Recent insights for better understanding the thermodynamic foundations of separation processes have renewed the interest in exploring energy-efficient distillation networks. Complex column networks have substantial potential for energy savings over conventional configurations. This article introduces a computational algorithm for synthesizing such complex energy-efficient networks. A robust feasibility criterion drives the selection of design specification and operating conditions. It will be shown that columns composed of sections whose liquid stage composition profiles have no gaps are realizable. To prove the rigor of design computations, numerous separation networks were synthesized and validated with the Aspen flowsheet simulator. By using our computational results as input, AspenPlus simulations converged in a few iterations. Our method builds on temperature collocation, a thermodynamically motivated search method for determining feasible operating conditions and design details for achieving the desired product targets. Our findings suggest that significant energy savings can be realized with rigorous complex networks synthesis for industrial separation problems. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 136-148, 2011