Simulation based optimization may use parametric runs or optimization techniques. We propose a hydraulic schematic for a multifunction multi-source solar system (MFMSYS) and we consider the area of the solar collector and the volume of the thermal storage tank as the parameters to be optimally sized for minimizing the total cost. An additional cost, which increases exponentially with the lack of thermal comfort, is introduced in the total cost function. The sizing is then an optimization without constraints problem. The running costs are estimated by dynamic simulation of the building and its associated solar system. The total cost function has a valley-like shape oriented almost along the volume of the storage tank. Consequently, the total cost is very little sensitive to changes in the volume of the storage tank. Although optimization techniques, such as Generalized Pattern Search-Particle Swarm Optimization (GPS-PSO) hybrid algorithm prove to correctly find the optimum set of parameters, they do not give information about the valley shape of the cost function around its minimum value. We adapted an optimization technique based on the Design of Experiments (DOE) to the sizing by simulation of MFMSYS. The method proves to be faster than GPS-PSO and gives the approximated shape of the cost function around the optimum point. The Hessian of this approximated cost function indicates the valley-shape form and allows choosing suboptimal values without significantly influencing the total cost. (C) 2011 Elsevier Ltd. All rights reserved.