Method for solving multi-fidelity optimization problems

A computer comprising a processor and memory encoded with data for causing the processor to perform a method for structural analysis, wherein the method comprises:

• determining a preliminary design of a structure based on an objective function and constraint functions both having a plurality of discrete fidelity levels m=1, . . . , M, wherein the constraint functions correspond to one or more requirements of the structure, generating an initial set of trial points based on the objective function and the constraint functions, constructing a plurality of surrogate functions based on the initial set of trial points, constructing and improving a plurality of surrogate functions of the objective function and of the constraint functions to identify a new set of trial points, wherein each surrogate function is a mixed variable surrogate function that corresponds to discrete fidelity level of the plurality of discrete fidelity levels which is based on a dimensionality of the mixed variable surrogate function, identifying an adjacent set of trial points when the new set of trial points is empty, wherein the adjacent set of trial points is different from the initial set of trial points and the surrogate functions are updated based on a mapping to the adjacent set of trial points to identify the new set of trial points, running at least one lower fidelity simulation by evaluating lower fidelity surrogate functions in ascending order to reduce a number of trial points in the new set;
• evaluating the reduced number of trial points with the objective function and at least one of the constraint functions as a high fidelity simulation;
• and providing at least one structural design based on the evaluation of the reduced number of trial points, wherein running the at least one lower fidelity simulation comprises looping through the plurality of discrete fidelity levels m=1 to M−1 in ascending order, where fidelity level M is a highest of the plurality of discrete fidelity levels, wherein for each iteration Sk is the new set of trial points, the objective function and at least one of the constraint functions are evaluated at points xϵSk at fidelity level m and the surrogate functions are updated;
• the surrogate functions are evaluated at points xϵSk at fidelity level M;
• and the trial points from Sk are removed for which the surrogate functions fail to return a value.

An article comprising non-transitory computer-readable memory encoded with material that, when executed, causes a computer to perform a method for structural analysis, wherein the method comprises:

• determining a preliminary design of a structure based on an objective function and constraint functions both having a plurality of discrete fidelity levels m=1, . . . , M, wherein the constraint functions correspond to one or more requirements of the structure, generating an initial set of trial points based on the objective function and the constraint functions;
• constructing and improving a plurality of surrogate functions of the objective function and of the constraint function to identify a new set of trial points, wherein each surrogate function is a mixed variable surrogate function that corresponds to a discrete fidelity level of the plurality of discrete fidelity levels which is based on a dimensionality of the mixed variable surrogate function, running at least one lower fidelity simulation by evaluating lower fidelity surrogate functions in ascending order to reduce a number of trial points in the new set;
• evaluating the reduced number of trial points with the objective function and at least one of the constraint functions as a high fidelity simulation;
• and providing at least one structural design based on the evaluation of the reduced number of trial points, wherein running the at least one lower fidelity simulation comprises looping through the plurality of discrete fidelity levels m=1 to M−1 in ascending order, where fidelity level M is a highest of the plurality of discrete fidelity levels, wherein for each iteration Sk is the new set of trial points, the objective function and at least one of the constraint functions are evaluated at points xϵSk at fidelity level m and the surrogate functions are updated;
• the surrogate functions are evaluated at points xϵSk at fidelity level M;
• and the trial points from Sk are removed for which the surrogate functions fail to return a value.