Implementation of a trust region model management strategy in the DAKOTA optimization toolkit

Abstract

A trust region-based optimization method has been incorporated into the DAKOTA optimization software toolkit. This trust region approach is designed to manage surrogate models of the objective and constraint functions during the optimization process. In this method, the surrogate functions are employed in a sequence of optimization steps, where the original expensive objective and constraint functions are used to update the surrogates during the optimization process. This sequential approximate optimization (SAO) strategy is demonstrated on two test cases, with comparisons to optimization results obtained with a quasi-Newton method. For both test cases the SAO strategy exhibits desirable convergence trends. In the first test case involving a smooth function, the SAO strategy converges to a slightly better minimum than the quasi-Newton method, although it uses twice as many function evaluations. In the second test case involving a function with many local minima, the SAO strategy generally finds better local minima than does the quasi-Newton method. The performance of the SAO strategy on this second test case demonstrates the utility of using this optimization method on engineering optimization problems, many of which contain multiple local optima.