We propose two mixed-integer linear programming based approaches for the 2-D orthogonal strip packing problem. Using the knowledge of the alternative forms of time representation in scheduling formulations, we show how to efficiently combine three different concepts into the xand ydimensions. One model features a discrete representation of the x-axis (strip width) and a continuous representatio...

The knapsack container loading problem is the problem of loading a subset of rectangular boxes into a rectangular container of fixed dimensions such that the volume of the packed boxes is maximized. A new heuristic based on the wall-building approach is proposed, which decomposes the problem into a number of layers which again are split into a number of strips. The packing of a strip may be for...

The geost constraint has been proposed to model and solve discrete placement problems involving multi-dimensional boxes (packing in space and time). The filtering technique is based on a sweeping algorithm that requires the ability for each constraint to compute a forbidden box around a given fixed point and within a surrounding area. Several cases have been studied so far, including integer li...

A new algorithm called adaptive cluster growth (ACG) for circuit packing (or detailed placement) in any rectilinear region is described; it is an analogy to the growth of a low-stress crystal in a cavity of any given shape. The algorithm ACG is suitable for the packing of circuit modules, either standard-cell or macrocell, in a rectilinear region by the refinement of a result of global placemen...

The paper deals with the purpose of one hybrid approach for solving the constrained two-dimensional cutting (2DC) problem. The authors study this hybrid approach that combines the genetic algorithm and the Tabu search method. For this problem, they assume a packing of a whole number of rectangular pieces to cut, and that all cuts are of guillotine type in one sheet of a fixed width and an infin...

In this paper, we study the 3D strip packing problem in which we are given a list of 3dimensional boxes and required to pack all of them into a 3-dimensional strip with length 1 and width 1 and unlimited height to minimize the height used. Our results are below: i) we give an approximation algorithm with asymptotic worst-case ratio 1.69103, which improves the previous best bound of 2 + ǫ by Jan...

We present a genetic programming system to evolve reusable heuristics for 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. This work contributes to a growing research area which represents a paradigm shift in search methodologies. Instead of using evolut...