Two methods are developed for a two-dimensional cutting problem with irregular shaped items. The concepts of inner-fit raster and no-fit raster are used to search for a feasible positioning of items on a rectangular container. The first method is a Biased Random Key Genetic Algorithm, which is a population method, while the other is a Variable Neighborhood Search, which is a single trajectory method. In the proposed methods, a solution is represented by a vector of items, and the positioning of items is achieved with three rules inspired by the bottom-left strategy. When positioning items, feasible positions can be skipped as a strategy to diversify the search and escape from local optima solutions. Numerical experiments performed on literature instances show that the methods are better than the current state-of-the-art method since they obtained equal or better solutions for all the instances. On average, the occupied area increased 6.44%, and the known optimal solution was obtained for 60% of the instances. The population-based method performed better overall, obtaining solutions with better-occupied areas.

针对具有不规则形状的物品的二维切割问题，开发了两种方法。内部适合栅格和不适合栅格的概念用于搜索矩形容器上物品的可行位置。第一种方法是有偏随机密钥遗传算法，它是一种总体方法，而另一种是可变邻域搜索，它是一种单轨迹方法。在所提出的方法中，解决方案以项目向量表示，并且通过左下策略启发的三个规则实现项目的定位。放置物品时，可以跳过可行的位置，以此作为使搜索多样化并从局部最优解中逃脱的策略。在文献实例上进行的数值实验表明，该方法比当前的最新技术要好，因为它们对于所有实例都获得了相同或更好的解决方案。平均而言，占用面积增加了6.44％，并且针对60％的实例获得了已知的最佳解。基于人口的方法总体上表现更好，获得了占用面积更大的解决方案。