彩色装箱问题的快速邻域搜索启发式算法
Fast Neighborhood Search Heuristics for the Colored Bin Packing Problem
AI总结：
针对彩色装箱问题，本文改造并设计启发式规则，提出快速邻域搜索，并构建基于 VNS 及融合 LP、VNS 与 GRASP 的数学启发式方法，实验表明其能在大规模实例上获得近优解。
摘要：
彩色装箱问题（Colored Bin Packing Problem，CBPP）是装箱问题（Bin Packing Problem，BPP）的推广。CBPP 要求将一组物品装入容量有限的箱子中，每个物品都具有重量和颜色，在最小化所用箱子数量的同时，还必须满足同一颜色的两个物品不能在同一箱子中相邻放置这一约束。本文中，我们提出了 BPP 启发式算法的适配版本，以及面向 CBPP 的新启发式算法。此外，我们提出了一组用于 CBPP 的快速邻域搜索算法。这些邻域被应用于一种基于变邻域搜索（Variable Neighborhood Search，VNS）的元启发式方法，以及一种将线性规划与元启发式算法 VNS 和贪婪随机自适应搜索过程（Greedy Randomized Adaptive Search，GRASP）相结合的数学启发式方法。结果表明，我们的数学启发式方法优于 VNS，并且两种方法都能够为大量实例找到近优解，即使对于包含许多物品的实例也是如此。
英文摘要：
The Colored Bin Packing Problem (CBPP) is a generalization of the Bin Packing Problem (BPP). The CBPP consists of packing a set of items, each with a weight and a color, in bins of limited capacity, minimizing the number of used bins and satisfying the constraint that two items of the same color cannot be packed side by side in the same bin. In this article, we proposed an adaptation of BPP heuristics and new heuristics for the CBPP. Moreover, we propose a set of fast neighborhood search algorithms for CBPP. These neighborhoods are applied in a meta-heuristic approach based on the Variable Neighborhood Search (VNS) and a matheuristic approach that combines linear programming with the meta-heuristics VNS and Greedy Randomized Adaptive Search (GRASP). The results indicate that our matheuristic is superior to VNS and that both approaches can find near-optimal solutions for a large number of instances, even for those with many items.
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。
