Handling Undefined Vectors in Expensive Optimization Problems

Abstract

When using computer simulations in engineering design optimization one often encounters vectors which ‘crash’ the simulation and so no fitness is associated with them. In this paper we refer to these as undefined vectors since the objective function is undefined there. Since each simulation run (a function evaluation) is expensive (anywhere from minutes to weeks of CPU time) only a small number of evaluations are allowed during the entire search and so such undefined vectors pose a risk of consuming a large portion of the optimization ‘budget’ thus stalling the search. To manage this open issue we propose a classification-assisted framework for expensive optimization problems, that is, where candidate vectors are classified in a pre-evaluation stage whether they are defined or not. We describe: a) a baseline single-classifier framework (no undefined vectors in the model) b) a non-classification assisted framework (undefined vectors in the model) and c) an extension of the classifier-assisted framework to a multi-classifier setup. Performance analysis using a test problem of airfoil shape optimization shows: a) the classifier-assisted framework obtains a better solution compared to the non-classification assisted one and b) the classifier can data-mine the accumulated information to provide new insights into the problem being solved.