An effective evolutionary algorithm for packing rectangles into a fixed size circular container

Abstract

We study the general problem of orthogonally packing rectangles in a fixed size circular container. This is a computationally challenging combinatorial optimization problem with important real-world applications and has recently received much attention from the operations research community. We propose an effective evolutionary algorithm for four variants of the problem, which integrates an improved decoding procedure and several dedicated search operators for population initialization and new solution generation. Computational results on 108 popular benchmark instances show that the proposed algorithm advances the state of the art in practically solving these four variants of the problem by finding 53 new best solutions (26 for the variants of maximizing the area of the packed items and 27 for the variants of maximizing the number of the packed items). We perform experiments to verify the design of key algorithmic components.