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Laser ablation is an effective process for forming vias in dielectric layers during the fabrication of multilayer substrates in microsystems packaging. In this paper, vias with diameters of 10-50 μm are ablated in DuPont Kapton E polyimide using an Anvik HexScan 2150 SXE excimer laser operating at 308 nm. A statistical experiment employing a 25-1 fractional factorial design is conducted to determine the significance of laser fluence, shot frequency, number of pulses, and the vertical and horizontal positions of the debris removal system on the ablated thickness of the dielectric, top via diameter, via wall angle, and via resistance. Resistance measurements on metal deposited in ablated vias are performed to characterize via quality. Neural networks (NNs) are trained using the error back-propagation algorithm to model the ablation process using the measurement data collected from the experiment. Genetic algorithms are then utilized in conjunction with the NN models to derive optimized process recipes for achieving target responses. The recipes identified are subsequently verified by experiment. These optimized recipes are found to improve ablation results by as much as 40% for the ablated film thickness, 30% for via diameter, 9% for via wall angle, and more than 100% for via resistance.