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A global optimization method has been developed for an engine simulation code and utilized in the search of optimal fuel injection strategies. This method uses a Lagrange interpolation function which interpolates engine output data generated at the vertices and the intermediate points of the input parameters. This interpolation function is then used to find a global minimum over the entire parameter set, which in turn becomes the starting point of a CFD-based optimization. The CFD optimization is based on a steepest descent method with an adaptive cost function, where the line searches are performed with a fast-converging backtracking algorithm. The adaptive cost function is based on the penalty method, where the penalty coefficient is increased after every line search. The parameter space is normalized and, thus, the optimization occurs over the unit cube in higher-dimensional space.

Optimal fuel injection strategies are obtained with a micro-genetic algorithm and an adaptive gradient method for a nonroad, medium-speed DI diesel engine equipped with a multi-orifice, asynchronous fuel injection system. The gradient optimization utilizes a fast-converging backtracking algorithm and an adaptive cost function which is based on the penalty method, where the penalty coefficient is increased after every line search. The micro-genetic algorithm uses parameter combinations of the best two individuals in each generation until a local convergence is achieved, and then generates a random population to continue the global search. The optimizations have been performed for a two pulse fuel injection strategy where the optimization parameters are the injection timings and the nozzle orifice diameters.