Abstract
Efficient Global Optimization (EGO) is a popular method that searches sequentially for the global optimum of a simulated system. EGO treats the simulation model as a black-box, and balances local and global searches. In deterministic simulation, EGO uses ordinary Kriging (OK), which is a special case of universal Kriging (UK). In our EGO variant we use intrinsic Kriging (IK), which eliminates the need to estimate the parameters that quantify the trend in UK. In random simulation, EGO uses stochastic Kriging (SK), but we use stochastic IK (SIK). Moreover, in random simulation, EGO needs to select the number of replications per simulated input combination, accounting for the heteroscedastic variances of the simulation outputs. A popular selection method uses optimal computer budget allocation (OCBA), which allocates the available total number of replications over simulated combinations. We derive a new allocation algorithm. We perform several numerical experiments with deterministic simulations and random simulations. These experiments suggest that (1) in deterministic simulations, EGO with IK outperforms classic EGO; (2) in random simulations, EGO with SIK and our allocation rule does not differ significantly from EGO with SK combined with the OCBA allocation rule.
Highlights
Optimisation methods for black-box simulations – either deterministic or random – have many applications, as our references will demonstrate
We develop stochastic intrinsic Kriging (IK) (SIK) combined with the two-stage sequential algorithm developed by Quan et al (2013)
We introduce a new algorithm that differs from Quan et al.’s algorithm in two ways: (i) For the underlying metamodel, we use SIK instead of stochastic Kriging (SK). (ii) In the allocation stage, we use (23) instead of optimal computer budget allocation (OCBA) to distribute an additional number of replications to the old and new sampled points
Summary
Optimisation methods for black-box simulations – either deterministic or random – have many applications, as our references will demonstrate. In most operational research (OR) applications, a single simulation run is computationally inexpensive, but there are extremely many input combinations; e.g., a single-server queueing model may have one input (namely, the traffic rate) that is continuous, so we can distinguish infinitely many input values but in finite time, we can simulate only a fraction of these values In all these situations, it is common to use metamodels, which are called emulators or surrogates. We develop stochastic IK (SIK) combined with the two-stage sequential algorithm developed by Quan et al (2013) The latter algorithm accounts for heteroscedastic noise variances and balances two source of noise; namely, spatial uncertainty due to the metamodel and random variability caused by the simulation. In our numerical experiments we use test functions of different dimensionality, to study the differences between (1) EGO variants in deterministic simulation; (2) two-stage algorithm variants in random simulation.
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