Abstract: The packing of rectangles is a NP-Complete problem and possesses widespread applications in the industry，such as the cutting of clothing，metal and composition of news.In this paper，circular-based crossover operator and circular-based mutation operator are adopted in the proposed adaptive genetic algorithm.With the combination of Improved Adaptive Genetic Algorithm（IAGA） and Improved Bottom-Left heuristic（IBL） algorithm，the packing of rectangles can be effectively solved.The comparison results show that genetic algorithm is more effective by using circular-based crossover operator and circular-based mutation operator and the satisfactory solution can be obtained in a reasonably short period of time by using hybrid IAGA.

Key words: Adaptive Genetic Algorithm（AGA）, packing of rectangles, heuristic placement algorithm, circular-based crossover operator, circular-based mutation operator

摘要： 矩形排样优化属于NPC问题，在工业界有着广泛的应用，如布料切割、金属下料和新闻组版等。提出了一种基于环形交叉算子和环形变异算子的自适应遗传算法，并将改进的自适应遗传算法和IBL启发式布局算法相结合，有效地解决了矩形排样优化问题。对比实验结果表明，环形交叉算子和环形变异算子对遗传算法是有效的，所提出的改进混合自适应遗传算法能够在一个较短的时间内找到满意解。

关键词: 自适应遗传算法, 矩形排样优化, 启发式布局算法, 环形交叉算子, 环形变异算子