Discrete-state simulated annealing with application to preliminary aircraft design.

摘要

Many design problems of engineering interest, such as the preliminary design of the blended wing body aircraft considered in the current work, have design surfaces which contain jump discontinuities that act as spurious local extrema. The line searches associated with gradient based optimizers are found to converge at the spurious local extrema created by these discontinuities, rendering future finite-difference gradients taken at these locations inaccurate. Gradient-based algorithms will tend to cycle through false search directions, often without moving, until they are halted.; Stochastic optimization techniques such as Simulated Annealing (SA) are not effected by such features since they generally do not require continuous design surfaces for sensitivity analyses. SA requires the user to set a cooling schedule which prescribes how the main control parameter, the temperature, is to be varied over the course of the optimization. The choice of a suitable cooling schedule is highly problem dependent and can have a profound effect on the performance of the algorithm. For the blended wing body test case, a parameter-tuned SA algorithm is able to locate substantially improved configurations compared to a conjugate gradient method.; Discrete-State Simulated Annealing (DSSA) is a version of SA having a generic cooling schedule which is completely independent of the problem being optimized. The generic cooling schedule is set based upon theoretical results from statistical thermodynamics. For the blended wing body test case, the DSSA algorithm performs well using the theoretically derived cooling schedule, providing results of a similar quality to those obtained using the standard, parameter-tuned SA algorithm without the computational overhead associated with the tuning of the parameters.; Finally, Discrete-State Simulated Annealing for Variable Complexity Models (DSSA/VCM) is introduced as a means of performing optimization for problems having analyses of variable fidelity available. The DSSA/VCM algorithm is found to provide an effective means of performing optimization for such problems, providing quality results at a computational cost that is a fraction of the cost of a full optimization employing only a high fidelity analysis. This helps overcome one of the main criticisms of stochastic optimization algorithms, namely that they require too many function calls for use with computationally expensive high fidelity analyses.