An EDA for the 2D knapsack problem with guillotine constraint

Abstract

In this paper we present an evolutionary heuristic for the 2D knapsack problem with guillotine constraint. In this problem we have a set of rectangles and there is a profit for each rectangle. The goal is to cut a subset of rectangles without overlap from a rectangular strip of width W and height H, so that the total profit of the rectangles from the subset is maximal. The sides of the rectangles are parallel to the strip sides and every cutting is restricted by orthogonal guillotine-cuts. A guillotine-cut is parallel to the horizontal or vertical side of the strip and cuts the strip into two separated rectangular strips. Our algorithm is an estimation of distribution algorithm (EDA), where recombination and mutation evolutionary operators are replaced by probability estimation and sampling techniques. Our EDA works with two probability models. It improves the quality of the solutions with local search procedures. The algorithm was tested on well-known benchmark instances from the literature.