Graph coloring models and metaheuristics for packing applications

Abstract

On the one hand, in the famous graph coloring problem, each vertex of the considered graph has to get a single color. If two vertices are connected with an edge, then their colors have to be different. The goal consists in coloring the graph with the smallest number of colors. On the other hand, consider the packing problem where items have to be loaded in a container. For each item, we have to decide in which container it will be assigned. As some pairs of items are incompatible, they cannot be loaded in the same container. The goal is to load all the items in a minimum number of containers. Even if the correspondence between these two problems is obvious (a vertex is an item, a color is a container, and an edge represents an incompatibility), there is no obvious bridge between the packing and the graph coloring literatures. In this chapter, some packing problems will be modeled and solved with graph coloring models and methods.