Heat exchanger networks are structures composed of a set of heat exchangers interconnected in order to reduce utilities consumption. During the network operation, heat exchangers may present a decrease of their thermal effectiveness caused by fouling, which corresponds to the undesirable accumulation of deposits over their thermal surface. In this context, this paper presents a proposal to increase the energy recovered in heat exchanger networks affected by fouling through the optimization of the distribution of the flow rates of the process streams. The problem corresponds to a dynamic optimization problem, because the flow rate optimization affects the surface temperature and velocity, which modifies the fouling rate, thus demanding the simultaneous analysis of the entire time horizon. The objective function is represented by the integral of the utility consumption during the operational time horizon. The main constraints include mass and energy balances, heat exchangers equations (P-NTU method), and fouling rate modeling. The mathematical structure of the problem corresponds to a nonlinear optimization. The utilization of the optimization scheme is illustrated by the analysis of two examples of heat exchanger networks.