Given a finite set of spheres of different sizes we study the three-dimensional Strip Packing Problem (3D-SPP) as well as the three-dimensional Knapsack Problem (3D-KP). The 3D-SPP asks for a placement of all spheres within a cuboidal strip of fixed width and height so that the variable length of the cuboidal strip is minimized. The 3D-KP requires packing of a subset of the spheres in a given c...

We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a r...

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 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 ...

In order to verify and test the performance of new packing algorithms relative to existing algorithms, test problems are needed. The scope of published test instances for 2D rectangular and irregular packing has been fairly limited in terms of object size, number and dimension of items. A systematic investigation into the performance of new algorithms requires the use of a range of test problem...

In this paper, we formulate and study a scheduling problem related to Smart Grids. Specifically, the goal is to schedule a set of power loads with same start time and deadlines using minimum peak power. A job can be scheduled anytime after the start time as long as it finished before the deadline. Certain jobs have the added flexibility of being scheduled intermittently i.e. with intermissions ...

We present a genetic programming hyper-heuristic system to evolve a ‘disposable’ heuristic for each of a wide range of benchmark instances of the two-dimensional strip packing problem. The evolved heuristics are constructive, and decide both which piece to pack next and where to place that piece, given the current partial solution. Usually, there is a trade-off between the generality of a packi...

In this paper we present approximation algorithms for the two dimensional strip packing problem with unloading constraints. In this problem, we are given a strip S of width 1 and unbounded height, and n items of C different classes, each item ai with height h(ai), width w(ai) and class c(ai). As in the strip packing problem, we have to pack all items minimizing the used height, but now we have ...