LAUSR

The single container packing problem consists of allocating a number of items inside one container in order to find the densest packing patterns without overlapping. As an important class of optimization problems, packing problems have numerous applications in industry and academia, such as applied mathematics, material manufacturing, material cutting, logistics, wireless communication and fashion industry. As an NP-hard problem, however, there is no exact algorithm to obtain optimality in polynomial time unless P = NP, and researchers have resorted to heuristics or approximation methods. Hifi and M’Hallah [1] reviewed the most relevant literature on efficient models and methods for packing circular items in different types of containers. The circle packing problem (CPP) is classified into two categories based on whether the circle items are equal [2] or unequal [3]. Other variants exist that consider additional constraints, such as the CPP with equilibrium constraints [4].