Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals

We have discovered a new family of three-dimensional crystal sphere packings that are strictly jammed (i.e., mechanically stable) and yet possess an anomalously low density. This family constitutes an uncountably infinite number of crystal packings that are subpackings of the densest crystal packings and are characterized by a high concentration of self-avoiding "tunnels" (chains of vacancies) that permeate the structures. The fundamental geometric characteristics of these tunneled crystals command interest in their own right and are described here in some detail. These include the lattice vectors (that specify the packing configurations), coordination structure, Voronoi cells, and density fluctuations. The tunneled crystals are not only candidate structures for achieving the jamming threshold (lowest-density rigid packing), but may have substantially broader significance for condensed matter physics and materials science.Comment: 19 pages, 5 figure

Novel approaches to container loading: from heuristics to hybrid tabu search

A thesis submitted for the degree of Doctor of Philosophy of the University ofBedford shireThis work investigates new approaches to the container loading problem which address the issue of how to load three-dimensional, rectangular items (e.g. boxes) into the container in such a way that maximum utilisation is made of the container space. This problem occurs in several industry sectors where the loading approach places cargo effectively into aeroplanes, ships, trailers or trucks in order to save considerable cost. In carrying out this work, the investigation starts by developing a new heuristic approach to the two-dimensional bin packing problem, which has lower complexity than container loading in the aspects of constraints and geometry. A novel approach, including the heuristic strategies and handling method for remaining areas, is developed that can produce good results when testing with benchmark and real world data. Based on the research for two-dimensional bin packing, a novel heuristic approach is developed to deal with the container loading problem with some practical constraints. The heuristic approach to container loading also includes heuristic strategies and the handling of remaining spaces. The heuristic strategies construct effective loading arrangements where combinations of identical or different box types are loaded in blocks. The handling method for remaining spaces further improves the loading arrangements through the representation, partitioning and merging of remaining spaces. The heuristic approach obtains better volume utilisation and the highest stability compared with other published heuristic approaches. However, it does not achieve as high a volume utilisation as metaheuristic approaches, e.g. genetic algorithms and tabu search.To improve volume utilisation, a new hybrid heuristic approach to the container loading problem is further developed based on the tabu search technique which covers the encoding, evaluation criterion and configuration of neighbourhood and candidate solutions. The heuristic strategies as well as the handling method for remaining spaces developed in the heuristic approach are used in this new hybrid tabu search approach. It is shown that the hybrid approach has better volume utilisation than the published approaches under the condition that all loaded boxes with one hundred per cent support from below. In addition, the experimental results show that both the heuristic and hybrid tabu search approaches can also be applied to the multiple container loading problem

Container Loading Problems: A State-of-the-Art Review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.In this paper, a review of the state-of-the-art in the field of container loading will be given. We will identify factors which - from a practical point of view - need to be considered when dealing with container loading problems and we will analyze whether and how these factors are represented in methods for the solution of such problems. Modeling approaches, as well as exact and heuristic algorithms will be reviewed. This will allow for assessing the practical relevance of the research which has been carried out in the field. We will also mention several issues which have not been dealt with satisfactorily so far and give an outlook on future research opportunities

Two-dimensional placement compaction using an evolutionary approach: a study

The placement problem of two-dimensional objects over planar surfaces optimizing given utility functions is a combinatorial optimization problem. Our main drive is that of surveying genetic algorithms and hybrid metaheuristics in terms of final positioning area compaction of the solution. Furthermore, a new hybrid evolutionary approach, combining a genetic algorithm merged with a non-linear compaction method is introduced and compared with referenced literature heuristics using both randomly generated instances and benchmark problems. A wide variety of experiments is made, and the respective results and discussions are presented. Finally, conclusions are drawn, and future research is defined

Moldable Items Packing Optimization

This research has led to the development of two mathematical models to optimize the problem of packing a hybrid mix of rigid and moldable items within a three-dimensional volume. These two developed packing models characterize moldable items from two perspectives: (1) when limited discrete configurations represent the moldable items and (2) when all continuous configurations are available to the model. This optimization scheme is a component of a lean effort that attempts to reduce the lead-time associated with the implementation of dynamic product modifications that imply packing changes. To test the developed models, they are applied to the dynamic packing changes of Meals, Ready-to-Eat (MREs) at two different levels: packing MRE food items in the menu bags and packing menu bags in the boxes. These models optimize the packing volume utilization and provide information for MRE assemblers, enabling them to preplan for packing changes in a short lead-time. The optimization results are validated by running the solutions multiple times to access the consistency of solutions. Autodesk Inventor helps visualize the solutions to communicate the optimized packing solutions with the MRE assemblers for training purposes