Highly Active Anti-Retroviral Therapy (HAART) regimens are employed to control HIV infection for extended periods of time, but with significant monetary cost and toxic side-effects. To mitigate these difficulties while achieving a similar viral suppression, interruptions in treatment have been explored. In this paper, we use a multiscale model of HIV infection with drug-resistant mutant strains to optimize these treatment interruptions for maximal viral suppression and minimal drug intake. Specifically, a genetic algorithm is used to maximize the duration of viral load below detection limit (<;100 virions/mL), while minimizing the average maximal plasma drug concentration (C^max) for triple-drug HAART regimens with NFV, AZT, and 3TC. Five treatment regimens of increasing complexity are investigated and compared with that of two optimized continuous HAART. The optimized treatment schedules lead to similar viremia-free periods while achieving significant reduction in the amount of drug used.