背包多边形装填问题的Shadoks求解方法
Shadoks Approach to Knapsack Polygonal Packing
AI总结：
针对2024年CG:SHOP挑战赛的背包多边形装填问题，提出结合整数线性规划、几何贪心启发式生成初始解，再经局部搜索优化的两阶段方法，最终获得赛事第一名。
摘要：
2024年CG:SHOP挑战赛聚焦背包多边形装填问题。每个问题实例包含一个被称为容器的凸多边形，以及一个物品多重集，其中每个物品是带有对应整数值的简单多边形。可行的装填方案需选取部分物品放入容器内，物品间无重叠且仅允许平移操作，目标是实现装填方案中物品总价值最大化。我们赢得第一名的求解方法分为两个主要步骤：首先，我们采用两种策略生成优质初始解，一种基于整数线性规划，另一种结合几何贪心启发式方法；第二步，我们通过局部搜索技术优化这些初始解，包括调整物品位置、探索潜在的物品替换方案，以提升装填的总价值。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
