The 2024 edition of the CG:SHOP Challenge focused on the knapsack polygonal packing problem. Each instance consists of a convex polygon known as the container and a multiset of items, where each item is a simple polygon with an associated integer value. A feasible packing solution places a selection of the items inside the container without overlapping and using only translations. The goal is to achieve a packing that maximizes the total value of the items in the solution. Our approach to win first place is divided into two main steps. First, we generate promising initial solutions using two strategies: one based on integer linear programming and the other on employing a combination of geometric greedy heuristics. In the second step, we enhance these solutions through local search techniques, which involve repositioning items and exploring potential replacements to improve the total value of the packing.

翻译：2024年CG:SHOP挑战赛聚焦于背包多边形排样问题。每个算例包含一个称为容器的凸多边形以及一个物品多重集合，其中每个物品均为附带整数值的简单多边形。可行的排样方案需将选定物品通过纯平移方式置于容器内部且互不重叠。优化目标在于实现排样方案中物品总价值的最大化。我们获得第一名的解决方案主要分为两个阶段：首先通过两种策略生成有潜力的初始解——一种基于整数线性规划，另一种采用几何贪心启发式组合方法；随后通过局部搜索技术对这些解进行增强，包括调整物品位置与探索潜在替换方案以提升排样总价值。