A framework for finding robust optimal solutions over time

Dynamic optimization problems (DOPs) are those whose specifications change over time, resulting in changing optima. Most research on DOPs has so far concentrated on tracking the moving optima (TMO) as closely as possible. In practice, however, it will be very costly, if not impossible to keep changing the design when the environment changes. To address DOPs more practically, we recently introduced a conceptually new problem formulation, which is referred to as robust optimization over time (ROOT). Based on ROOT, an optimization algorithm aims to find an acceptable (optimal or sub-optimal) solution that changes slowly over time, rather than the moving global optimum. In this paper, we propose a generic framework for solving DOPs using the ROOT concept, which searches for optimal solutions that are robust over time by means of local fitness approximation and prediction. Empirical investigations comparing a few representative TMO approaches with an instantiation of the proposed framework are conducted on a number of test problems to demonstrate the advantage of the proposed framework in the ROOT context.     

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Lamarckian memetic algorithms: local optimum and connectivity structure analysis

Memetic algorithms (MAs) represent an emerging field that has attracted increasing research interest in recent times. Despite the popularity of the field, we remain to know rather little of the search mechanisms of MAs. Given the limited progress made on revealing the intrinsic properties of some commonly used complex benchmark problems and working mechanisms of Lamarckian memetic algorithms in general non-linear programming, we introduce in this work for the first time the concepts of local optimum structure and generalize the notion of neighborhood to connectivity structure for analysis of MAs. Based on the two proposed concepts, we analyze the solution quality and computational efficiency of the core search operators in Lamarckian memetic algorithms. Subsequently, the structure of local optimums of a few representative and complex benchmark problems is studied to reveal the effects of individual learning on fitness landscape and to gain clues into the success or failure of MAs. The connectivity structure of local optimum for different memes or individual learning procedures in Lamarckian MAs on the benchmark problems is also investigated to understand the effects of choice of memes in MA design.     

Knowledge Extraction from Aerodynamic Design Data and its Application to 3D Turbine Blade Geometries

Applying numerical optimisation methods in the field of aerodynamic design optimisation normally leads to a huge amount of heterogeneous design data. While most often only the most promising results are investigated and used to drive further optimisations, general methods for investigating the entire design dataset are rare. We propose methods that allow the extraction of comprehensible knowledge from aerodynamic design data represented by discrete unstructured surface meshes. The knowledge is prepared in a way that is usable for guiding further computational as well as manual design and optimisation processes. A displacement measure is suggested in order to investigate local differences between designs. This measure provides information on the amount and direction of surface modifications. Using the displacement data in conjunction with statistical methods or data mining techniques provides meaningful knowledge from the dataset at hand. The theoretical concepts have been applied to a data set of 3D turbine stator blade geometries. The results have been verified by means of modifying the turbine blade geometry using direct manipulation of free form deformation (DMFFD) techniques. The performance of the deformed blade design has been calculated by running computational fluid dynamic (CFD) simulations. It is shown that the suggested framework provides reasonable results which can directly be transformed into design modifications in order to guide the design process.