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The Multi-points Expected Improvement criterion or $$q$$ -EI has recently been studied in batch-sequential Bayesian Optimization. This paper deals with a new way of computing $$q$$ -EI, without using Monte-Carlo simulations, through a closed-form formula. The latter allows a very fast computation of $$q$$ -EI for reasonably low values of $$q$$ typically, less than 10. New parallel kriging-based optimization strategies, tested on different toy examples, show promising results.

Fast Computation of the Multi-Points Expected Improvement with Applications in Batch Selection