On Acceleration of Evolutionary Algorithms Taking Advantage of A Posteriori Error Analysis

A variety of important engineering and scientific tasks may be formulated as non-linear, constrained optimization problems. Their solution often demands high computational power. It may be reached by means of appropriate hardware, software or algorithm improvements. The Evolutionary Algorithms (EA) approach to solution of such problems is considered here. The EA are rather slow methods; however, the main advantage of their application is observed in the case of non-convex problems. Particularly high efficiency is demanded in the case of solving large optimization problems. Examples of such problems in engineering include analysis of residual stresses in railroad rails and vehicle wheels, as well as the Physically Based Approximation (PBA) approach to smoothing experimental and/or numerical data. Having in mind such analysis in the future, we focus our current research on the significant EA efficiency increase. Acceleration of the EA is understood here, first of all, as decreasing the total computational time required to solve an optimization problem. Such acceleration may be obtained in various ways. There are at least two gains from the EA acceleration, namely i) saving computational time, and ii) opening a possibility of solving larger optimization problems, than it would be possible with the standard EA. In our recent research we have preliminarily proposed several new speed-up techniques based on simple concepts. In this paper we mainly develop acceleration techniques based on simultaneous solutions averaging well supported by a non-standard application of parallel calculations, and a posteriori solution error analysis. The knowledge about the solution error is used to EA acceleration by means of appropriately modified standard evolutionary operators like selection, crossover, and mutation. Efficiency of the proposed techniques is evaluated using several benchmark tests. These tests indicate significant speed-up of the involved optimization process. Further concepts and improvements are also currently being developed and tested

Tracking moving optima using Kalman-based predictions

The dynamic optimization problem concerns finding an optimum in a changing environment. In the field of evolutionary algorithms, this implies dealing with a timechanging fitness landscape. In this paper we compare different techniques for integrating motion information into an evolutionary algorithm, in the case it has to follow a time-changing optimum, under the assumption that the changes follow a nonrandom law. Such a law can be estimated in order to improve the optimum tracking capabilities of the algorithm. In particular, we will focus on first order dynamical laws to track moving objects. A vision-based tracking robotic application is used as testbed for experimental comparison

Evolutionary design of a full-envelope full-authority flight control system for an unstable high-performance aircraft

The use of an evolutionary algorithm in the framework of H1 control theory is being considered as a means for synthesizing controller gains that minimize a weighted combination of the infinite norm of the sensitivity function (for disturbance attenuation requirements) and complementary sensitivity function (for robust stability requirements) at the same time. The case study deals with a complete full-authority longitudinal control system for an unstable high-performance jet aircraft featuring (i) a stability and control augmentation system and (ii) autopilot functions (speed and altitude hold). Constraints on closed-loop response are enforced, that representing typical requirements on airplane handling qualities, that makes the control law synthesis process more demanding. Gain scheduling is required, in order to obtain satisfactory performance over the whole flight envelope, so that the synthesis is performed at different reference trim conditions, for several values of the dynamic pressure, used as the scheduling parameter. Nonetheless, the dynamic behaviour of the aircraft may exhibit significant variations when flying at different altitudes, even for the same value of the dynamic pressure, so that a trade-off is required between different feasible controllers synthesized at different altitudes for a given equivalent airspeed. A multiobjective search is thus considered for the determination of the best suited solution to be introduced in the scheduling of the control law. The obtained results are then tested on a longitudinal non-linear model of the aircraft

A Review of Geophysical Modeling Based on Particle Swarm Optimization

This paper reviews the application of the algorithm particle swarm optimization (PSO) to perform stochastic inverse modeling of geophysical data. The main features of PSO are summarized, and the most important contributions in several geophysical felds are analyzed. The aim is to indicate the fundamental steps of the evolution of PSO methodologies that have been adopted to model the Earth’s subsurface and then to undertake a critical evaluation of their benefts and limitations. Original works have been selected from the existing geophysical literature to illustrate successful PSO applied to the interpretation of electromagnetic (magnetotelluric and time-domain) data, gravimetric and magnetic data, self-potential, direct current and seismic data. These case studies are critically described and compared. In addition, joint optimization of multiple geophysical data sets by means of multi-objective PSO is presented to highlight the advantage of using a single solver that deploys Pareto optimality to handle diferent data sets without conficting solutions. Finally, we propose best practices for the implementation of a customized algorithm from scratch to perform stochastic inverse modeling of any kind of geophysical data sets for the beneft of PSO practitioners or inexperienced researchers

Modern considerations for the use of naive Bayes in the supervised classification of genetic sequence data

2021 Spring.Includes bibliographical references.Genetic sequence classification is the task of assigning a known genetic label to an unknown genetic sequence. Often, this is the first step in genetic sequence analysis and is critical to understanding data produced by molecular techniques like high throughput sequencing. Here, we explore an algorithm called naive Bayes that was historically successful in classifying 16S ribosomal gene sequences for microbiome analysis. We extend the naive Bayes classifier to perform the task of general sequence classification by leveraging advancements in computational parallelism and the statistical distributions that underlie naive Bayes. In Chapter 2, we show that our implementation of naive Bayes, called WarpNL, performs within a margin of error of modern classifiers like Kraken2 and local alignment. We discuss five crucial aspects of genetic sequence classification and show how these areas affect classifier performance: the query data, the reference sequence database, the feature encoding method, the classification algorithm, and access to computational resources. In Chapter 3, we cover the critical computational advancements introduced in WarpNL that make it efficient in a modern computing framework. This includes efficient feature encoding, introduction of a log-odds ratio for comparison of naive Bayes posterior estimates, description of schema for parallel and distributed naive Bayes architectures, and use of machine learning classifiers to perform outgroup sequence classification. Finally in Chapter 4, we explore a variant of the Dirichlet multinomial distribution that underlies the naive Bayes likelihood, called the beta-Liouville multinomial. We show that the beta-Liouville multinomial can be used to enhance classifier performance, and we provide mathematical proofs regarding its convergence during maximum likelihood estimation. Overall, this work explores the naive Bayes algorithm in a modern context and shows that it is competitive for genetic sequence classification

Numerical Algorithms for Algebraic Stabilizations of Scalar Convection-Dominated Problems

In dieser Arbeit wurden Finite-Elemente-Verfahren mit algebraischer Fluss\-kor\-rek\-tur (AFC) f\"ur station\"are Konvektions-Diffusions-Reaktions Gleichungen untersucht. Die beiden Hauptaspekte, die studiert wurden, sind iterative L\"oser f\"ur die auftretenden nichtlinearen Gleichungen und adaptive Gitterverfeinerung basierend auf a posteriori Fehlersch\"atzern. Die wichtigsten Ergebnisse der Arbeit sind im Folgenden zusammengefasst. Zun\"achst wurden Studien zu den L\"osern vorgestellt. Es wurden mehrere iterative L\"oser untersucht, darunter Fixpunktans\"atze und Methoden vom Newton-Typ. Die Newton Methoden reduzierten die Anzahl der Iterationen f\"ur bestimmte Beispiele, aber sie waren ineffizient bez\"uglich der Rechenzeit. Der einfachste Fixpunktansatz, n\"amlich \fpr, war auf Grund seiner Matrixeigenschaften am effizientesten. Algorithmische Komponenten, wie die Anderson-Beschleunigung, reduzierten die Anzahl der Iterationen in einigen Beispielen, aber sie lieferte keine Ergebnisse f\"ur den BJK-Limiter. In drei Dimensionen wurde ein iterativer L\"oser f\"ur feinere Gitter ben\"otigt, aber auch hier war \fpr die effizienteste Herangehensweise. Unabh\"angig von der Dimension war es einfacher, die Probleme mit dem Kuzmin-Limiter als mit dem BJK-Limiter zu l\"osen. Der zweite Hauptaspekt sind Studien zur a posteriori Fehlersch\"atzung. Es wurden zwei Ans\"atze zur Bestimmung einer oberen Schranke in der Energie\-norm untersucht, ein auf Resi\-duen basierender Ansatz (\emph{AFC-Energie} Technik) und ein anderer mit der SUPG-L\"osung (\emph{AFC-SUPG-Energie} Technik). Beide Techniken liefern keine robusten Sch\"atzungen bez\"uglich $\varepsilon$, aber es zeigte sich, dass der \emph{AFC-SUPG Energie} Ansatz einen besseren Effektivit\"ats\-index besa{\ss}. F\"ur den BJK-Limiter war die Effektivit\"at besser als f\"ur den Kuzmin-Limiter mit dem \emph{AFC-Energie} Ansatz, w\"ahrend beim \emph{AFC-SUPG Energie} Ansatz die Wahl des Limiters keine Rolle spielte. Im Zuge der adaptiven Gitterverfeinerung kann das Problem lokal diffusions-dominant werden. In diesem Falle muss man den BJK-Limiter verwenden, da man beim Kuzmin-Limiter eine reduzierte Konvergenzordnung beobachten kann. Im Hinblick auf die adaptive Gitterverfeinerung wurden Grenzschichten unterschiedlichen Typs besser mit dem \emph{AFC-Energie} Ansatz verfeinert als mit dem \emph{AFC-SUPG Energie} Ansatz. Schlie{\ss}lich wurden die Ergebnisse f\"ur die a posteriori Fehlersch{\"a}tzung auf Gitter mit h{\"a}ngenden Knoten angewandt. Zun\"achst wurden Ergebnisse bez\"uglich h\"angender Knoten von Lagrange-Elementen niedriger Ordnung auf Elemente h\"oherer Ordnung erweitert. Es zeigte sich in numerischen Studien, dass der Kuzmin-Limiter auf Gittern mit h{\"a}ngenden Knoten dem DMP nicht gen\"ugt, w{\"a}hrend der BJK-Limiter Ergebnisse lieferte, die dem DMP entsprachen. Die Grenzschichten wurden auf konform abgeschlossenen Gittern wesentlich besser approximiert als auf Gittern mit h{\"a}ngenden Knoten. Insgesamt sollte man Gitter mit h{\"a}ngenden Knoten nicht f\"ur AFC Verfahren verwenden.This thesis studies the Algebraic Flux Correction (AFC) schemes for the steady-state convection-diffusion-reaction equations. The work is done on two major aspects of these schemes, namely the iterative solvers for the nonlinear equations and a posteriori error estimation. The major findings of the thesis are summarized below. First, studies concerning the solvers are presented. Several iterative solvers are studied including fixed-point approaches and Newton-type methods. Newton methods reduce the number of iterations for certain examples but it is computationally inefficient. The most simple fixed point approach, namely the fixed point right-hand side is the most efficient because of its matrix structure. Algorithmic components such as Anderson acceleration reduced the number of iterations in some examples but it failed to give results for the BJK limiter. In three dimensions, an iterative solver is needed for finer meshes but here also the fixed point right-hand side is the most efficient. Irrespective of the dimension, it is easier to solve the problem with the Kuzmin limiter as that of the BJK limiter. In conclusion, one might get fewer iterations, with advanced methods but the simple fixed-point approach with dynamic damping is the most efficient in both dimensions. Second, studies for a posteriori error estimation is presented. Two approaches for finding the upper bound are investigated in the energy norm, one residual-based (AFC-Energy technique), and others using the SUPG solution (AFC-SUPG Energy technique). The AFC-Energy estimator is shown not to be robust with respect to $\varepsilon$ and hence, the AFC-SUPG approach gave a better effectivity index. For the BJK limiter, the effectivity is better than the Kuzmin limiter with the AFC-Energy approach, whereas for the AFC-SUPG approach the choice of limiter did not play a role. With adaptive grid refinement, the problem could become locally diffusion dominated and hence one has to use the BJK limiter as one can observe reduced order of convergence for the Kuzmin limiter. In regards to adaptive grid refinement, the AFC-Energy approach approximated the layer much better as compared to the AFC-SUPG approach. Lastly, the results for a posteriori error estimation are extended to grids with hanging nodes. First, results regarding hanging nodes are extended from lower-order Lagrange elements to higher-order elements. It was shown that the Kuzmin limiter fails to satisfy DMP on grids with hanging nodes, whereas the BJK limiter satisfies the DMP. The layers are properly approximated on conformally closed grids in comparison to grids with hanging nodes. Altogether, one should not use grids with hanging nodes for AFC schemes

Finite elements for scalar convection-dominated equations and incompressible flow problems - A never ending story?

The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics. Second, a number of, in our opinion, important problems in these fields are discussed