Simultaneous Optimal Uncertainty Apportionment and Robust Design Optimization of Systems Governed by Ordinary Differential Equations

The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness, suboptimal performance, and higher build costs. Treatment of small geometric uncertainty in the context of manufacturing tolerances is a well studied topic. Traditional sequential design methodologies have recently been replaced by concurrent optimal design methodologies where optimal system parameters are simultaneously determined along with optimally allocated tolerances; this allows to reduce manufacturing costs while increasing performance. However, the state of the art approaches remain limited in that they can only treat geometric related uncertainties restricted to be small in magnitude. This work proposes a novel framework to perform robust design optimization concurrently with optimal uncertainty apportionment for dynamical systems governed by ordinary differential equations. The proposed framework considerably expands the capabilities of contemporary methods by enabling the treatment of both geometric and non-geometric uncertainties in a unified manner. Additionally, uncertainties are allowed to be large in magnitude and the governing constitutive relations may be highly nonlinear. In the proposed framework, uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach allows statistical moments of the uncertain system to be explicitly included in the optimization-based design process. The framework formulates design problems as constrained multi-objective optimization problems, thus enabling the characterization of a Pareto optimal trade-off curve that is off-set from the traditional deterministic optimal trade-off curve. The Pareto off-set is shown to be a result of the additional statistical moment information formulated in the objective and constraint relations that account for the system uncertainties. Therefore, the Pareto trade-off curve from the new framework characterizes the entire family of systems within the probability space; consequently, designers are able to produce robust and optimally performing systems at an optimal manufacturing cost. A kinematic tolerance analysis case-study is presented first to illustrate how the proposed methodology can be applied to treat geometric tolerances. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design at an optimal manufacturing cost, accounting for the entire family of systems within the associated probability space. This case-study highlights the general nature of the new framework which is capable of optimally allocating uncertainties of multiple types and with large magnitudes in a single calculation

A Logical Approach to Efficient Max-SAT solving

Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in finding efficient solving techniques. Most of this work focus on the computation of good quality lower bounds to be used within a branch and bound DPLL-like algorithm. Most often, these lower bounds are described in a procedural way. Because of that, it is difficult to realize the {\em logic} that is behind. In this paper we introduce an original framework for Max-SAT that stresses the parallelism with classical SAT. Then, we extend the two basic SAT solving techniques: {\em search} and {\em inference}. We show that many algorithmic {\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in {\em logic} terms with our framework in a unified manner. Besides, we introduce an original search algorithm that performs a restricted amount of {\em weighted resolution} at each visited node. We empirically compare our algorithm with a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-sat evaluation ever reported, show that our algorithm is generally orders of magnitude faster than any competitor

Data Correcting Algorithms in Combinatorial Optimization

This paper describes data correcting algorithms. It provides the theory behind the algorithms and presents the implementation details and computational experience with these algorithms on the asymmetric traveling salesperson problem, the problem of maximizing submodular functions, and the simple plant location problem.

SAT-based Analysis, (Re-)Configuration & Optimization in the Context of Automotive Product documentation

Es gibt einen steigenden Trend hin zu kundenindividueller Massenproduktion (mass customization), insbesondere im Bereich der Automobilkonfiguration. Kundenindividuelle Massenproduktion führt zu einem enormen Anstieg der Komplexität. Es gibt Hunderte von Ausstattungsoptionen aus denen ein Kunde wählen kann um sich sein persönliches Auto zusammenzustellen. Die Anzahl der unterschiedlichen konfigurierbaren Autos eines deutschen Premium-Herstellers liegt für ein Fahrzeugmodell bei bis zu 10^80. SAT-basierte Methoden haben sich zur Verifikation der Stückliste (bill of materials) von Automobilkonfigurationen etabliert. Carsten Sinz hat Mitte der 90er im Bereich der SAT-basierten Verifikationsmethoden für die Daimler AG Pionierarbeit geleistet. Darauf aufbauend wurde nach 2005 ein produktives Software System bei der Daimler AG installiert. Später folgten weitere deutsche Automobilhersteller und installierten ebenfalls SAT-basierte Systeme zur Verifikation ihrer Stücklisten. Die vorliegende Arbeit besteht aus zwei Hauptteilen. Der erste Teil beschäftigt sich mit der Entwicklung weiterer SAT-basierter Methoden für Automobilkonfigurationen. Wir zeigen, dass sich SAT-basierte Methoden für interaktive Automobilkonfiguration eignen. Wir behandeln unterschiedliche Aspekte der interaktiven Konfiguration. Darunter Konsistenzprüfung, Generierung von Beispielen, Erklärungen und die Vermeidung von Fehlkonfigurationen. Außerdem entwickeln wir SAT-basierte Methoden zur Verifikation von dynamischen Zusammenbauten. Ein dynamischer Zusammenbau repräsentiert die chronologische Zusammenbau-Reihenfolge komplexer Teile. Der zweite Teil beschäftigt sich mit der Optimierung von Automobilkonfigurationen. Wir erläutern und vergleichen unterschiedliche Optimierungsprobleme der Aussagenlogik sowie deren algorithmische Lösungsansätze. Wir beschreiben Anwendungsfälle aus der Automobilkonfiguration und zeigen wie diese als aussagenlogisches Optimierungsproblem formalisiert werden können. Beispielsweise möchte man zu einer Menge an Ausstattungswünschen ein Test-Fahrzeug mit minimaler Ergänzung weiterer Ausstattungen berechnen um Kosten zu sparen. DesWeiteren beschäftigen wir uns mit der Problemstellung eine kleinste Menge an Fahrzeugen zu berechnen um eine Testmenge abzudecken. Im Rahmen dieser Arbeit haben wir einen Prototypen eines (Re-)Konfigurators, genannt AutoConfig, entwickelt. Unser (Re-)Konfigurator verwendet im Kern SAT-basierte Methoden und besitzt eine grafische Benutzeroberfläche, welche interaktive Konfiguration erlaubt. AutoConfig kann mit Instanzen von drei großen deutschen Automobilherstellern umgehen, aber ist nicht alleine darauf beschränkt. Mit Hilfe dieses Prototyps wollen wir die Anwendbarkeit unserer Methoden demonstrieren

New strategies for the aerodynamic design optimization of aeronautical configurations through soft-computing techniques

Premio Extraordinario de Doctorado de la UAH en 2013Lozano Rodríguez, Carlos, codir.This thesis deals with the improvement of the optimization process in the aerodynamic design of aeronautical configurations. Nowadays, this topic is of great importance in order to allow the European aeronautical industry to reduce their development and operational costs, decrease the time-to-market for new aircraft, improve the quality of their products and therefore maintain their competitiveness. Within this thesis, a study of the state-of-the-art of the aerodynamic optimization tools has been performed, and several contributions have been proposed at different levels: -One of the main drawbacks for an industrial application of aerodynamic optimization tools is the huge requirement of computational resources, in particular, for complex optimization problems, current methodological approaches would need more than a year to obtain an optimized aircraft. For this reason, one proposed contribution of this work is focused on reducing the computational cost by the use of different techniques as surrogate modelling, control theory, as well as other more software-related techniques as code optimization and proper domain parallelization, all with the goal of decreasing the cost of the aerodynamic design process. -Other contribution is related to the consideration of the design process as a global optimization problem, and, more specifically, the use of evolutionary algorithms (EAs) to perform a preliminary broad exploration of the design space, due to their ability to obtain global optima. Regarding this, EAs have been hybridized with metamodels (or surrogate models), in order to substitute expensive CFD simulations. In this thesis, an innovative approach for the global aerodynamic optimization of aeronautical configurations is proposed, consisting of an Evolutionary Programming algorithm hybridized with a Support Vector regression algorithm (SVMr) as a metamodel. Specific issues as precision, dataset training size, geometry parameterization sensitivity and techniques for design of experiments are discussed and the potential of the proposed approach to achieve innovative shapes that would not be achieved with traditional methods is assessed. -Then, after a broad exploration of the design space, the optimization process is continued with local gradient-based optimization techniques for a finer improvement of the geometry. Here, an automated optimization framework is presented to address aerodynamic shape design problems. Key aspects of this framework include the use of the adjoint methodology to make the computational requirements independent of the number of design variables, and Computer Aided Design (CAD)-based shape parameterization, which uses the flexibility of Non-Uniform Rational B-Splines (NURBS) to handle complex configurations. The mentioned approach is applied to the optimization of several test cases and the improvements of the proposed strategy and its ability to achieve efficient shapes will complete this study

New strategies for the aerodynamic design optimization of aeronautical configurations through soft-computing techniques

Premio Extraordinario de Doctorado de la UAH en 2013Lozano Rodríguez, Carlos, codir.This thesis deals with the improvement of the optimization process in the aerodynamic design of aeronautical configurations. Nowadays, this topic is of great importance in order to allow the European aeronautical industry to reduce their development and operational costs, decrease the time-to-market for new aircraft, improve the quality of their products and therefore maintain their competitiveness. Within this thesis, a study of the state-of-the-art of the aerodynamic optimization tools has been performed, and several contributions have been proposed at different levels: -One of the main drawbacks for an industrial application of aerodynamic optimization tools is the huge requirement of computational resources, in particular, for complex optimization problems, current methodological approaches would need more than a year to obtain an optimized aircraft. For this reason, one proposed contribution of this work is focused on reducing the computational cost by the use of different techniques as surrogate modelling, control theory, as well as other more software-related techniques as code optimization and proper domain parallelization, all with the goal of decreasing the cost of the aerodynamic design process. -Other contribution is related to the consideration of the design process as a global optimization problem, and, more specifically, the use of evolutionary algorithms (EAs) to perform a preliminary broad exploration of the design space, due to their ability to obtain global optima. Regarding this, EAs have been hybridized with metamodels (or surrogate models), in order to substitute expensive CFD simulations. In this thesis, an innovative approach for the global aerodynamic optimization of aeronautical configurations is proposed, consisting of an Evolutionary Programming algorithm hybridized with a Support Vector regression algorithm (SVMr) as a metamodel. Specific issues as precision, dataset training size, geometry parameterization sensitivity and techniques for design of experiments are discussed and the potential of the proposed approach to achieve innovative shapes that would not be achieved with traditional methods is assessed. -Then, after a broad exploration of the design space, the optimization process is continued with local gradient-based optimization techniques for a finer improvement of the geometry. Here, an automated optimization framework is presented to address aerodynamic shape design problems. Key aspects of this framework include the use of the adjoint methodology to make the computational requirements independent of the number of design variables, and Computer Aided Design (CAD)-based shape parameterization, which uses the flexibility of Non-Uniform Rational B-Splines (NURBS) to handle complex configurations. The mentioned approach is applied to the optimization of several test cases and the improvements of the proposed strategy and its ability to achieve efficient shapes will complete this study

MaxSAT Evaluation 2018 : Solver and Benchmark Descriptions

Non peer reviewe