Defragmenting the Module Layout of a Partially Reconfigurable Device

Modern generations of field-programmable gate arrays (FPGAs) allow for partial reconfiguration. In an online context, where the sequence of modules to be loaded on the FPGA is unknown beforehand, repeated insertion and deletion of modules leads to progressive fragmentation of the available space, making defragmentation an important issue. We address this problem by propose an online and an offline component for the defragmentation of the available space. We consider defragmenting the module layout on a reconfigurable device. This corresponds to solving a two-dimensional strip packing problem. Problems of this type are NP-hard in the strong sense, and previous algorithmic results are rather limited. Based on a graph-theoretic characterization of feasible packings, we develop a method that can solve two-dimensional defragmentation instances of practical size to optimality. Our approach is validated for a set of benchmark instances.Comment: 10 pages, 11 figures, 1 table, Latex, to appear in "Engineering of Reconfigurable Systems and Algorithms" as a "Distinguished Paper

Extreme-Point-based Heuristics for the Three-Dimensional Bin Packing problem

One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points at which to place the items inside the bins, because the performance of exact and heuristic solution methods is actually strongly influenced by the choice of a placement rule. We introduce the extreme point concept and present a new extreme point-based rule for packing items inside a three-dimensional container. The extreme point rule is independent from the particular packing problem addressed and can handle additional constraints, such as fixing the position of the items. The new extreme point rule is also used to derive new constructive heuristics for the three-dimensional bin-packing problem. Extensive computational results show the effectiveness of the new heuristics compared to state-of-the-art results. Moreover, the same heuristics, when applied to the two-dimensional bin-packing problem, outperform those specifically designed for the proble

The Generalized Bin Packing Problem

In the Generalized Bin Packing Problem a set of items characterized by volume and profit and a set of bins of different types characterized by volume and cost are given. The goal consists in selecting those items and bins which optimize an objective function which combines the cost of the used bins and the profit of the selected items. We propose two methods to tackle the problem: branch-and-price as an exact method and beam search as a heuristics, derived from the branch-and-price. Our branch-and-price method is characterized by a two level branching strategy. At the first level the branching is performed on the number of available bins for each bin type. At the second level it consists on pairs of items which can or cannot be loaded together. Exploiting the branch-and-price skeleton, we then present a variegated beam search heuristics, characterized by different beam sizes. We finally present extensive computational results which show a high accuracy of the exact method and a very good efficiency of the proposed heuristics

The Generalized Bin Packing Problem with bin-dependent item profits

In this paper, we introduce the Generalized Bin Packing Problem with bin-dependent item profits (GBPPI), a variant of the Generalized Bin Packing Problem. In GBPPI, various bin types are available with their own capacities and costs. A set of compulsory and non-compulsory items are also given, with volume and bin-dependent profits. The aim of GBPPI is to determine an assignment of items to bins such that the overall net cost is minimized. The importance of GBPPI is confirmed by a number of applications. The introduction of bin-dependent item profits enables the application of GBPPI to cross-country and multi-modal transportation problems at strategic and tactical levels as well as in last-mile logistic environments. Having provided a Mixed Integer Programming formulation of the problem, we introduce efficient heuristics that can effectively address GBPPI for instances involving up to 1000 items and problems with a mixed objective function. Extensive computational tests demonstrate the accuracy of the proposed heuristics. Finally, we present a case study of a well-known international courier operating in northern Italy. The problem approached by the international courier is GBPPI. In this case study, our methodology outperforms the policies of the company

More-Dimensional Packing with Order Constraints

We present a first systematic study on more-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture. They can be interpreted as more-dimensional generalizations of scheduling problems. Using graph-theoretic structures to describe feasible solutions, we develop a novel exact branch-and-bound algorithm. This extends previous work by Fekete and Schepers; a key tool is a new order-theoretic characterization of feasible extensions of a partial order to a given complementarity graph that is tailor-made for use in a branch-and-bound environment. The usefulness of our approach is validated by computational results

Modelos e algoritmos para o problema de minimização de padrões

Dissertação de mestrado em Engenharia IndustrialNesta dissertação, estudamos um problema de optimização combinatória designado por Problema de Minimização de Padrões. O problema é um problema de corte no qual se consideram custos de setup. Existe um número muito reduzido de métodos para a resolução exacta do Problema de Minimização de Padrões. Aqueles que são descritos na literatura apenas permitem resolver algumas instâncias de pequena dimensão. Com esta dissertação, pretendemos contribuir para a resolução exacta do problema explorando um modelo que foi proposto recentemente na literatura. Os modelos de Programação Inteira propostos na literatura são descritos na primeira parte do texto. Descrevemos também os algoritmos exactos que foram definidos com base nesses modelos e apresentamos algumas das melhores heurísticas de resolução que foram desenvolvidas para este problema. Na segunda parte da dissertação, analisamos em detalhe um modelo proposto recentemente na literatura para o Problema de Minimização de Padrões. Esse modelo é um modelo de Programação Inteira, obtido com base numa nova decomposição de um modelo não-linear. Exploramos formas de reforçar esse modelo, e analisamos algoritmos que permitam obter soluções óptimas inteiras a partir do método de partição e avaliação e do método de geração de colunas. A diferença entre os algoritmos reside nas regras de partição que foram usadas. É sabido que combinar o método de partição e avaliação com o método de geração de colunas não é trivial. A partição feita com base nas variáveis do modelo de geração de colunas provoca a regeneração das colunas presentes no problema mestre. A forma de evitar esse problema passa por aumentar a complexidade do subproblema. Nesta dissertação, as regras de partição são baseadas em variáveis originais, e como tal não alteram significativamente a dificuldade dos subproblemas de geração de colunas. Foram conduzidos experiências computacionais para avaliar a qualidade dos esquemas de partição propostos. Essas experiências foram realizadas usando instâncias da literatura, e sem recorrer a qualquer heurística. Os resultados das experiências são apresentados no final da dissertação.In this dissertation, we study a combinatorial optimization problem called the Pattern Minimization Problem. The problem is a cutting stock problem in which setup costs are considered. The number of exact algorithms that were proposed in the literature for this problem is very small. Those that were proposed can only solve a limited number of small and medium instances. With this dissertation, our aim is to contribute to the exact resolution of this problem by exploring a model that was proposed recently in the literature. The Integer Programming models proposed in the literature are described in the first part of this text. We also describe the exact algorithms that were defined based on these models and we present the best heuristics that were developed to solve this problem. In the second part of this dissertation, we analyse in detail a model proposed recently in the literature for the Pattern Minimization Problem. This model is an Integer Programming model that is obtained by applying a new decomposition to a non-linear model. We explore ways of strengthening the model, and we analyse algorithms for computing integer solution using the branch-and-bound method and the column generation method. The difference among our algorithms is in the branching scheme that is used. It is well known that combinig branch-and-bound with column generation is not trivial. When the partition is done on the variables of the column generation model, regeneration occurs. To avoid this regeneration, we have to increase the complexity of the pricing subproblem. In this dissertation, the branching rules are based on original variables and hence the complexity of the subproblem is almost unchanged. Computational experiments were conducted to evaluate the quality of the branching schemes proposed. These experiences were conducted on instances from the literature, and without using any heuristic. The results of these experiments are presented at the end of this dissertation