The Colorful 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 mixes 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 instances, even for instances
with many items.

通过改进 BPP 启发式算法以及提出新的 CBPP 启发式算法，并结合基于变量邻域搜索 (VNS) 和数学启发式方法的邻域搜索算法，我们的研究表明，我们的数学启发式方法优于 VNS，两种方法都可以在大量实例中找到近乎最优的解，甚至对于具有许多物品的实例也是如此。