We consider the 3-staged Strip Packing Problem, in which rectangular items have to be arranged onto a rectangular strip of fixed width, such that the items can be obtained by three stages of guillotine cuts while the required strip height is to be minimized. We propose a new logic-based Benders decomposition with two kinds of Benders cuts and compare it with a compact integer linear programming...

This article addresses the Strip Packing Problem with Unloading Constraints (SPU). In this problem, we are given a strip of fixed width and unbounded height, and n items of C different classes. As in the well-known two-dimensional Strip Packing problem, we have to pack all items minimizing the used height, but now we have the additional constraint that items of higher classes cannot block the w...

Most existing placement algorithms were designed to handle blocks that are rectangular in shape. In this paper, we show how a genetic algorithm (GA) is used to construct an optimal arrangement of two-dimensional rectilinear blocks. Our approach does not require the orientation of each block to be fixed. To transform the placement problem to a GA problem, we devised a decoding technique known as...

This research presents an application of Ant colony optimization meta-heuristic to the bin packing problems. Hybridization of Ant tuning strategy has introduced to improve the results obtained from basic ant system by utilizing the behaviour of artificial ants to perform local search. The objective is to pack the arbitrary sized three dimensional rectangular prismatic bins into the container of...

We propose a satisfiability testing (SAT) based exact approach for solving the two-dimensional strip packing problem (2SPP). In this problem, we are given a set of rectangles and one large rectangle called a strip. The goal of the problem is to pack all rectangles without overlap, into the strip by minimizing the overall height of the packing. We show the method solves a 2SPP by translating it ...

Main subject of this thesis are approximation algorithms for scheduling and packing, two classical geometrical problems in combinatorial optimization. It is divided into three parts. In the first part we consider a generalization of the strip packing problem or geometrical cutting stock problem. In strip packing a given set of rectangles has to be placed into a strip of fixed width and infinite...

In this paper, the use of beam search and look-ahead strategies for solving the strip packing problem (SPP) is investigated. Given a strip of fixed width W, unlimited length L, and a set of n circular pieces of known radii, the objective is to determine the minimum length of the initial strip that packs all the pieces. An augmented algorithm which combines beam search and a look-ahead strategie...

In this work we consider an hybrid metaheuristic approach to solve the Strip Packing Problem. In the hybrid algorithm, we use an Variable Neighbourhood Search (VNS) to improve the quality of part of the solution obtained with a Greedy Randomized Adaptive Search Procedure (GRASP). Then, the results achieved with the hybrid method are compared with those existing in the literature. From these res...

In the two-dimensional strip packing problem a number of rectangles have to be packed without rotation or overlap into a strip such that the height of the strip used is minimal. The width of the rectangles is bounded by 1 and the strip has width 1 and infinite height. We study the online version of this packing problem. In the online version the rectangles are given to the online algorithm one ...