We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm —for staged pat...

in a graph g = (v,e), a subset s  v is said to be an open packing set if no two vertices of s have a common neighbour in g. the maximum cardinality of an open packing set is called the open packing number and is denoted by rho^o. this paper further studies on this parameter by obtaining some new bounds.

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...

We undertake an empirical study in which the performance of a good genetic algorithm is tested against some well-known bin packing heuristics on a range of two-dimensional bin packing problems. We restrict our study to problems involving guillotine patterns which are produced using a series of vertical and horizontal edge–to–edge cuts. Many applications of two-dimensional cutting and packing in...

We study the Parallel Task Scheduling problem Pm|sizej |Cmax with a constant number of machines. This problem is known to be strongly NP-complete for each m ≥ 5, while it is solvable in pseudo-polynomial time for each m ≤ 3. We give a positive answer to the long-standing open question whether this problem is strongly NP -complete for m = 4. As a second result, we improve the lower bound of 12 1...

T paper presents a binary search heuristic algorithm for the rectangular strip-packing problem. The problem is to pack a number of rectangles into a sheet of given width and infinite height so as to minimize the required height. We first transform this optimization problem into a decision problem. A least-waste-first strategy and a minimal-inflexion-first strategy are proposed to solve the rela...

Many systems can be modeled with hard and various size spheres, therefore packing and geometrical structures of such sets are of great importance. In this paper, rigid spherical particles distributed in different sizes are randomly packed in confined spaces, using a parallel algorithm. Mersenne Twister algorithm was used to generate pseudorandom numbers for initial coordination of particles. Di...

transfer table is an essential stage between roughing and finishing rolling stands in a hot-strip rolling mill. high temperature and long time that strip is exposed to air at this stage cause a considerable heat loss that accounts for uneven temperature distribution, non-uniform surfaces, reduced product quality and increased production costs. using thermal shields on the transfer table is cons...

This paper presents a two-stage intelligent search algorithm for a two-dimensional strip packing problem without guillotine constraint. In the first stage, a heuristic algorithm is proposed, which is based on a simple scoring rule that selects one rectangle from all rectangles to be packed, for a given space. In the second stage, a local search and a simulated annealing algorithm are combined t...