Filtration of particle debris is an important component of the polymer fiber melt-spinning process. The filter lifespan is determined by the pressure drop across the filter, which increases as debris accumulates inside the filtration medium. The cost of filter replacement is high, as is the cost of a loss of the finished fiber product due to debris inclusion in the spun fiber. We use a multiobjective genetic algorithm to examine the trade-off curve that evolves from these competing goals. A "blackbox" simulator models the debris deposition, and we choose filter porosity and pore diameter as the design variables. We provide numerical results and analysis for two sets of competing objectives.