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Branching via Cutting Plane Selection: Improving Hybrid Branching
No full textCutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017
Segmentation of tooth enamel microstructure images using classical image processing and U-Net approaches
No full textTooth enamel is the hardest tissue in human organism, formed by prism layers in regularly alternating directions. These prisms form the Hunter-Schreger Bands (HSB) pattern when under side illumination, which is composed of light and dark stripes resembling fingerprints. We have shown in previous works that HSB pattern is highly variable, seems to be unique for each tooth and can be used as a biometric method for human identification. Since this pattern cannot be acquired with sensors, the HSB region in the digital photograph must be identified and correctly segmented from the rest of the tooth and background. Although these areas can be manually removed, this process is not reliable as excluded areas can vary according to the individual‘s subjective impression. Therefore, the aim of this work was to develop an algorithm that automatically selects the region of interest (ROI), thus, making the entire biometric process straightforward. We used two different approaches: a classical image processing method which we called anisotropy-based segmentation (ABS) and a machine learning method known as U-Net, a fully convolutional neural network. Both approaches were applied to a set of extracted tooth images. U-Net with some post processing outperformed ABS in the segmentation task with an Intersection Over Union (IOU) of 0.837 against 0.766. Even with a small dataset, U-Net proved to be a potential candidate for fully automated in-mouth application. However, the ABS technique has several parameters which allow a more flexible segmentation with interactive adjustments specific to image properties
Linear Programming in MILP Solving - A Computational Perspective
No full textMixed-integer linear programming (MILP) plays a crucial role in the field of mathematical optimization and is especially relevant for practical applications due to the broad range of problems that can be modeled in that fashion. The vast majority of MILP solvers employ the LP-based branch-and-cut approach. As the name suggests, the linear programming (LP) subproblems that need to be solved therein influence their behavior and performance significantly.
This thesis explores the impact of various LP solvers as well as LP solving techniques on the constraint integer programming framework SCIP Optimization Suite. SCIP allows for comparisons between academic and open-source LP solvers like Clp and SoPlex, as well as commercially developed, high-end codes like CPLEX, Gurobi, and Xpress.
We investigate how the overall performance and stability of an MILP solver can be improved by new algorithmic enhancements like LP solution polishing and persistent scaling that we have implemented in the LP solver SoPlex. The former decreases the fractionality of LP solutions by selecting another vertex on the optimal hyperplane of the LP relaxation, exploiting degeneracy. The latter provides better numerical properties for the LP solver throughout the MILP solving process by preserving and extending the initial scaling factors, effectively also improving the overall performance of SCIP. Both enhancement techniques are activated by default in the SCIP Optimization Suite.
Additionally, we provide an analysis of numerical conditions in SCIP through the lens of the LP solver by comparing different measures and how these evolve during the different stages of the solving process. A side effect of our work on this topic was the development of TreeD: a new and convenient way of presenting the search tree interactively and animated in the three-dimensional space. This visualization technique facilitates a better understanding of the MILP solving process of SCIP.
Furthermore, this thesis presents the various algorithmic techniques like the row representation and iterative refinement that are implemented in SoPlex and that distinguish the solver from other simplex-based codes. Although it is often not as performant as its competitors, SoPlex demonstrates the ongoing research efforts in the field of linear programming with the simplex method.
Aside from that, we demonstrate the rapid prototyping of algorithmic ideas and modeling approaches via PySCIPOpt, the Python interface to the SCIP Optimization Suite. This tool allows for convenient access to SCIP's internal data structures from the user-friendly Python programming language to implement custom algorithms and extensions without any prior knowledge of SCIP's programming language C. TreeD is one such example, demonstrating the use of several Python libraries on top of SCIP. PySCIPOpt also provides an intuitive modeling layer to formulate problems directly in the code without having to utilize another modeling language or framework.
All contributions presented in this thesis are readily accessible in source code in SCIP Optimization Suite or as separate projects on the public code-sharing platform GitHub
Rapid Prototyping for Coordinated Views of Multi-scale Spatial and Abstract Data: A Grammar-based Approach
No full textVisualization grammars are gaining popularity as they allow visualization specialists and experienced users to quickly create static and interactive views. Existing grammars, however, mostly focus on abstract views, ignoring three-dimensional (3D) views, which are very important in fields such as natural sciences. We propose a generalized interaction grammar for the problem of coordinating heterogeneous view types, such as standard charts (e.g., based on Vega-Lite) and 3D anatomical views. An important aspect of our web-based framework is that user interactions with data items at various levels of detail can be systematically integrated and used to control the overall layout of the application workspace. With the help of a concise JSON-based specification of the intended workflow, we can handle complex interactive visual analysis scenarios. This enables rapid prototyping and iterative refinement of the visual analysis tool in collaboration with domain experts. We illustrate the usefulness of our framework in two real-world case studies from the field of neuroscience. Since the logic of the presented grammar-based approach for handling interactions between heterogeneous web-based views is free of any application specifics, it can also serve as a template for applications beyond biological research
Transcoding unicode characters with AVX-512 instructions
No full textIntel includes in its recent processors a powerful set of instructions capable of processing 512-bit registers with a single instruction (AVX-512). Some of these instructions have no equivalent in earlier instruction sets. We leverage these instructions to efficiently transcode strings between the most common formats: UTF-8 and UTF-16. With our novel algorithms, we are often twice as fast as the previous best solutions. For example, we transcode Chinese text from UTF-8 to UTF-16 at more than 5 GiB s−1 using fewer than 2 CPU instructions per character. To ensure reproducibility, we make our software freely available as an open-source library. Our library is part of the popular Node.js JavaScript runtime
Computational Approaches for Peroxisomal Protein Localization
No full textComputational approaches are practical when investigating putative peroxisomal proteins and for sub-peroxisomal protein localization in unknown protein sequences. Nowadays, advancements in computational methods and Machine Learning (ML) can be used to hasten the discovery of novel peroxisomal proteins and can be combined with more established computational methodologies. Here, we explain and list some of the most used tools and methodologies for novel peroxisomal protein detection and localization
Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics
No full textHigh-dimensional metastable molecular dynamics (MD) can often be characterised by a few features of the system, that is, collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples
Incremental Heuristics for Periodic Timetabling
No full textWe present incremental heuristics for the Periodic Event Scheduling Problem (PESP), the standard mathematical tool to optimize periodic timetables in public transport. The core of our method is to solve successively larger subinstances making use of previously found solutions. Introducing the technical notion of free stratifications, we formulate a general scheme for incremental heuristics for PESP. More practically, we use line and station information to create heuristics that add lines or stations one by one, and we evaluate these heuristics on instances of the benchmarking library PESPlib. This approach is indeed viable, and leads to new incumbent solutions for six PESPlib instances