This paper introduces a model and a structured procedure to optimize the shape and structure (relative sizes, aspect ratios) of a multi-effect humidification-dehumidification (MEH) desalination unit. The constructal approach is used for this investigation. Considering maximum production rate as the objective function, optimum design parameters of the MEH unit are derived by using the genetic algorithm method under the fixed total volume condition. The available volume is optimally distributed through the system so that the production rate is maximized. The results showed that the inlet cold and hot water temperatures and the column heights play important roles in the constructal design of a MEH unit, especially as the total volume increases. Moreover, the tube diameters and the number of condenser tubes should be suitably selected based on the values of the condenser, the humidifier inlet water temperatures and the column heights. The constructal principle invoked in this paper represents that geometrical form of systems can be deduced from a single principle and provides designers with tools for their conceptual design. (C) 2011 Elsevier B.V. All rights reserved.