Packing unequal circles into a square container based on the narrow action spaces

Abstract

We address the NP-hard problem of finding a non-overlapping dense packing pattern for n Unequal Circle items in a two-dimensional Square Container (PUC-SC) such that the size of the container is minimized. Based on our previous work on Action Space-based Global Optimization (ASGO) that approximates each circle item as a square item to find large unoccupied spaces efficiently, we propose an optimization algorithm based on the Partitioned Action Space and Partitioned Circle Items (PAS-PCI). The PAS is used to partition the narrow action space on the long side to find two equal action spaces to fully utilize the unoccupied spaces. The PCI are used to partition the circle items into four groups based on item sizes for the basin-hopping strategy. Experiments on two sets of benchmark instances show the effectiveness of the proposed method. In comparison with our previous ASGO algorithm on the 68 tested instances published with ASGO, PAS-PCI not only achieves smaller containers in 64 instances and matches the other 4 but also runs faster in most instances. In comparison with the best record of the Packomania website for 94 instances, PAS-PCI finds smaller containers for 82 and matches the other 12. Note that we updated 19 records (47-48, 51-54, 57, 61-72) that had remained unchanged since 2013.

Adaptive Large Neighborhood Search for Circle Bin Packing Problem

“…On the other hand, the global optimization technique [33] tries to solve the packing problem by improving the solution iteratively based on an initial solution, which is subdivided into two types. The first type is called the quasi-physical quasi-human algorithm [34,35,36], which is mostly motivated by some physical phenomenon, or some wisdom observed in human activities [37,38]. The second type is called the meta-heuristic optimization, mainly built by defining an evaluation function that employs a trade-off of randomisation and local search that directs and re-models the basic heuristic to generate feasible solutions.…”