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Running stochastic simulation-optimization solvers on a testbed of diverse problem instances allows users to evaluate their empirical performance, but obtaining meaningful results requires executing many replications. When problem instances feature realistic simulators, the associated computational costs are often prohibitively expensive. Cheaper, synthetic problem instances generally fail to preserve essential aspects of simulators, and a solver’s performance on them may not be representative of its performance in practice. We propose a novel class of problem instance designed to imitate important features of simulation test problems and generate representative solver performance data at relatively low computational cost. We augment existing models predominantly used for emulation, namely, Gaussian processes, generalized lambda models, and kernel regression models, with an approximation of a Gaussian copula process. This adaptation facilitates efficient coordinated sampling across solutions (via common random numbers) and across solvers (via the sharing of sample-path functions) while keeping the number of user-specified parameters manageable. 

To characterize the “average” of a set of graphs, one can compute the sample Fr ́echet mean. We prove the following result: if we use the Hamming distance to compute distances between graphs, then the Fr ́echet mean of an ensemble of inhomogeneous random graphs is obtained by thresholding the expected adjacency matrix: an edge exists between the vertices i and j in the Fr ́echet mean graph if and only if the corresponding entry of the expected adjacency matrix is greater than 1/2. We prove that the result also holds for the sample Fr ́echet mean when the expected adjacency matrix is replaced with the sample mean adjacency matrix. This novel theoretical result has some significant practical consequences; for instance, the Fr ́echet mean of an ensemble of sparse inhomogeneous random graphs is the empty graph.