Most combinatorial auction models (problem of winner determination ) does not allow the bidder to renew its offer that these mechanisms are static, however, in reality bidders are tough competition while it be left time for the auction. In this work we give the formulation of the dynamic model of the bi-objective winner determination problem, allowing bidders to renew their bids until the end of time allocated to the auction, based on the English auction mechanism. then we propose an algorithm of resolution based on hybridization of metaheuristic and exact methods, when fuzzy dominance relation is used for the comparison and classification of non-dominated solutions.