This work presents a hybrid stochastic-deterministic algorithm for optimal design of process flowsheets, i.e., finding the optimal design variables and operating conditions of multiple interconnected units using rigorous phenomenological chemical engineering models. Unlike previous studies that propose hybrid deterministic and stochastic algorithms in sequential and nested arrangements, the present work proposes a parallel configuration to perform the hybridization. The proposed hybrid algorithm combines a stochastic method (SM) with the deterministic Discrete-Steepest Descent Algorithm with Variable Bounding (DSDA-VB). The SM and DSDA-VB strategies interact in parallel by exchanging new feasible solutions identified by the SM and improved search bounds determined by the DSDA-VB. The proposed method is illustrated using a thermally coupled system and a sequence of reactive, extractive, and traditional distillation columns. The results indicate that the proposed algorithm outperforms the traditional Differential Evolution with Tabu List (DETL) algorithm, showing faster and improved convergence.