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This paper presents a multi-fidelity RBF (radial basis function) surrogate-based optimization framework (MRSO) for computationally expensive multi-modal optimization problems when multi-fidelity (high-fidelity (HF) and low-fidelity (LF)) models are available. The HF model is expensive and accurate while the LF model is cheaper to compute but less accurate. To exploit the correlation between the LF and HF models and improve algorithm efficiency, in MRSO, we first apply the DYCORS (dynamic coordinate search algorithm using response surface) algorithm to search on the LF model and then employ a potential area detection procedure to identify the promising points from the LF model. The promising points serve as the initial start points when we further search for the optimal solution based on the HF model. The performance of MRSO is compared with 6 other surrogate-based optimization methods (4 are using a single-fidelity surrogate and the rest 2 are using multi-fidelity surrogates). The comparisons are conducted on a multi-fidelity optimization test suite containing 10 problems with 10 and 30 dimensions. Besides the benchmark functions, we also apply the proposed algorithm to a practical and computationally expensive capacity planning problem in manufacturing systems which involves discrete event simulations. The experimental results demonstrate that MRSO outperforms all the compared methods.

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Stability of queues is of fundamental importance in the application of queueing models. To establish the stability of a queue, one has to utilize a mathematical model to describe the evolution of the queue and then defines stability on the model. However, the types of stability are various according to their underlying processes. In this study, we survey the different underlying processes of a [Formula: see text] queue, classify the various types of stability and study the relations among them. Furthermore, from the viewpoint of sample-path, we propose a new result regarding the growth rate of the queue time when the traffic intensity equals 1.

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