Numerical Methodologies For Robust Optimizations Of Inverse Problems

Synchronizing with the ever-increasing demand on high quality products to function in variable operating conditions and environments, the study of robust design methodologies and techniques has become a new topical area in design optimizations in nearly all engineering and applied science disciplines. Nowadays the robust design technique has become the state of the art for making product performance insensitive to varying manufacturing conditions, environmental and product-to-product variations. Although its immense importance has been widely acknowledged for different engineering disciplines, there are still many open issues both in practical and theoretical aspects that need to be addressed, especially in the computation of electromagnetic fields. In other words, the computational burden for a robust optimizer is significantly higher than that for its global counterpart, and in this regard, the available robust methodologies may become computationally inefficient for inverse problems where high fidelity models and analysis are commonly used for performance evaluations.Based on the available robust design methodologies of fellow researchers from different engineering disciplines, a comprehensive and symmetric study of robust optimal design methodologies and techniques, especially the evolutionary algorithm is conducted. More concretely, the study focuses on issues such as the measures and approaches to reduce the huge computational burden of solution strategies, the improvements of evolutionary algorithm in both algorithm structures and parameter updating mechanisms, as well some special key techniques.Firstly, a robust oriented particle swarm optimization algorithm is proposed for inverse problem. In the proposed algorithm; the neighborhood is redefined; a strategy for efficient expected fitness assignments, and the mechanism for generating new neighborhood solutions, as well as the distance weighted formulation for expected fitness computation are proposed. Also, improvements on algorithm structures and parameters such as new updating formulae for velocity and position vector, the introduction of an age variable, and the out of boundary control are included.Secondly, an evolutionary algorithm based on Probabilistic Models, a cross entropy method is extended successfully to study the robust optimization of inverse problem. To efficiently compute the robust performances, the normal distribution function is used as the probability density function, and a methodology for evaluating and assigning robust performance to promising solutions is proposed.Thirdly, some key issues for robust optimizations of inverse problems are addressed. To summary up, the support vector machine is proposed as a response surface model of the objective and constraint function, and combined with evolutionary algorithm to develop an efficient numerical methodology; the polynomial chaos expansion is used as a stochastic response surface model for efficient computations of the expectancy metric of the objective function; and a novel driving mechanism to bias the next iteration cycles to search for both global and robust optimal solutions is introduced.To validate the proposed methodology and method, they are extensively experienced on different case studies. The case studies include the optimal designs of inverted-S antenna, antenna arrays, and the TEAM (Testing of Electromagnetic Analysis Method) Workshop Problem22. The numerical results as reported positively confirm the feasibility and advantage of the present work.