integrating differential evolution algorithm with modified hybrid ga for solving nonlinear optimal control problems

‎here‎, ‎we give a two phases algorithm based on integrating differential evolution (de) algorithm with modified hybrid genetic algorithm (mhga) for solving the associated nonlinear programming problem of a nonlinear optimal control problem‎. ‎in the first phase‎, ‎de starts with a completely random initial population where each individual‎, ‎or solution‎, ‎is a random matrix of control input values in time nodes‎. ‎after phase 1‎, ‎to achieve more accurate solutions‎, ‎we increase the number of time nodes‎. ‎the values of the associated new control inputs are estimated by linear or spline interpolations using the curves computed in the phase 1‎. ‎in addition‎, ‎to maintain the diversity in the population‎, ‎some additional individuals are added randomly‎. ‎next‎, ‎in the second phase‎, ‎mhga starts by the new population constructed by the above procedure and tries to improve the obtained solutions at the end of phase 1‎. ‎we implement our proposed algorithm on some well-known nonlinear optimal control problems‎. ‎the numerical results show the proposed algorithm can find almost better solution than other proposed algorithms‎.