A Genetic Algorithm for theTwo-Dimensional Knapsack Problemwith Rectangular Pieces

Given a set of rectangular pieces and a rectangular container, the two-dimensional knapsackproblem (2D-KP) consists of orthogonally packing a subset of the pieces within the container suchthat the sum of the values of the packed pieces is maximized. If the value of a piece is given by itsarea the objective is to maximize the covered area of the container. A genetic algorithm (GA) isproposed addressing the guillotine case of the 2D-KP as well as the non-guillotine case. Moreover,an orientation constraint may optionally be taken into account and the given piece set may beconstrained or unconstrained.[...]