Abstract: Aiming at the organization mode of designing mother plates and slabs before the production implementation in the demand-oriented production of medium and heavy plate,the integrated optimal design problem of mother plate and slab was investigated,in which flexibility in cross section and length of mother plate and slab and transformation relationship between mother plate and slab were taken into consideration together.It was modelled and solved as a cutting stock problem by considering making decisions on cross section and length of mother plate and slab simultaneously.The flexibility was transformed into constraints and a non linear mixed integer programming model with an objective minimizing the total quantity of surplus material and material loss in manufacturing process was built.A hybrid optimal algorithm combined tabu search and column generation was employed: tabu search was mainly used to deal with optimal choice of slab cross section.A one-to-many encoding scheme was adopted to reduce the dimensions of search space;a code string was decoded to make decisions on the length of mother plates and slabs and cutting patterns.A sub-problem was a mother plate design problem considering length flexibility and material processing loss and could be solved with a modified algorithm based on column generation.Applicable essential factors of tabu search such as neighborhood structure and tabu object were designed according to problem characteristics.The case experiments with the data instance from a steel plant showed that the modeling and solving method was feasible and effective.

Key words: cutting stock problem, mother plate design, slab design, tabu search, column generation

摘要： 针对中厚板面向订单的生产是先设计母板及板坯后实施的生产组织模式,研究综合考虑母板、板坯允许的多种断面与长度规格及其转换关系的母板板坯集成优化设计问题,将其归结为一种同时对母板、板坯断面及长度规格不确定性进行决策的下料问题。以最小化无订单余材和热轧切边等加工过程材料损失为目标,将板坯的断面与长度设计柔性转化为模型的约束条件,建立非线性混合整数规划模型;设计结合禁忌搜索与列生成技术的混合优化求解算法：禁忌搜索编码采用一对多的映射方式降低搜索空间维数,以进行板坯断面的优化选择;解码时对母板、板坯长度和下料方法进行设计,子问题为考虑长度柔性和材料加工损耗的母板设计问题,通过设计改进的列生成方法求解;针对问题特征设计了适用的邻域结构、禁忌对象等算法要素。基于某钢铁企业生产数据进行案例计算,结果表明了所提模型及求解方法的可行性和有效性。

关键词: 下料问题, 母板设计, 板坯设计, 禁忌搜索, 列生成