A New Quasi-Human Algorithm for Solving the Packing Problem of Unit Equilateral Triangles

The packing problem of unit equilateral triangles not only has the theoretical significance but also offers broad prospects in material processing and network resource optimization. Because this problem is nondeterministic polynomial (NP) hard and has the feature of continuity, it is necessary to limit the placements of unit equilateral triangles before optimizing and obtaining approximate solution (e.g., the unit equilateral triangles are not allowed to be rotated). This paper adopts a new quasi-human strategy to study the packing problem of unit equilateral triangles. Some new concepts are put forward such as side-clinging action, and an approximation algorithm for solving the addressed problem is designed. Time complexity analysis and the calculation results indicate that the proposed method is a polynomial time algorithm, which provides the possibility to solve the packing problem of arbitrary triangles

A New Quasi-Human Algorithm for Solving the Packing Problem of Unit Equilateral Triangles

The packing problem of unit equilateral triangles not only has the theoretical significance but also offers broad prospects in material processing and network resource optimization. Because this problem is nondeterministic polynomial (NP) hard and has the feature of continuity, it is necessary to limit the placements of unit equilateral triangles before optimizing and obtaining approximate solution (e.g., the unit equilateral triangles are not allowed to be rotated). This paper adopts a new quasi-human strategy to study the packing problem of unit equilateral triangles. Some new concepts are put forward such as side-clinging action, and an approximation algorithm for solving the addressed problem is designed. Time complexity analysis and the calculation results indicate that the proposed method is a polynomial time algorithm, which provides the possibility to solve the packing problem of arbitrary triangles

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Modeling, image processing and attitude estimation of high speed star sensors

Attitude estimation and angular velocity estimation are the most critical components of a spacecraft's guidance, navigation and control. Usually, an array of tightlycoupled sensors (star trackers, gyroscopes, sun sensors, magnetometers) is used to estimate these quantities. The cost (financial, mass, power, time, human resources) for the integration of these separate sub-systems is a major deterrent towards realizing the goal of smaller, cheaper and faster to launch spacecrafts/satellites. In this work, we present a novel stellar imaging system that is capable of estimating attitude and angular velocities at true update rates of greater than 100Hz, thereby eliminating the need for a separate star tracker and gyroscope sub-systems. High image acquisition rates necessitate short integration times and large optical apertures, thereby adding mass and volume to the sensor. The proposed high speed sensor overcomes these difficulties by employing light amplification technologies coupled with fiber optics. To better understand the performance of the sensor, an electro-optical model of the sensor system is developed which is then used to design a high-fidelity night sky image simulator. Novel star position estimation algorithms based on a two-dimensional Gaussian fitting to the star pixel intensity profiles are then presented. These algorithms are non-iterative, perform local background estimation in the vicinity of the star and lead to significant improvements in the star centroid determination. Further, a new attitude determination algorithm is developed that uses the inter-star angles of the identified stars as constraints to recompute the body measured vectors and provide a higher accuracy estimate of the attitude as compared to existing methods. The spectral response of the sensor is then used to develop a star catalog generation method that results in a compact on-board star catalog. Finally, the use of a fiber optic faceplate is proposed as an additional means of stray light mitigation for the system. This dissertation serves to validate the conceptual design of the high update rate star sensor through analysis, hardware design, algorithm development and experimental testing

Improved Constrained Global Optimization for Estimating Molecular Structure From Atomic Distances

Determination of molecular structure is commonly posed as a nonlinear optimization problem. The objective functions rely on a vast amount of structural data. As a result, the objective functions are most often nonconvex, nonsmooth, and possess many local minima. Furthermore, introduction of additional structural data into the objective function creates barriers in finding the global minimum, causes additional computational issues associated with evaluating the function, and makes physical constraint enforcement intractable. To combat the computational problems associated with standard nonlinear optimization formulations, Williams et al. (2001) proposed an atom-based optimization, referred to as GNOMAD, which complements a simple interatomic distance potential with van der Waals (VDW) constraints to provide better quality protein structures. However, the improvement in more detailed structural features such as shape and chirality requires the integration of additional constraint types. This dissertation builds on the GNOMAD algorithm in using structural data to estimate the three-dimensional structure of a protein. We develop several methods to make GNOMAD capable of effectively and efficiently handling non-distance information including torsional angles and molecular surface data. In specific, we propose a method for using distances to effectively satisfy known torsional information and show that use of this method results in a significant improvement in the quality of α-helices and β-strands within the protein. We also show that molecular surface data in combination with our improved secondary structure estimation method and long-range distance data offer increased accuracy in spatial proximity of α-helices and β-strands within the protein, and thus provide better estimates of tertiary protein structure. Lastly, we show that the enhanced GNOMAD molecular structure estimation framework is effective in predicting protein structures in the context of comparative modeling

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes