Surrogate-Model Accelerated Random Search algorithm for global optimization with applications to inverse material identification

Abstract

An optimization algorithm is proposed which is applicable for the global optimization of computationally expensive functions with specific applications in material identification. The methodology, referred to as the Surrogate-Model Accelerated Random Search (SMARS) algorithm, is a non-gradient based iterative application of a random search algorithm and the surrogate-model method for optimization. The random search algorithm drives the global search portion of SMARS, thoroughly probing the search space to find optimal regions. The surrogate-model method then applies an artificial neural network to map local regions of the search space, and produce computationally inexpensive estimates to the solution, thereby accelerating the search. Through simulated examples, the SMARS algorithm is shown to be both robust and efficient. First, the minimization of a well known function with multiple local minima was considered to demonstrate the SMARS optimization capabilities with a known complex response surface. Then, two examples were considered for the inverse characterization of material properties. The identification of parameters of a rheological viscoelasticity model was considered first, and shows the SMARS algorithm’s tolerance to non-uniqueness over a large search space. Lastly, the identification of the distribution of thermal diffusivity for a functionally graded material was considered, and displays the SMARS capabilities to solve high-dimensional inverse problems. In all three examples, the performances of two traditional global search algorithms, a genetic algorithm and a random search algorithm, were compared to that of the SMARS algorithm. In all cases, the SMARS algorithm outperformed both traditional algorithms by attaining more accurate solutions with fewer function evaluations.