The present paper deals with an optimization approach for long-lived transuranic isotopes transmutation carrying out in Accelerator Driven System (ADS). The proposed methods consider the distributions of actinides nuclear concentration in the charged fuel as optimization arguments. The time-evolution of isotopes nuclear concentration fits in a system of ordinary differential equations (ODE), that is considered as dynamical constraints. A gradient-based optimization algorithm is constructed for this system so that the overall reactivity is minimized. Moreover, constraints on robustness and value of effective multiplication factor are incorporated during numerical optimization. Initial nuclear concentration values giving the best results for transuranic isotopes burn-up are computed based on this approach. The paper includes calculation results of actinides nuclear concentration and percentage ratio change, as well as effective multiplication factor and accelerator current dynamics for such initial fuel charge.