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Because of constraints in exact modeling, measuring and computing, it is inevitable that algorithms that solve real world problems have to avoid errors. Hence, proposing models to handle error, and designing algorithms that work well in practice, are challenging fields. In this paper, we introduce a model called the λ-geometry model   to handle a dynamic form of imprecision, which allows the precision to change monotonically in the input data of geometric algorithms. λ-geometry is a generalization of region-based models and provides the output of problems as functions, with respect to the level of precision. This type of output helps to design exact algorithms and is also useful in decision making processes. Furthermore, we study the problem of orthogonal range searching in one and two dimensional space under the model of λ-geometry, and propose efficient algorithms to solve it.

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This paper presents the development of a computational tool for the simulation of flow behavior in the fin-and-tube heat exchangers with phase change in the coolant side, for which the finite volume method was used for exchanger modeling and representation of the connection of the tubes was made using graph theory. Because the hydrodynamic phenomena and the 2 phase flow is not well developed, the model supports various empirical correlations for calculating the pressure drop and heat transfer coefficient. As a result a computational tool for simulating of fin-and-tube heat exchangers that allows the modeling of the refrigerant flow in single phase or two-phase state was obtained. With the model of the exchanger was possible to predict the flow behavior of an evaporator under conditions of dry and wet fins give error values below 6% with respect to the experimental data.

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In this paper, the aerodynamic shape optimization problems with uncertain operating conditions has been addressed. After a review of robust control theory and the possible approaches to take into account uncertainties, the use of Taguchi robust design methods in order to overcome single point design problems in Aerodynamics is proposed. Under the Taguchi concept, a design with uncertainties is converted into an optimization problem with two objectives which are the mean performance and its variance, so that the solutions are as less sensitive to the uncertainty of the input parameters as possible. Furthermore, the Multi-Criterion Evolutionary Algorithms (MCEAs) are used to capture a set of compromised solutions (Pareto front) between these two objectives. The flow field is analyzed by Navier-Stokes computation using an unstructured mesh. The proposed approach drives to the solution of a multi-objective optimization problem that is solved using a modification of a Nondominated Sorting Genetic Algorithm (NSGA). In order to reduce the number of expensive evaluations of the fitness function a Response Surface Modeling (RSM) is employed to estimate the fitness value using the polynomial approximation model. During the solution of the optimization problem a Semi-torsional Spring Analogy is used for the adaption of the computational mesh to all the obtained geometrical configurations. The proposed approach is applied to the robust optimization of the 2D high lift devices of a business aircraft by maximizing the mean and minimizing the variance of the lift coefficients with uncertain free-stream angle of attack at landing and takeoff flight conditions, respectively.

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