Given a finite set of circles of different sizes we study the Strip Packing Problem (SPP) as well as the Knapsack Problem (KP). The SPP asks for a placement of all circles (without overlap) within a rectangular strip of fixed width so that the variable length of the strip is minimized. The KP requires packing of a subset of the circles in a rectangle of fixed dimensions so that the wasted area ...

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...

This paper presents a new approach for the design of a multiband uniplanar CPW-fed monopole antenna. The antenna consists of a fork like monopole strip to which is added an inverted U-shaped strip. The three branch fork like strip can create three resonant bands within the WLAN range while the placement of the inverted U-shaped strip provides a better impedance matching for the lowest resonant ...

We study the strip packing problem, a classical packing problem which generalizes both bin packing and makespan minimization. Here we are given a set of axis-parallel rectangles in the two-dimensional plane and the goal is to pack them in a vertical strip of fixed width such that the height of the obtained packing is minimized. The packing must be non-overlapping and the rectangles cannot be ro...

In this paper, we consider the two-dimensional rectangular strip packing problem, in the case where there is a perfect packing; that is, there is no wasted space. One can think of the problem as a jigsaw puzzle with oriented rectangular pieces. Although this comprises a quite special case for strip packing, we have found it useful as a subroutine in related work. We demonstrate a simple pruning...

In rectangle packing problems we are given the task of positioning some axis-aligned rectangles inside a given plane region, so that they do not overlap with each other. In the Maximum Weight Independent Set of Rectangles (MWISR) problem, their position is already fixed and we can only select which rectangles to choose, while trying to maximize their total weight. In the Strip Packing problem, ...

In this paper we propose an iterative hybrid heuristic approach consisting of two phases to solve the Rectangle Packing Problem. In the first phase, a strip width value W is fixed and the corresponding Strip Packing Problem is solved using an efficient hybrid GRASP-VNS heuristic. In the second one, a new value W is determined. The above phases are repeated until the stopping condition is met. T...

In this paper we propose a new exact procedure for the two-dimensional orthogonal packing problem, based on F. Clautiaux et al. approach [4]. The principle consists in searching first the positions of the items on the horizontal axis, so as that, at each position, the sum of the heights of the items does not exceed the height of the bin. Each time a valid placement of all the items is encounter...