In this paper, the formulation of the constraint on heat transfer feasibility in the synthesis/design optimization of complex energy systems is discussed, with particular emphasis on the case in which the matching among the hot and cold thermal streams within the system is not defined a priori. The mathematical nature of the set of inequality constraints expressing the internal availability of thermal power at different temperature levels is examined and some examples are shown illustrating the way these constraints bound the feasible region of the search space and affect the hypersurface of the so-called optimum response surface, which results from considering a reduced number of degrees of freedom of the optimization problem. A brief discussion is also proposed about the choice of the algorithm and the variables for the optimization process. (C) 2011 Elsevier Ltd. All rights reserved.