The two-dimensional discrete bin-packing problem (2BP ) consists in minimizing the number of identical rectangles used to pack a set of smaller rectangles. This problem is NP-hard. It occurs in industry if pieces of steel, wood, or paper have to be cut from larger rectangles. It belongs to the family of cutting and packing problems, more precisely to the class of TwoDimensional Single Bin Size ...

We study a variant of the classical bin-packing problem, the ordered open-end bin-packing problem, where first a bin can be filled to a level above 1 as long as the removal of the last piece brings the bin’s level back to below 1 and second, the last piece is the largest-indexed piece among all pieces in the bin. We conduct both worst-case and average-case analyses for the problem. In the worst...

Differential evolution (DE) is a powerful algorithm to find an optimal solution in real world problems. Nevertheless, the binomial crossover parameter is an important issue for the success of the algorithm. The proper selection of the binomial crossover parameter depends on the problem at hand. In this work, the effect of the binomial crossover in the DE/Rand/1/bin, DE/Best/1/Bin and DE/Current...

Motivated by bursty bandwidth allocation and the of virtual machines to servers in cloud, we consider online problem packing items with random sizes into unit-capacity bins. Items arrive sequentially, but on arrival, an item’s actual size is unknown; only its probabilistic information available decision maker. Without knowing this size, maker must irrevocably pack item bin or place it a new bin...

Bin packing is a well studied problem which has many applications. In this paper we design a robust APTAS for the problem. The robust APTAS receives a single input item to be added to the packing at each step. It maintains an approximate solution throughout this process, by slightly adjusting the solution for each new item. At each step, the total size of items which may migrate between bins mu...

Two-dimensional bin packing problems are highly relevant combinatorial optimization problems. They find a large number of applications, for example, in the context of transportation or warehousing, and for the cutting of different materials such as glass, wood or metal. In this work we deal with the oriented two-dimensional bin packing problem under free guillotine cutting. In this specific pro...

The standard procedure for measuring correlations between pairs of spike trains is to count the numbers of spikes occurring within a specified set of time intervals partitioning the continuous time line into discrete bins of width w (seconds). One then computes the Pearson correlation between pairs of the bin occupancy vectors. This method introduces a form of quantization noise, similar to tha...

MsatAllele is a computer package built on R to visualize and bin the raw microsatellite allele size distributions. The method is based on the creation of an R database with exported files from the open-source electropherogram peak-reading program STRAND. Contrary to other binning programs, in this program, the bin limits are not fixed and are automatically defined by the data stored in the data...

In this paper we present a theoretical analysis of the deterministic on-line Sum of Squares algorithm (SS) for bin packing, introduced and studied experimentally in [8], along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time O(nB). It performs remarkably well from...