This paper introduces a new approach to kriging surrogate model sampling points allocation. By introducing the second (dual) kriging during the model construction, the existing sampling points are reallocated to reduce overall memory requirements. Moreover, a new algorithm is proposed for selecting the position of the next sampling point by utilizing a modified expected improvement criterion.
In electromagnetic design, uncertainties in design variables are inevitable, thus in addition to pursuing the theoretical optimum of the objective function the evaluation of robustness of the optimum solution is also critical. Several methodologies exist to tackle robust optimization, such as worst case optimization and gradient index; this paper investigates the use of standard deviation and mean value of objective function under uncertainty of variables. A modified Kriging model with the ability of balancing exploration and exploitation is employed to facilitate the objective function prediction. Two TEAM benchmark problems are solved using different methodologies to compare the advantages and disadvantages of different robust optimization approaches.Index Terms-Gradient index (GI), Kriging, six sigma quality (SSQ) approach, worst case optimization (WCO).
Abstract-A kriging based optimization approach is proposed for problems with large datasets and high dimensionality. Memory usage is maintained via model centering aided by minimizing the impact of information loss on accuracy of new point prediction using points aggregation techniques. The 8-parameter TEAM problem 22 is revisited in the context of computational efficiency and accuracy.
Abstract:The paper introduces a new approach to kriging based multi-objective optimization by utilizing a local probability of improvement as the infill sampling criterion and the nearest neighbor check to ensure diversification and uniform distribution of Pareto fronts. The proposed method is computationally fast and linearly scalable to higher dimensions.
Due to unavoidable uncertainties related to material properties and manufacturing processes, the robustness of the optimal solution must be considered when designing electromagnetic devices. In this paper, the worst-case optimisation (WCO) and the worst-vertex-based WCO are proposed to evaluate the robustness of both performance and constraints under uncertainty. To reduce computing times when searching for the robust solution a predicted objective function is used, obtained with the help of a kriging algorithm which explores the searching space using the concept of rewards. Finally, to avoid some of the shortcomings of WCO, the concept of average performance evaluation is developed.
Abstract:The paper discusses some of the recent advances in kriging based worst-case design optimisation and proposes a new two-stage approach to solve practical problems. The efficiency of the infill points allocation is improved significantly by adding an extra layer of optimisation enhanced by a validation process.
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