Research On Variable-fidelity Optimization Methods Based On Lower Confidence Bound Criterion

Due to the advantages of fusing data from different simulation sources and low modeling cost,variable-fidelity surrogate model has attracted much attention on computationally expensive optimization problems.To improve the efficiency for engineering optimization,researchers attempted to combine the variable-fidelity surrogate model and efficient global optimization.Nevertheless,there are still plenty of deficiency in this field:(1)the lower confidence bound(LCB)criterion is prohibitive to be employed directly into variable-fidelity optimization,variable-fidelity LCB criterion is scarce;(2)in the recently developed methods,constraints are all tackled by the probability of feasible(Po F)function,which is inaccurate around the constraint boundary,which leads algorithm unable to converge to global optimum;(3)recent variable-fidelity optimization methods are all unable to be directly parallelize,corresponding parallelization strategies need to explore.Therefore,this thesis will research on these three directions,including variable-fidelity surrogate assisted unconstrained optimization,constrained optimization,and parallel optimization.The specific research work is specified as follows:(1)A Variable-Fidelity Lower Confidence Bounding(VF-LCB)optimization approach is proposed to adaptive the standard LCB criterion to variable-fidelity optimization.The proposal method considers the cost ratio between different analysis models,the coefficient of variation for high-fidelity prediction,and the uncertainty of different fidelity.Then the location and fidelity level of newly added sample is decided based on the VF-LCB function.From the experimental results,the proposed method is more efficient and robust dealing with unconstrained optimization problems.(2)A Variable-Fidelity Constrained Lower Confidence Bounding(VF-CLCB)optimization approach is proposed to improve capability of solving constrained optimization problems.VF-CLCB method defines a novel function named lower confidence bound of constraints to improve the accuracy near constraint boundaries.Then an infill sampling function combined with penalty method is used to converge to global feasible optimum.By testing through eight numerical examples and an engineering case,the proposed method is found to significantly outperform the compared methods.(3)To parallelize the variable-fidelity surrogate-based optimization methods,the author develops two parallel methods,which are Parallel Variable-Fidelity Lower Confidence Bounding(PVF-LCB)approach and Parallel Variable-Fidelity Constrained Lower Confidence Bounding(PVF-CLCB)approach for unconstrained and constrained optimization problems,respectively.A variable-fidelity influence impact function is defined to select multiple potential sample points.In addition,an adaptive allocation strategy is developed to allocate the computation resources between objective and constraint functions.By testing from identical examples,it is found that the proposal methods can significantly accelerate the optimization process by several computers computing simultaneously.In summary,this these is devoted to research on variable-fidelity optimization based on LCB criterion and provides inspiration and reference for variable-fidelity optimization.