This paper introduces a bi-objective winner determination problem which is based on English auctions. Most models of combinatorial auctions (winner determination problem) do not allow the bidder to update his offer, due to the fact that these mechanisms are static. However in reality bidders are in rough competition while there is time for auction. In this work we give a mathematical formulation of the dynamic model of the bi-objective winner determination problem, where the objectives are: (i) maximization of the total income, (ii) maximization of the number of items sold. This problem is based on the English auction mechanism, which allows bidders to renew their bids until the end of the exercise period. Then the solution is proposed by giving an algorithm based on an hybridization of a metaheuristic with a fuzzy dominance relation. A numerical experimentation using this algorithm on simulated data gives rise to satisfactory results.