Optimization. An attempt at describing the State of the Art

This paper is an attempt at describing the State of the Art of the vast field of continuous optimization. We will survey deterministic and stochastic methods as well as hybrid approaches in their application to single objective and multiobjective optimization. We study the parameters of optimization algorithms and possibilities for tuning them. Finally, we discuss several methods for using approximate models for computationally expensive problems

Runtime Analysis for the NSGA-II: Proving, Quantifying, and Explaining the Inefficiency For Many Objectives

The NSGA-II is one of the most prominent algorithms to solve multi-objective optimization problems. Despite numerous successful applications, several studies have shown that the NSGA-II is less effective for larger numbers of objectives. In this work, we use mathematical runtime analyses to rigorously demonstrate and quantify this phenomenon. We show that even on the simple $m$-objective generalization of the discrete OneMinMax benchmark, where every solution is Pareto optimal, the NSGA-II also with large population sizes cannot compute the full Pareto front (objective vectors of all Pareto optima) in sub-exponential time when the number of objectives is at least three. The reason for this unexpected behavior lies in the fact that in the computation of the crowding distance, the different objectives are regarded independently. This is not a problem for two objectives, where any sorting of a pair-wise incomparable set of solutions according to one objective is also such a sorting according to the other objective (in the inverse order)

Optimization of current carrying multicables

Intense electric currents in cable bundles contribute to hotspot generation and overheating of essential car elements, especially in connecting structures. An important aspect in this context is the influence of the positioning of wires in cable harnesses. In order to find an appropriate multicable layout with minimized maximum temperatures, we formulate an optimization problem. Depending on the packing density of the cable bundle, it is solved via different optimization strategies: in case of loosely packed cable bundles solely by a gradient based strategy (shape optimization), densely packed ones by arrangement heuristics combined with a standard genetic algorithm, others by mixed strategies. In the simulation model, the temperature dependence of electric resistances and different parameter values for the multitude of subdomains are respected. Convective and radiative effects are summarized by a heat transfer coefficient in a nonlinear boundary condition. Finite elements in combination with an interior-point method and a genetic algorithm allow the solution of the optimization problem for a large number of cable bundle types. Furthermore, we present an adjoint method for the solution of the shape optimization problem. The jumps at the interfaces of different materials are essential for the Hadamard representation of the shape gradient. Numerical experiments are carried out to demonstrate the feasibility and scope of the present approach

From RNA folding to inverse folding: a computational study: Folding and design of RNA molecules

Since the discovery of the structure of DNA in the early 1953s and its double-chained complement of information hinting at its means of replication, biologists have recognized the strong connection between molecular structure and function. In the past two decades, there has been a surge of research on an ever-growing class of RNA molecules that are non-coding but whose various folded structures allow a diverse array of vital functions. From the well-known splicing and modification of ribosomal RNA, non-coding RNAs (ncRNAs) are now known to be intimately involved in possibly every stage of DNA translation and protein transcription, as well as RNA signalling and gene regulation processes. Despite the rapid development and declining cost of modern molecular methods, they typically can only describe ncRNA's structural conformations in vitro, which differ from their in vivo counterparts. Moreover, it is estimated that only a tiny fraction of known ncRNAs has been documented experimentally, often at a high cost. There is thus a growing realization that computational methods must play a central role in the analysis of ncRNAs. Not only do computational approaches hold the promise of rapidly characterizing many ncRNAs yet to be described, but there is also the hope that by understanding the rules that determine their structure, we will gain better insight into their function and design. Many studies revealed that the ncRNA functions are performed by high-level structures that often depend on their low-level structures, such as the secondary structure. This thesis studies the computational folding mechanism and inverse folding of ncRNAs at the secondary level. In this thesis, we describe the development of two bioinformatic tools that have the potential to improve our understanding of RNA secondary structure. These tools are as follows: (1) RAFFT for efficient prediction of pseudoknot-free RNA folding pathways using the fast Fourier transform (FFT)}; (2) aRNAque, an evolutionary algorithm inspired by Lévy flights for RNA inverse folding with or without pseudoknot (A secondary structure that often poses difficulties for bio-computational detection). The first tool, RAFFT, implements a novel heuristic to predict RNA secondary structure formation pathways that has two components: (i) a folding algorithm and (ii) a kinetic ansatz. When considering the best prediction in the ensemble of 50 secondary structures predicted by RAFFT, its performance matches the recent deep-learning-based structure prediction methods. RAFFT also acts as a folding kinetic ansatz, which we tested on two RNAs: the CFSE and a classic bi-stable sequence. In both test cases, fewer structures were required to reproduce the full kinetics, whereas known methods (such as Treekin) required a sample of 20,000 structures and more. The second tool, aRNAque, implements an evolutionary algorithm (EA) inspired by the Lévy flight, allowing both local global search and which supports pseudoknotted target structures. The number of point mutations at every step of aRNAque's EA is drawn from a Zipf distribution. Therefore, our proposed method increases the diversity of designed RNA sequences and reduces the average number of evaluations of the evolutionary algorithm. The overall performance showed improved empirical results compared to existing tools through intensive benchmarks on both pseudoknotted and pseudoknot-free datasets. In conclusion, we highlight some promising extensions of the versatile RAFFT method to RNA-RNA interaction studies. We also provide an outlook on both tools' implications in studying evolutionary dynamics

Nanoindentation testing of soft polymers : computation, experiments and parameters identification

Since nanoindentation technique is able to measure the mechanical properties of extremely thin layers and small volumes with high resolution, it also became one of the important testing techniques for thin polymer layers and coatings. This dissertation is focusing on the characterization of polymers using nanoindentation, which is dealt with numerical computation, experiments and parameters identification. An analysis procedure is developed with the FEM based inverse method to evaluate the hyperelasticity and time-dependent properties. This procedure is firstly verified with a parameters re-identification concept. An important issue in this dissertation is to take the error contributions in real nanoindentation experiments into account. Therefore, the effects of surface roughness, adhesion force, friction and the real shape of the tip are involved in the numerical model to minimize the systematic error between the experimental responses and the numerical predictions. The effects are quantified as functions or models with corresponding parameters to be identified. Finally, data from uniaxial or biaxial tensile tests and macroindentation tests are taken into account. The comparison of these different loading situations provides a validation of the proposed material model and a deep insight into nanoindentation of polymers.Da Nanoindentation die Messung der mechanischen Eigenschaften von dünnen Schichten und kleinen Volumen mit hoher Auflösung ermöglicht, hat sich diese Messmethode zu einer der wichtigsten Testmethoden für dünne Polymerschichten und -beschichtungen entwickelt. Diese Dissertation konzentriert sich auf die Charakterisierung von Polymeren mittels Nanoindentation, die in Form von numerischen Berechnungen, Experimenten und Parameteridentifikationen behandelt wird. Es wurde ein Auswertungsverfahren mit einer FEM basierten inversen Methode zur Berechnung der Hyperelastizität und der zeitabhängigen Eigenschaften entwickelt. Dieses Verfahren wird zunächst mit einem Konzept der Parameter Re-Identifikation verifiziert. Fehlerquellen wie Oberflächenrauheit, Adhäsionskräfte, Reibung und die tatsächlichen Form der Indenterspitze werden in das numerische Modell eingebunden, um die Abweichungen der numerischen Vorhersagen von den experimentellen Ergebnissen zu minimieren. Diese Einflüsse werden als Funktionen oder Modelle mit dazugehörigen, zu identifizierenden Parametern, quantifiziert. Abschließend werden Messwerte aus uni- oder biaxialen Zugversuchen und Makroindentationsversuchen betrachtet. Der Vergleich dieser verschiedenen Belastungszustände liefert eine Bestätigung des vorgeschlagenen Materialmodells und verschafft einen tieferen Einblick in die bei der Nanoindentation von Polymeren ablaufenden Mechanismen