An algorithmic-evolutionary synthesis procedure is proposed for flexible heat exchanger networks(HEN) under multiple-periods of operation. After a feasible network is synthesized at each period, they are combined to form a feasible super network structure which requires maxi-mum energy recovery (MER) at each period and features minimum number of units(MNU). Beginning energy recovery(MER)at each period and features minimum number of units(MNU). Beginning with the initial feasible super network structure, all the super network structures can be enumerated to generate the minimum cost super network structure. The key steps in the procedure are constituted of must-matches searches at each period and path tracing/list processing constructions that allow not only combination of networks of each period but also development of super network structures adjacent to the initial super network structure in some sense, while keeping maximum energy recovery at each period and minimum number of units. Then a trade-off between MER and MNU is performed to strictly reduce objective function values. The constructions and procedures are rigorously established and effectiveness of the composite algorithm is demonstrated via several test problems. These tests show that the proposed approach can find the optimum networks for the known standard problems, and new MNU/MER networks are identified which to date have not been reported in the literature.