This work evaluates different optimization algorithms for Computational Fluid Dynamics (CFD) simulations of engine combustion. Due to the computational expense of CFD simulations, emulators built with machine learning algorithms were used as surrogates for the optimizers.
Two types of emulators were used: a Gaussian Process (GP) and a weighted variety of machine learning methods called SuperLearner (SL). The emulators were trained using a dataset of 2048 CFD simulations that were run concurrently on a supercomputer. The Design of Experiments (DOE) for the CFD runs was obtained by perturbing nine input parameters using a Monte Carlo method. The CFD simulations were of a heavy duty engine running with a low octane gasoline-like fuel at a partially premixed compression ignition mode.
Ten optimization algorithms were tested, including types typically used in research applications. Each optimizer was allowed 800 function evaluations and was randomly tested 100 times. The optimizers were evaluated for the median, minimum, and maximum merits obtained in the 100 attempts. Some optimizers required more sequential evaluations, thereby resulting in longer wall clock times to reach an optimum.
The best performing optimization methods were particle swarm optimization (PSO), differential evolution (DE), GENOUD (an evolutionary algorithm), and Micro-Genetic Algorithm (GA). These methods found a high median optimum as well as a reasonable minimum optimum of the 100 trials. Moreover, all of these methods were able to operate with less than 100 successive iterations, which reduced the wall clock time required in practice.
Two methods were found to be effective but required a much larger number of successive iterations: the DIRECT and MALSCHAINS algorithms. A random search method that completed in a single iteration performed poorly in finding 1 Currently at Southwest Research Institute, San Antonio, Texas optimum designs, but was included to illustrate the limitation of highly concurrent search methods. The last three methods, Nelder-Mead, BOBYQA, and COBYLA, did not perform as well.