An Evolutionary Algorithm for solving the Two-Dimensional Irregular Shape Packing Problem combined with the Knapsack Problem

This work presents an evolutionary algorithm to solve a joint problem of the Packing Problem and the Knapsack Problem, where the objective is to place items (with shape, value and weight) in a container (defined by its shape and capacity), maximizing the container's value, without intersections

Optimized Packing Titanium Alloy Powder Particles

To obtain high-quality and durable parts by 3D printing, specific characteristics (porosity and proportion of various sizes of particles) in the mixture used for printing or sintering must be assured. To predict these characteristics, a mathematical model of optimized packing polyhedral objects (particles of titanium alloys) in a cuboidal container is presented, and a solution algorithm is developed. Numerical experiments demonstrate that the results obtained by the algorithm are very close to experimental findings. This justifies using numerical simulation instead of expensive experimentation

Demand-based optimization for adaptive multi-beam satellite communication systems

Satellite operators use multiple spot beams of high throughput satellite systems to provide internet services to broadband users. However, in recent years, new mobile broadband users with diverse demand requisites are growing, and satellite operators are obliged to provide services agreed in the Service Level Agreements(SLA) to remote rural locations, mid-air aeroplanes and mid-ocean ships. Furthermore, the expected demand is spatio-temporal which varies along the geographical location of the mobile users with time and hence, creating more dynamic, non uniformly distributed, and time sensitive demand profiles. However, the current satellite systems are only designed to perform similarly irrespective of the changes in demand profiles. Hence, a practical approach to meet such heterogeneous demand is to design adaptive systems by exploiting the advancements in recently developed technologies such as precoding, active antenna array, digital beamforming networks, digital transparent payload and onboard signal processing. Accordingly, in this work, we investigate and develop advanced demand-based resource optimization modules that fit future payload capabilities and satisfy the satellite operators’ interests. Furthermore, instead of boosting the satellite throughput (capacity maximization), the goal is to optimize the available resources such that the satellite offered capacity on the ground continuously matches the geographic distribution of the traffic demand and follows its variations in time. However, we can introduce adaptability at multiple levels of the transmission chain of the satellite system, either with long term flexibility (optimization over frequency, time, power, beam pattern and footprint) or short term flexibility (optimization over user scheduling). These techniques can be optimized as either standalone or in parallel or even jointly for maximum demand satisfaction. However, in the scope of this thesis, we have designed real time optimizations only for some of the radio resource schemes. Firstly, we explore beam densification, where by increasing the number of beams, we improve the antenna gain values at the high demand hot-spot regions. However, such increase in the number of beams also increase the interbeam interference and badly affects SINR performance. Hence, in the first part of Chapter 2 of this thesis, we focus on finding an optimal number of beams for given high demand hot-spot region of a demand distribution profile. Also, steering the beams towards high demand regions, further increase the demand satisfaction. However, the positioning of the beams need to be carefully planned. On one hand, closely placed beams result in poor SINR performance. On the other hand, beams that are placed far away will have poor antenna gain values for the users away from the beam centers. Hence, in the second part of Chapter 2, we focus on finding optimized beam positions for maximum demand satisfaction in high demand hot-spot regions. Also, we propose a dynamic frequency-color coding strategy for efficient spectrum and interference management in demand-driven adaptive systems. Another solution is the proposed so-called Adaptive Multi-beam Pattern and Footprint (AMPF) design, where we fix the number of beams and based on the demand profile, we configure adaptive beam shapes and sizes along with their positions. Such an approach shall distribute the total demand across all the beams more evenly avoiding overloaded or underused beams. Such optimization was attempted in Chapter 3 using cluster analysis. Furthermore, demand satisfaction at both beam and user level was achieved by carefully performing demand driven user scheduling. On one hand, scheduling most orthogonal users at the same time may yield better capacity but may not provide demand satisfaction. This is majorly because users with high demand need to be scheduled more often in comparison to users with low demand irrespective of channel orthogonality. On the other hand, scheduling users with high demand which are least orthogonal, create strong interbeam interference and affect precoding performance. Accordingly, two demand driven scheduling algorithms (Weighted Semi-orthogonal scheduling (WSOS) and Interference-aware demand-based user scheduling) are discussed in Chapter 4. Lastly, in Chapter 5, we verified the impact of parallel implementation of two different demand based optimization techniques such as AMPF design and WSOS user scheduling. Evidently, numerical results presented throughout this thesis validate the effectiveness of the proposed demand based optimization techniques in terms of demand matching performance compared to the conventional non-demand based approaches

Thermodynamic and Structural Phase Behavior of Colloidal and Nanoparticle Systems.

We design and implement a scalable hard particle Monte Carlo simulation toolkit (HPMC), and release it open source. Common thermodynamic ensembles can be run in two dimensional or three dimensional triclinic boxes. We developed an efficient scheme for hard particle pressure measurement based on volume perturbation. We demonstrate the effectiveness of low order virial coefficients in describing the compressibility factor of fluids of hard polyhedra. The second virial coefficient is obtained analytically from particle asphericity and can be used to define an effective sphere with similar low-density behavior. Higher-order virial coefficients --- efficiently calculated with Mayer Sampling Monte Carlo --- are used to define an exponential approximant that exhibits the best known semi-analytic characterization of hard polyhedron fluid state functions. We present a general method for the exact calculation of convex polyhedron diffraction form factors that is more easily applied to common shape data structures than the techniques typically presented in literature. A proof of concept user interface illustrates how a researcher might investigate the role of particle form factor in the diffraction patterns of different particles in known structures. We present a square-triangle dodecagonal quasicrystal (DQC) in a binary mixture of nanocrystals (NCs). We demonstrate how the decoration of the square and triangle tiles naturally gives rise to partial matching rules via symmetry breaking in layers perpendicular to the dodecagonal axis. We analyze the geometry of the experimental tiling and, following the ``cut and project'' theory, lift the square and triangle tiling pattern to four dimensional space to perform phason analysis historically applied only in simulation and atomic systems. Hard particle models are unsuccessful at explaining the stability of the binary nanoparticle super lattice. However, with a simple isotropic soft particle model, we are able to demonstrate seeded growth of the experimental structure in simulation. These simulations indicate that the most important stabilizing properties of the short range structure are the size ratio of the particles and an A--B particle attraction.PhDMaterials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/120906/1/eirrgang_1.pd

A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey

The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-Integer Programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, the current family of exact MIP models for nesting cannot efficiently solve both large problem instances and instances containing polygons with complex geometries. In order to improve the efficiency of the current MIP models, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Finally, we provide a detailed reproducibility protocol and dataset based on our Java software library as supplementary material to allow the exact replication of our models, experiments, and results

Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams

In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities. The data sets are represented by closed curves and the data set relationships are depicted by the overlaps between these curves. Both the sets and their intersections are easily visible as the closed curves are preattentively processed and form common regions that have a strong perceptual grouping effect. Besides set relations such as intersection, containment and disjointness, the cardinality of the sets and their intersections can also be depicted in the same diagram (referred to as area-proportional) through the size of the curves and their overlaps. Size is a preattentive feature and so similarities, differences and trends are easily identified. Thus, such diagrams facilitate data analysis and reasoning about the sets. However, drawing these diagrams manually is difficult, often impossible, and current automatic drawing methods do not always produce appropriate diagrams. This dissertation presents novel automatic drawing methods for different types of Euler diagrams and a user study of how such diagrams can help probabilistic judgement. The main drawing algorithms are: eulerForce, which uses a force-directed approach to lay out Euler diagrams; eulerAPE, which draws area-proportional Venn diagrams with ellipses. The user study evaluated the effectiveness of area- proportional Euler diagrams, glyph representations, Euler diagrams with glyphs and text+visualization formats for Bayesian reasoning, and a method eulerGlyphs was devised to automatically and accurately draw the assessed visualizations for any Bayesian problem. Additionally, analytic algorithms that instantaneously compute the overlapping areas of three general intersecting ellipses are provided, together with an evaluation of the effectiveness of ellipses in drawing accurate area-proportional Venn diagrams for 3-set data and the characteristics of the data that can be depicted accurately with ellipses

Surface modeling and rendering with line segments

Master'sMASTER OF SCIENC