The use of Surrogate-based optimization has become increasingly prevalent in the design of engineering systems. When using these optimization algorithms a major problem has been the choice of an adequate stopping criterion. The traditional goal of stopping criteria has been convergence to the optimum. But this is not very practical when each cycle (iteration) is very expensive and convergence is slow. In this paper we propose a stopping criterion to be used when continuing with one more cycle is justified only if it yields at least a specified improvement in the objective function. We develop this criterion for a variant of the Efficient Global Optimization (EGO) that maximizes the probability of improving the objective beyond a target, and where this target is adaptively set. The EGO with adaptive target (EGO-AT) is particularly suited for such a criterion, because it automatically estimates two important ingredients for the decision: What is a reasonable target for improvement in the next cycle, and what is the probability of achieving that target. The effectiveness of this stopping criterion is demonstrated for three analytic examples. For these examples it is shown that it is possible to combine the two ingredients in such a way that it leads to the correct decision about 70% of the time.
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