An adaptive wavelet method for solving mixed-integer dynamic optimization problems with discontinuous controls and application to alkali–surfactant–polymer flooding

ABSTRACT This article presents an adaptive rationalized Haar function approximation method to solve dynamic optimization with mixed-integer and discontinuous controls. Three measures are taken to deal with the discontinuity. First, the problem is converted into a multi-stage optimization problem by non-uniform control vector parameterization. Secondly, an adaptive strategy is proposed to regulate the interval division and the order of Haar function vectors. Thirdly, a structure detection method is presented to refine the subintervals, in which adjacent arcs with the same input type are merged into one to modify redundant subintervals. During this approximation solution, the mixed-integer restriction is realized by the integer truncation strategy. Combined with the Hamiltonian function, a validation principle is shown to verify the optimality of the solution. Finally, the proposed method is applied to solve the enhanced oil recovery for alkali–surfactant–polymer flooding. The effectiveness of the method is illustrated through simulation.