Analysis on the less flexibility first (LFF) algorithm and its application to the container loading problem.

Wu Yuen-Ting.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 88-90).Abstracts in English and Chinese.Chapter 1. --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.2 --- Research Objective --- p.4Chapter 1.3 --- Contribution --- p.5Chapter 1.4 --- Structure of this thesis --- p.6Chapter 2. --- Literature Review --- p.7Chapter 2.1 --- Genetic Algorithms --- p.7Chapter 2.1.1 --- Pre-processing step --- p.8Chapter 2.1.2 --- Generation of initial population --- p.10Chapter 2.1.3 --- Crossover --- p.11Chapter 2.1.4 --- Mutation --- p.12Chapter 2.1.5 --- Selection --- p.12Chapter 2.1.6 --- Results of GA on Container Loading Algorithm --- p.13Chapter 2.2 --- Layering Approach --- p.13Chapter 2.3 --- Mixed Integer Programming --- p.14Chapter 2.4 --- Tabu Search Algorithm --- p.15Chapter 2.5 --- Other approaches --- p.16Chapter 2.5.1 --- Block arrangement --- p.17Chapter 2.5.2 --- Multi-Directional Building Growing algorithm --- p.17Chapter 2.6 --- Comparisons of different container loading algorithms --- p.18Chapter 3. --- Principle of LFF Algorithm --- p.8Chapter 3.1 --- Definition of Flexibility --- p.8Chapter 3.2 --- The Less Flexibility First Principle (LFFP) --- p.23Chapter 3.3 --- The 2D LFF Algorithm --- p.25Chapter 3.3.1 --- Generation of Corner-Occupying Packing Move (COPM) --- p.26Chapter 3.3.2 --- Pseudo-packing and the Greedy Approach --- p.27Chapter 3.3.3 --- Real-packing --- p.30Chapter 3.4 --- Achievement of 2D LFF --- p.31Chapter 4. --- Error Bound Analysis on 2D LFF --- p.21Chapter 4.1 --- Definition of Error Bound --- p.21Chapter 4.2 --- Cause and Analysis on Unsatisfactory Results by LFF --- p.33Chapter 4.3 --- Formal Proof on Error Bound --- p.39Chapter 5. --- LFF for Container Loading Problem --- p.33Chapter 5.1 --- Problem Formulation and Term Definitions --- p.48Chapter 5.2 --- Possible Problems to be solved --- p.53Chapter 5.3 --- Implementation in Container Loading --- p.54Chapter 5.3.1 --- The Basic Algorithm --- p.56Chapter 5.4 --- A Sample Packing Scenario --- p.62Chapter 5.4.1 --- Generation of COPM list --- p.63Chapter 5.4.2 --- Pseudo-packing and the greedy approach --- p.66Chapter 5.4.3 --- Update of corner list --- p.69Chapter 5.4.4 --- Real-Packing --- p.70Chapter 5.5 --- Ratio Approach: A Modification to LFF --- p.70Chapter 5.6 --- LFF with Tightness Measure: CPU time Cut-down --- p.75Chapter 5.7 --- Experimental Results --- p.77Chapter 5.7.1 --- Comparison between LFF and LFFR --- p.77Chapter 5.7.2 --- "Comparison between LFFR, LFFT and other algorithms" --- p.78Chapter 5.7.3 --- Computational Time for different algorithms --- p.81Chapter 5.7.4 --- Conclusion of the experimental results --- p.83Chapter 6. --- Conclusion --- p.85Bibiography --- p.8

Survey on Combinatorial Register Allocation and Instruction Scheduling

Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a compiler. In the last three decades, combinatorial optimization has emerged as an alternative to traditional, heuristic algorithms for these two tasks. Combinatorial optimization approaches can deliver optimal solutions according to a model, can precisely capture trade-offs between conflicting decisions, and are more flexible at the expense of increased compilation time. This paper provides an exhaustive literature review and a classification of combinatorial optimization approaches to register allocation and instruction scheduling, with a focus on the techniques that are most applied in this context: integer programming, constraint programming, partitioned Boolean quadratic programming, and enumeration. Researchers in compilers and combinatorial optimization can benefit from identifying developments, trends, and challenges in the area; compiler practitioners may discern opportunities and grasp the potential benefit of applying combinatorial optimization

The sensor based manipulation of irregularly shaped objects with special application to the semiconductor industry

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (leaves 91-94).by Vivek Anand Sujan.S.M

Two-Dimensional Bin Packing Problem with Guillotine Restrictions

This thesis, after presenting recent advances obtained for the two-dimensional bin packing problem, focuses on the case where guillotine restrictions are imposed. A mathematical characterization of non-guillotine patterns is provided and the relation between the solution value of the two-dimensional problem with guillotine restrictions and the two-dimensional problem unrestricted is being studied from a worst-case perspective. Finally it presents a new heuristic algorithm, for the two-dimensional problem with guillotine restrictions, based on partial enumeration, and computationally evaluates its performance on a large set of instances from the literature. Computational experiments show that the algorithm is able to produce proven optimal solutions for a large number of problems, and gives a tight approximation of the optimum in the remaining cases

A tale of two packing problems : improved algorithms and tighter bounds for online bin packing and the geometric knapsack problem

In this thesis, we deal with two packing problems: the online bin packing and the geometric knapsack problem. In online bin packing, the aim is to pack a given number of items of different size into a minimal number of containers. The items need to be packed one by one without knowing future items. For online bin packing in one dimension, we present a new family of algorithms that constitutes the first improvement over the previously best algorithm in almost 15 years. While the algorithmic ideas are intuitive, an elaborate analysis is required to prove its competitive ratio. We also give a lower bound for the competitive ratio of this family of algorithms. For online bin packing in higher dimensions, we discuss lower bounds for the competitive ratio and show that the ideas from the one-dimensional case cannot be easily transferred to obtain better two-dimensional algorithms. In the geometric knapsack problem, one aims to pack a maximum weight subset of given rectangles into one square container. For this problem, we consider online approximation algorithms. For geometric knapsack with square items, we improve the running time of the best known PTAS and obtain an EPTAS. This shows that large running times caused by some standard techniques for geometric packing problems are not always necessary and can be improved. Finally, we show how to use resource augmentation to compute optimal solutions in EPTAS-time, thereby improving upon the known PTAS for this case.In dieser Arbeit betrachten wir zwei Packungsprobleme: Online Bin Packing und das geometrische Rucksackproblem. Bei Online Bin Packing versucht man, eine gegebene Menge an Objekten verschiedener Größe in die kleinstmögliche Anzahl an Behältern zu packen. Die Objekte müssen eins nach dem anderen gepackt werden, ohne zukünftige Objekte zu kennen. Für eindimensionales Online Bin Packing beschreiben wir einen neuen Algorithmus, der die erste Verbesserung gegenüber dem bisher besten Algorithmus seit fast 15 Jahren darstellt. Während die algorithmischen Ideen intuitiv sind, ist eine ausgefeilte Analyse notwendig um das Kompetitivitätsverhältnis zu beweisen. Für Online Bin Packing in mehreren Dimensionen geben wir untere Schranken für das Kompetitivitätsverhältnis an und zeigen, dass die Ideen aus dem eindimensionalen Fall nicht direkt zu einer Verbesserung führen. Beim geometrischen Rucksackproblem ist es das Ziel, eine größtmögliche Teilmenge gegebener Rechtecke in einen einzelnen quadratischen Behälter zu packen. Für dieses Problem betrachten wir Approximationsalgorithmen. Für das Problem mit quadratischen Objekten verbessern wir die Laufzeit des bekannten PTAS zu einem EPTAS. Die langen Laufzeiten vieler Standardtechniken für geometrische Probleme können also vermieden werden. Schließlich zeigen wir, wie Ressourcenvergrößerung genutzt werden kann, um eine optimale Lösung in EPTAS-Zeit zu berechnen, was das bisherige PTAS verbessert.Google PhD Fellowshi