We describe how active feedback routines can be applied at a limited repetition rate (5 Hz) to optimize high-power (> 10 TW) laser interactions with clustered gases. Optimization of x-ray production from an argon cluster jet, using a genetic algorithm, approximately doubled the measured energy through temporal modification of the 150 mJ driving laser pulse. This approach achieved an increased radiation yield through exploration of a multi-dimensional parameter space, without requiring detailed a priori knowledge of the complex cluster dynamics. The optimized laser pulses exhibited a slow rising edge to the intensity profile, which enhanced the laser energy coupling into the cluster medium, compared to the optimally compressed FWHM pulse (40 fs). Our work suggests that this technique can be more widely utilized for control of intense pulsed secondary radiation from petawatt-class laser systems.