3D packing of balls in different containers by VNS

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel UniversityIn real world applications such as the transporting of goods products, packing is a major issue. Goods products need to be packed such that the smallest space is wasted to achieve the maximum transportation efficiency. Packing becomes more challenging and complex when the product is circular/spherical. This thesis focuses on the best way to pack three-dimensional unit spheres into the smallest spherical and cubical space. Unit spheres are considered in lieu of non-identical spheres because the search mechanisms are more difficult in the latter set up and any improvements will be due to the search mechanism not to the ordering of the spheres. The two-unit sphere packing problems are solved by approximately using a variable neighborhood search (VNS) hybrid heuristic. A general search framework belonging to the Artificial Intelligence domain, the VNS offers a diversification of the search space by changing neighborhood structures and intensification by thoroughly investigating each neighborhood. It is exible, easy to implement, adaptable to both continuous and discrete optimization problems and has been use to solve a variety of problems including large-sized real-life problems. Its runtime is usually lower than other meta heuristic techniques. A tutorial on the VNS and its variants along with recent applications and areas of applicability of each variant. Subsequently, this thesis considers several variations of VNS heuristics for the two problems at hand, discusses their individual efficiencies and effectiveness, their convergence rates and studies their robustness. It highlights the importance of the hybridization which yields near global optima with high precision and accuracy, improving many best- known solutions indicate matching some, and improving the precision and accuracy of others. Keywords: variable neighborhood search, sphere packing, three-dimensional packing, meta heuristic, hybrid heuristics, multiple start heuristics

Voxel-Based Solution Approaches to the Three-Dimensional Irregular Packing Problem

Research on the three-dimensional (3D) packing problem has largely focused on packing boxes for the transportation of goods. As a result, there has been little focus on packing irregular shapes in the operational research literature. New technologies have raised the practical importance of 3D irregular packing problems and the need for efficient solutions. In this work, we address the variant of the problem where the aim is to place a set of 3D irregular items in a container, while minimizing the container height, analogous to the strip packing problem. In order to solve this problem, we need to address two critical components; efficient computation of the geometry and finding high-quality solutions. In this work, we explore the potential of voxels, the 3D equivalent of pixels, as the geometric representation of the irregular items. In this discretised space, we develop a geometric tool that extends the concept of the nofit polygon to the 3D case. This enables us to provide an integer linear programming formulation for this problem that can solve some small instances. For practical size problems, we design metaheuristic optimisation approaches. Because the literature is limited, we introduce new benchmark instances. Some are randomly generated and some represent realistic models from the additive manufacturing area. Our results on the literature benchmark data and on our new instances show that our metaheuristic techniques achieve the best known solutions for a wide variety of problems in practical computation times

Clusters of polyhedra in spherical confinement

What is the best way to pack objects into a container? This simple question, one that is relevant to everyday life, biology, and nanoscience, is easy to state but surprisingly difficult to answer. Here, we use computational methods to determine dense packings of a set of polyhedra inside a sphere, for up to 60 constituent packers. Our dense packings display a wide variety of symmetries and structures, and indicate that the presence of the spherical container suppresses packing effects due to polyhedral shape. Our results have implications for a range of biological phenomena and experimental applications, including blood clotting, cell aggregation, drug delivery, colloidal engineering, and the creation of metamaterials

Coding on Flag Manifolds for Limited Feedback MIMO Systems

The efficiency of the physical layer in modern communication systems using multi-input multi-output (MIMO) techniques is largely based on the availability of channel state information (CSI) at the transmitter. In many practical systems, CSI needs to be quantized at the receiver side before transmission through a limited rate feedback channel. This is typically done using a codebook-based precoding transmission, where the receiver transmits the index of a codeword from a pre-designed codebook shared with the transmitter. To construct such codes one has to discretize complex flag manifolds. For single-user MIMO with a maximum likelihood receiver, the spaces of interest are Grassmann manifolds. With a linear receiver and network MIMO, the codebook design is related to discretization of Stiefel manifolds and more general flag manifolds. In this thesis, coding in flag manifolds is studied. In a first part, flag manifolds are defined as metric spaces corresponding to subsurfaces of hyperspheres. The choice of distance defines the geometry of the space and impacts clustering and averaging (centroid computation) in vector quantization, as well as coding theoretical packing bounds and optimum constructions. For two transmitter antenna systems, the problem reduces to designing spherical codes. A simple isomorphism enables to analytically derive closed-form codebooks with inherent low-implementation complexity. For more antennas, the concept of orbits of symmetry groups is investigated. Optimum codebooks, having desirable implementation properties as described in industry standardization, can be obtained using orbits of specific groups. For large antenna systems and base station cooperation, a product codebook strategy is also considered. Such a design requires to jointly discretize the Grassmann and Stiefel manifolds. A vector quantization algorithm for joint Grassmann-Stiefel quantization is proposed. Finally, the pertinence of flag codebook design is illustrated for a MIMO system with linear receiver

Microscale modeling of fluid flow in porous medium systems

Proper mathematical description of macroscopic porous medium flows is essential for the study of a wide range of subsurface contamination scenarios. Existing mathematical formulations, however, demonstrate inadequacies that preclude the accurate description of many systems. Multi-scale models developed using thermodynamically constrained averaging theory (TCAT) rigorously define macroscopic variables in terms of more well-understood microscopic counterparts, permitting detailed analysis of macroscopic model forms based on microscale simulation and experiment. Within this framework, the primary objectives of microscale modeling are to elucidate important physical mechanisms and to inform both the form of macroscale closure relations as well as associated parameter values. In order to meet these goals, numerical tools must include: (1) simulations that provide accurate microscopic solutions for physical phenomena in large, complex domains; (2) morphological analysis tools that can be used to upscale simulation results to larger scales as dictated by the associated theoretical framework. Development of a numerical toolbox for microscale porous medium studies is considered in line with these objectives, including both implementation and optimization strategies. High-performance implementations of the lattice Boltzmann method are developed to simulate one- and two-phase flows using several computing platforms. A modified marching cubes algorithm is developed to explicitly construct all entities in a two-phase system, including all interfaces between the fluid and solid phases in addition to the three phase contact curve. These entities serve as a numerical skeleton for upscaling multiphase porous medium simulation results to the macroscale. Based on these tools, development of macroscopic constitutive laws is illustrated for a special case of anisotropic flow in porous media. In this example, microscale simulation is used to demonstrate a limitation of existing macroscopic forms for cases in which the momentum resistance depends on the flow direction in addition to the orientation. A modified macroscopic form is proposed in order to properly account for this phenomenon

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

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

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

Primary Structure and Solution Conditions Determine Conformational Ensemble Properties of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are a class of proteins that do not exhibit well-defined three-dimensional structures. The absence of structure is intrinsic to their amino acid sequences, which are characterized by low hydrophobicity and high net charge per residue compared to folded proteins. Contradicting the classic structure-function paradigm, IDPs are capable of interacting with high specificity and affinity, often acquiring order in complex with protein and nucleic acid binding partners. This phenomenon is evident during cellular activities involving IDPs, which include transcriptional and translational regulation, cell cycle control, signal transduction, molecular assembly, and molecular recognition. Although approximately 30% of eukaryotic proteomes are intrinsically disordered, the nature of IDP conformational ensembles remains unclear. In this dissertation, we describe relationships connecting characteristics of IDP conformational ensembles to their primary structures and solution conditions. Using molecular simulations and fluorescence experiments on a set of base-rich IDPs, we find that net charge per residue segregates conformational ensembles along a globule-to-coil transition. Speculatively generalizing this result, we propose a phase diagram that predicts an IDP\u27s average size and shape based on sequence composition and use it to generate hypotheses for a broad set of intrinsically disordered regions (IDRs). Simulations reveal that acid-rich IDRs, unlike their oppositely charged base-rich counterparts, exhibit disordered globular ensembles despite intra-chain repulsive electrostatic interactions. This apparent asymmetry is sensitive to simulation parameters for representing alkali and halide salt ions, suggesting that solution conditions modulate IDP conformational ensembles. We refine the ion parameters using a calibration procedure that relies exclusively on crystal lattice properties. Simulations with these parameters recover swollen coil behavior for acid-rich IDRs, but also uncover a dependence on sequence patterning for polyampholytic IDPs. These contributions initiate an endeavor to elucidate general principles that enable prediction of an IDP\u27s conformational ensemble based on primary structure and solution conditions, a goal analogous to structure prediction for folded proteins. Such principles would provide a molecular basis for understanding the roles of IDPs in physiology and pathophysiology, guide development of agents that modulate their behavior, and enable their rational design from chosen specifications

Sedimentological effects of aeolian processes active in the Tentsmuir area, Fife, Scotland

Present day coastal accretion at Tentsmuir is manifest in the form of hummocky dune accumulations along the shoreline. The mode and variability of the distribution of surface sediments by the wind and the magnitude of accumulation of wind laid deposits in the Tentsmuir beach-dune complex is a measure of Aeolian activity in the area. In the Tentsmuir area fine to medium grained well sorted beach sands are entrained by high to moderate energy, seasonal, directionally unimodal to bimodal winds of low variability. During the winter season the dominant winds are from the south west (blowing towards the sea) whereas, generally during the spring the more effective winds are derived from the east (blowing towards land). The bimodal winds are composed of contrasting unimodally directional winds blowing for shorter durations. Daily sea breezes are observed during the summer. Field measurements of sand transport rates, with the aid of sand traps during anemometer determined wind speeds ranging from 4 m s-1 to 20 m s-1, in the study area show that while the onshore transport vector results in rapid foredune development, the longshore and offshore component contributes to a positive beach sediment budget. However, the net beach sediment budget is a complex interplay of Aeolian, wave and tidal processes. Shear velocities on the Tentsmuir beaches ranged from 18.5 cm s-1 to 52 cm s-1 and the focal point, u' and z' values were 1.75 m s-1 and 0.03 cm respectively. In general, the variability of the short-term Aeolian sand transport rates in the Tentsmuir beach-dune subenvironments is controlled by (i) variation in wind velocity, (ii) presence or absence of vegetation, (iii) ground surface moisture, and (iv) the sand size and source limitation. The potential sand input by the onshore winds during the last eleven years is estimated to have been approximately 28,532 m3. During the same period the potential amount of sand blown towards the sea was 109,570 m3. The amount of predicted onshore sediment input (28,532 m3) compares well with the 33,000 m3 of sand estimated to have accumulated in the lee of the beach at Tentsmuir Point The close agreement of the measured and predicted values of Aeolian transport suggests that the White (1979) expression, used in the present study to predict transport rates on the beach, provides fairly reliable estimates. Very high velocity offshore winds (>9 ms-1 produce a shelly deflation surface along the backshore, surface parallel sand sheets and sand strips on the foreshore; adhesion plane bed and adhesion structures along the moist/wet tidal margin and pyramidal dunes (offshore transport across a dune ridge >2.5m high.). Onshore high velocity winds result in the formation of surface parallel sand strips on the foreshore and a high volume of Aeolian sediment accumulation in the backshore and foredune area. Prolonged days of high velocity unidirectional winds result in the formation of barchans. Medium to high wind velocities (~6-9 ms-1) produce ballistically rippled foreshore sand lobes, lee dunes downwind of tidal debris, adhesion structures (offshore/longshore transport) and some sand accumulation in the foredune area (onshore transport). Abundant parallel laminated sand, pinchout laminae, sand lenses, precipitation deposits, trough crossbeds, plant remains at places overlying beach shell layers constitute a prograding coastal dune facies at Tentsmuir