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This paper describes a simple, but effective sampling method for optimizingand learning a discrete approximation (or surrogate) of a multi-dimensionalfunction along a one-dimensional line segment of interest. The method does notrely on derivative information and the function to be learned can be acomputationally-expensive ``black box'' function that must be queried viasimulation or other means. It is assumed that the underlying function isnoise-free and smooth, although the algorithm can still be effective when theunderlying function is piecewise smooth. The method constructs a smoothsurrogate on a set of equally-spaced grid points by evaluating the truefunction at a sparse set of judiciously chosen grid points. At each iteration,the surrogate's non-tabu local minima and maxima are identified as candidatesfor sampling. Tabu search constructs are also used to promote diversification.If no non-tabu extrema are identified, a simple exploration step is taken bysampling the midpoint of the largest unexplored interval. The algorithmcontinues until a user-defined function evaluation limit is reached. Numerousexamples are shown to illustrate the algorithm's efficacy and superiorityrelative to state-of-the-art methods, including Bayesian optimization andNOMAD, on primarily nonconvex test functions.

LineWalker: Line Search for Black Box Derivative-Free Optimization and Surrogate Model Construction