AI 中文总结
本文提出一种基于滚动时域最优控制框架的新方法，将通用装配线平衡问题建模为混合整数非线性规划问题，通过任务与资源分配优化完成时间，经实验验证其鲁棒性与有效性。
AI 中文摘要
本文提出了一种利用滚动时域最优控制框架解决通用装配线平衡问题（General Assembly Line Balancing Problem, GALBP）的新方法。该方法为装配线构建的离散模型具有灵活的表示能力，无需对特定生产线配置做假设。控制动作旨在通过最小化完成时间来优化工业装配线，同时满足任务 precedence（优先顺序）、工作站容量、资源需求等约束条件。控制动作分别通过任务分配矩阵和资源分配矩阵表示，前者将任务分配给特定工作站，后者将资源分配给工作站。该优化问题被建模为混合整数非线性规划（Mixed-Integer Nonlinear Programming, MINLP）问题。滚动时域方法固有的鲁棒性可确保为装配线提供最优解，有效应对突发变化。数值实验表明，所提出的控制综合方法具有鲁棒性和有效性，可高效分配任务与资源，最小化总完成时间。
英文摘要
This paper introduces a novel approach to the General Assembly Line Balancing Problem (GALBP) by utilizing a receding horizon optimal control framework. The proposed discrete model for the assembly line offers a flexible representation, avoiding assumptions about specific line configurations. The control actions aim to optimize the industrial assembly line by minimizing the completion time while adhering to constraints such as task precedence, workstation capacity, and resource requirements. Control actions are represented through task assignment and resource allocation matrices, assigning tasks to specific workstations and assigning resources to workstations, respectively. The optimization problem is formulated as a Mixed-Integer Nonlinear Programming (MINLP) problem. The inherent robustness of the receding horizon approach ensures optimal solutions for the assembly line, effectively adapting to sudden changes. Numerical experiments demonstrate the robustness and effectiveness of the proposed control synthesis in efficiently distributing tasks and resources, minimizing the overall completion time.
