The tuned mass damper inerter is becoming a well-recognized device for reducing building vibrations. However, connecting it to different floors may pose architectural and practical challenges. To overcome this limitation, the dual tuned mass damper inerter (DTMDI) system is investigated for controlling a 10-story benchmark building with 2% inherent damping, where the TMDI mass is variably distributed between two auxiliary masses and the mechanical inerter terminals are connected to two masses of a double tuned mass damper. An optimization process is carried out to find the optimal frequency ratio, damping ratio, and mass ratio of the absorbers with the aim of minimizing the infinity norm of the transfer function of floor drifts. Genetic Algorithm as an evolutionary method, Particle Swarm Optimization as the most popular swarm intelligent method, along with the recently developed Escaping Bird Search, are customized for the current problem. Comparison of the results indicates a significant superiority of EBS in convergence rate and quality of the mean results about 40% among the treated cases, and its capability to escape from local optima. After optimal design of the control systems, behavioral comparison of a single-inerter system with the secondary terminal connected to different floors and the proposed DTMDI system reveals the superior performance of the proposed configuration under a set of far-field and near-field ground motions including forward directivity and fling-step effects.