(55g) A Novel Optimization Algorithm to Assess the Stress Relaxation Characteristics of Soft Materials

Determining parameter values of the Quasi Linear Viscoelastic (QLV) model is important for understanding the nonlinear viscoelastic behavior of soft biological materials. QLV parameters are evaluated by nonlinear regression of the model to data; however, currently used methodologies are confounded by multiple optima and other surface features that trap or divert searches. The search for the global optimum requires substantial human intervention. Further, the right values for stopping criteria thresholds on the objective function and decision variables (model parameters), or their iteration-to-iteration changes depends on a priori knowledge of the system. As a result, the coefficient values from nonlinear regression strongly depend on the initial guesses for parameters values and stopping criteria thresholds, and may not determine the global minimum, thus providing incorrect parametric values.

This work describes two novel techniques to avoid these problems. First, regression is initiated ?N? times from random initial values of the model coefficients. This novel multistart approach finds multiple minima, and when the number of starts is large enough, the best-of-N results has a high probability of representing the global optimum. Probability analysis has led to an equation that determines the necessary value of N, given the desired confidence that one of the best fraction of optima is to be discovered. Secondly, this work uses a single, novel stopping criterion which terminates optimization when the improvement in objective function is statistically insignificant relative to the variance in the data. The technique calculates the root-mean-squared (RMS) deviations from a randomly selected (RS) subset of the data at each iteration, and terminates optimization when the RMS-RS value shows no statistical improvement with iteration number. The single stopping criterion is scale independent, and requires no user values. The combined use of these two techniques solves the problem of finding and stopping at the [probable] global optimum without a priori knowledge.

Experimental results were obtained using porous composite scaffolds formed by etching the surface of poly (lactic-co-glycolic acid) (PLGA) membranes to produce nano scale surface features and adding chitosan-gelatin porous components by freeze drying. Samples were stretched by ?ramp and hold? experiments in hydrated conditions. Parametric values were obtained for the analytical form of the QLV model using a variety of optimization algorithms. The output obtained showed a 10-fold reduction in value of sum squared error for the multistart algorithm.