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 ...

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 ...

In this paper we study the Multiple Strip Packing (MSP) problem, a generalization of the well-known Strip Packing problem. For a given set of rectangles, r1, . . . , rn, with heights and widths ≤ 1, the goal is to find a non-overlapping orthogonal packing without rotations into k ∈ N strips [0, 1]× [0,∞), minimizing the maximum of the heights. We present an approximation algorithm with absolute...

The irregular strip packing problem asks to place a set of polygons within a rectangular strip of fixed height without overlap, so as to minimize the strip width required. We consider an overlap minimization problem which minimizes the amount of overlap penalty for all pairs of polygons within a given bound of strip width. We propose a local search algorithm which translates a polygon in horizo...

This paper presents an extended local search algorithm (ELS) for the irregular strip packing problem. It adopts two neighborhoods, swapping two given polygons in a placement and placing one polygon into a new position. The local search algorithm is used to minimize the overlap on the basis of the neighborhoods mentioned above and the unconstrained nonlinear programming model is adopted to furth...

This paper presents a greedy randomized adaptive search procedure (GRASP) for the strip packing problem, which is the problem of placing a set of rectangular pieces into a strip of a given width and infinite length so as to minimize the required length. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform ex...

We consider a symmetric random walk of length n that starts at the origin and takes steps uniformly distributed on the real interval ?1; +1]. We study the large-n behavior of the expected maximumexcursion and prove a very precise estimate. This estimate applies to the problem of packing n rectangles into a unit-width strip; in particular, it makes much more precise the known upper bound on the ...