This paper proposes a new algorithm for solving multidimensional optimization problems using filling curves. Our approach is based on the use of \(\alpha \) -dense filling curves but introducing an adaptive strategy. This strategy dynamically refines the search space by eliminating regions that are unlikely to contain the minimum value of the objective function. Conversely, areas with a higher potential to contain the minimum are explored more intensively. This can help improve the quality of solutions and the efficiency of calculations. The adaptive strategy makes it possible to reduce the initial optimization problem to the resolution of its dual problem with a reduced set of admissible solutions. Furthermore, we develop an optimization algorithm for the dual problem containing two subroutines: a first to find the starting point of the algorithm and a second to solve it. We apply this method to identify the seroprevalence and force of infection of the hepatitis A virus following the increase in the number of cases of infections in central-west Tunisia.