The edge and vertex-disjoint path problems together with their unsplittable flow generalization are NP-hard problems with a multitude of applications in areas such as routing, scheduling and bin packing. Given the hardness of the problems, we study polynomial-time approximation algorithms with bounded performance guarantees. We introduce techniques which yield new algorithms for a wide range of...

The aim of this article is to apply the methodology of genetic algorithms to the packing problem encountered in a sticker company. Owing to the nature of the packing operation in this company the problem is not easily solved with exact integer linear programming algorithms (Gilmore and Gomory, 1963). Industrial applications of packing methodology can be found in (Dyson and Gregory, 1974), (Farl...

We introduce a constraint for one-dimensional bin packing. This constraint uses propagation rules incorporating knapsack-based reasoning, as well as a lower bound on the number of bins needed. We show that this constraint can significantly reduce search on bin packing problems. We also demonstrate that when coupled with a standard bin packing search strategy, our constraint can be a competitive...

The paper deals with multi-dimensional cutting and packing and metaheuristic algorithms. A brief overview of this area is presented, and the general Tabu Search framework of Lodi, Martello and Vigo [LMV99a] is considered in detail. Computational results on multi-dimensional bin packing problems are reported, and possible methods for extending the framework to other packing problems are finally ...

The rectangle packing problem often appears in encasement and cutting as well as very large-scale integration design. To solve this problem, many algorithms such as genetic algorithm, simulated annealing and other heuristic algorithms have been proposed. In this paper, a new heuristic algorithm is recommended based on two important concepts, namely, the corner-occupying action and caving degree...

We present a new heuristic for 2D-packing of rectangles inside a rectangular area where the aesthetics of the resulting packing is amenable to generating large collages of photographs or images. The heuristic works by maintaining a sorted collection of vertical segments covering the area to be packed. The segments define the leftmost boundaries of rectangular and possibly overlapping areas that...

Cutting and packing (C & P) problem is to allocate a set of items to larger rectangular standardized units by minimizing the waste. Bin packing, strip packing and cutting stock problem is well-known classical C & P problem. An overview is provided of several meta-heuristics algorithms of swarm intelligence from the literature for the 2D C & P problem. The objective of this paper is to present a...

In this paper, the effects of container size on the porosity of random loose packing of mono size particles have been investigated using an Event Dynamics (ED) based model. Simultaneous effects of square container walls on particles packing and their order are also investigated. Our simulation results indicate higher container size will increase the total packing factor and high density regions...

Recently, Renault (2016) studied the dual bin packing problem in the per-request advice model of online algorithms. He showed that given O(1/ǫ) advice bits for each input item allows approximating the dual bin packing problem online to within a factor of 1 + ǫ. Renault asked about the advice complexity of dual bin packing in the tape-advice model of online algorithms. We make progress on this q...

This paper proposes a visualization tool for analyzing the behavior of metaheuristic algorithms. It works by reproducing graphically the solutions generated in execution time. The tool was evaluated analyzing the Hybrid Grouping Genetic Algorithm for Bin Packing (HGGA_BP). It was used to solve a benchmark with 17 instances of the one dimensional Bin Packing problem (1D-BPP). The use of the visu...