Balancing exploration and exploitation in robust multiobjective electromagnetic design optimisation

Design optimisation of electromagnetic and electromechanical devices is usually aided by numerical simulations, such as the finite element method, which often carry high computational costs, especially if three-dimensional transient modelling is required. Thus in addition to the task of finding the global optimum, while avoiding local minima traps, there is the additional requirement of achieving the final solution efficiently with as few objective function evaluations as possible. With this in mind several surrogate modelling techniques have been developed to replace, under controlled environment, the computationally expensive accurate field modelling by fast approximate substitutes. This thesis looks at a particular technique known as kriging, which in other applications has been demonstrated to provide accurate representations, even of complicated responses, based on a limited set of observations whilst providing an error estimate of the predictions and hence increasing the confidence in the answer. In the iterative optimisation process the critical issue is where to position the next point for evaluation to find a sensible compromise between conflicting goals to explore the search space thoroughly but at the same time exploit information already available. This thesis proposes several novel algorithms based on reinforcement learning theory using the concept of rewards for balancing exploration and exploitation automatically and adaptively. The performance of these algorithms has been assessed comprehensively using carefully selected test functions and real engineering problems (taken from TEAM workshops) and compared with the results published in literature. The kriging approach has generally been found to outperform significantly other available methods. One of the practical limitations, however, was found to be large-scale multi-dimensional or multi-objective tasks because of the need to create special correlation matrices for the kriging predictions to work. Several techniques have been developed and implemented to alleviate such problems and control the memory space occupied by such matrices. Finally, in practical design problems, the issue of robustness of the design has to be considered – related to manufacturing tolerances, material variability, etc – which requires the designer not only to find the theoretical optimum but also assess its quality (sensitivity) within specified uncertainties of variables. Several strategies for evaluation of design robustness assisted by kriging modelling have been developed and implemented in combination with commercial electromagnetic design software.