Solving Computationally Expensive Optimization Problems with CPU Time- Correlated Functions

摘要

In this paper, we characterize a new class of optimization problems in which objective function values are correlated with the computational time required to obtain these values. That is, as the optimal solution is approached, the computational time required to compute an objective function values decreases significantly. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration process, and the goal is to find the parameter values of a predetermined reference image by comparing the flow dynamics from the numerical simulation and the reference image through the image comparison process. In designing an approach to numerically solve the more general class of problems in an efficient way, we make use of surrogates based on CPU times of previously evaluated points, rather than their function values, all within the search step framework of mesh adaptive direct search algorithms. Because of the expected CPU time correlation, a time cutoff parameter was added to the objective function evaluation to allow its termination during the comparison process if the computational time exceeds a specified threshold. The approach was tested using the NOMADm and DACE MATLABr software packages, and results are presented.