A mixed-integer nonlinear program (MINLP) algorithm to optimize catalyst turnover number (TON) and product yield by simultaneously modulating discrete variables - catalyst types - and continuous variables - temperature, residence time, and catalyst loading - was implemented and validated. Several simulated case studies, with and without random measurement error, demonstrate the algorithm robustness in finding optimal conditions in the presence of side reactions and other complicating nonlinearities. This algorithm was applied to the real-time optimization of a Suzuki-Miyaura cross-coupling reaction in an automated microfluidic reaction platform comprising a liquid handler, an oscillatory flow reactor, and an online LC/MS. The algorithm, based on a combination of branch and bound and adaptive response surface methods, identified experimental conditions that maximize TON subject to a yield constraint from a pool of eight catalyst candidates in just 60 experiments, considerably fewer than a previous version of the algorithm.