A hybrid evolutionary algorithm for the two-dimensional packing problem

Abstract

This paper presents a hybrid evolutionary algorithm for the two-dimensional non-guillotine packing problem. The problem consists of packing many rectangular pieces into a single rectangular sheet in order to maximize the total area of the pieces packed. Moreover, there is a constraint on the maximum number of times that a piece may be used in a packing pattern. The set of packing patterns is processed by an evolutionary algorithm. Three mutation operators and two types of quality functions are used in the algorithm. The best solution obtained by the evolutionary algorithm is used as the initial solution in a tree search improvement procedure. This approach is tested on a set of benchmark problems taken from the literature and compared with the results published by other authors.