The phase diagrams of complex fluids are essential for understanding solubility and miscibility, properties of central importance in polymer formulation. At a typical industrial resolution of 10 wt%, exhaustive exploration of a ternary phase diagram requires simulation or experimentation at 63 composition points, a number which grows exponentially with the number of components. Using a new objective function derived from Self-Consistent Field Theory (SCFT) computations coupled with a constrained Bayesian optimization algorithm, we demonstrate efficient search of phase boundaries in a sample two-phase ternary modeled by polymer SCFT with 50% fewer simulations than an exhaustive search. Our approach is general, gradient-free, and can be applied to either simulation or experimental campaigns.