Abstract: This paper studies the multi-objective rectangle packing problem combined with lot-sizing problem by multi-objective heuristic evolutionary algorithm. Establish a multi-objective optimization model containing the raw materials cost minimization and parts inventory cost minimization. Initialize the patterns by heuristic algorithm and then use improved fast non-dominated sorting algorithm getting the cutting program. Through the results and comparison with other algorithms, this algorithm can solve small rectangle packing problem with high utilization and low total cost in a fast time.

Key words: rectangle packing, lot-sizing, multi-objective optimization, heuristic, evolutionary algorithm

摘要： 设计多目标启发式进化算法，研究了一种考虑批量问题的二维矩形件排样问题，建立了含有原材料成本最小化和零件库存成本最小化的多目标优化模型。先用启发式算法初始化下料方式，再用改进的快速非支配排序算法进行优化求解，确定下料方案。通过实验结果以及与其他算法的对比表明，在中等规模的矩形件排样问题中，该算法能够在较快的时间内既保证较高的原料利用率，又能降低该问题的总成本，证明了该算法的有效性。

关键词: 矩形件排样, 批量问题, 多目标优化, 启发式, 进化算法