A SAT-based Method for Solving the Two-dimensional Strip Packing Problem

A Comparative Study of Exact Algorithms for the Two Dimensional Strip Packing Problem

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

Symmetry breaking generalized disjunctive formulation for the strip packing problem

The two-dimensional strip packing is a special case of “Cutting and Packing” problems that arises in many applications. The problem seeks to pack a given set of rectangles into a strip of given width in order to minimize its length. Some applications in which the strip packing problem arises are: Cutting pieces from wooden boards, cutting pieces from glass or steel sheets, optimal layout of ind...

A new metaheuristic genetic-based placement algorithm for 2D strip packing

Given a container of fixed width, infinite height and a set of rectangular block, the 2D-strip packing problem consists of orthogonally placing all the rectangles such that the height is minimized. The position is subject to confinement of no overlapping of blocks. The problem is a complex NP-hard combinatorial optimization, thus a heuristic based on genetic algorithm is proposed to solve it. I...

 Abstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...

Elzaki transform method for finding solutions to two-dimensional elasticity problems in polar coordinates formulated using Airy stress functions

In this paper, the Elzaki transform method is used for solving two-dimensional (2D) elasticity problems in plane polar coordinates. Airy stress function was used to express the stress compatibility equation as a biharmonic equation. Elzaki transform was applied with respect to the radial coordinate to a modified form of the stress compatibility equation, and the biharmonic equation simplified t...