Synthesizers can be used to replicate or approximate existing sounds. Not surprisingly, quality of synthesis depends on the selection of suitable synthesizer parameters. Optimization techniques such as genetic algorithms (GAs) have successfully been used to perform this task in the past. We build on previous work using GAs by examining how they can be used to estimate the parameters of a complex commercial synthesizer that contains several synthesis engines, effects and LFOs. A particular challenge associated with this synthesizer is that the sounds it produces are not fully deterministic. These traits make the parameter search space larger and more complex in comparison to previously studied synthesizers. In order to tackle this difficult problem we propose using a GA with multiple objectives. This approach makes it possible to handle the complexity of the problem and furthermore affords more flexibility to the user who receives a set of similar sounds rather than a single sound as with previous systems. In collaboration with the company that designed this synthesizer, we use a Non-dominated Sorting Genetic Algorithm-II to automatically tune the synthesizer parameters in order to approximate a given target sound. Our system has been validated with experimental measures for both contrived and non-contrived sounds.