一种基于一类截集的可能性均值和方差的定义，并将其引入到各种资源约束条件下的平行机、多agent系统的工期设定调度问题中；在各种调度模型仿真实验结果基础上，拓展到深度学习研究中，建立了Fuzzy Restricted Boltzmann Machine 等机器学习模型，给出了学习算法，并讨论了在文本聚类、图像识别中的应用。该项目先后有9篇论文被《IEEE Transactions on Fuzzy Systems》、《计算数学》等国内外期刊录用发表，其中SCI 3篇，EI三篇，北大中文核心期刊3篇。