Akamatsu (2007a,b) proposed a new dynamic traffic congestion control scheme called tradable network permits, and demonstrated its efficiency properties for general road networks. To implement tradable permit markets, this paper proposes a novel auction mechanism with capacity control. This mechanism employs an evolutionary approach to achieve a dynamic system optimal allocation of network permits in a computationally efficient manner. We prove that the proposed mechanism has the following desirable properties: (i) truthful bidding is a dominant strategy for each user on each day and (ii) the permit allocation pattern under the mechanism converges to a dynamic system optimal allocation pattern.