This article describes alternative GDP formulation and convex hull representations for process synthesis problems and their implementation in a unique MINLP process synthesizer MIPSYN. A special translation of variables in mixed-integer, relaxed, and logic-based variations has been proposed, which enables modeling and solving process alternatives in a narrowed lifted space of variables, defined by nonzero lower and upper bounds. Based on these translation variations, alternative formulations have been developed for convex hulls, multiple-term generalized disjunctive programming problems, and logic-based outer-approximation algorithm, all of them being specialized for the synthesis of process flowsheets. Several studies were performed and three different large-scale synthesis problems were solved to test the performance and efficiency of different formulations. This initial research indicates that the proposed alternative convex hull representation usually outperforms the conventional one when solving both MILP and NLP steps in highly combinatorial MINLP process networks problems. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 2896-2913, 2009