An Effective Heuristic Algorithm for the Two-Dimensional Variable-Size Bin Packing Problem with Circular Containers

This paper studies the two-dimensional variable-size bin packing problem with circular containers (2DVSBPPCC), a generalization of the well-known bin packing problem. The goal of this problem is to pack all the rectangular items into several bins and minimize the total cost of these bins. To solve this problem, we design a decoding procedure that converts a given sequence of items into a packing configuration and a swap operator that deals with infeasible containers. Based on this decoding procedure and this swap operator, we propose a highly efficient heuristic algorithm called the adaptive search algorithm. To evaluate the performance of the proposed adaptive search algorithm, we carry out experiments on numerous benchmark instances. The computational results show that the proposed algorithm is very efficient. Experimental analysis on the benchmark instances shows that the swap operator that exchanges a pair of containers plays an important role for the high performance of the algorithm.