This study addresses the bi-level multi-objective optimization problems raised in reliability-based robust design optimization (RBRDO) of engineering applications through establishing a state-of-the-art game theoretic scenario. A novel bi-level decentralized decision-making approach is proposed using the synergy of RBRDO, game theory, Monte Carlo simulation (MCS), and genetic programming (GP). The application of the proposed approach is elaborated in a case study of robust synthesis of high-speed path-generating four-bar mechanisms. The four performance criteria, namely, accuracy (TE), robustness (TE and 2TE), reliability (fG) at the upper level, and quality of motion (TA) at the lower level are assigned to four players so that each of whom is in charge of one objective criterion. The peak input driving torque (TS) is associated with the upper-level problem. The GP meta-model is used to capture the Stackelberg protocol that is, constructing the follower’s rational reaction set (RRS) and the Nash bargaining function is hired to model the cooperative behavior. The obtained results show a considerable enhancement in reliability and robust behavior of mechanism, while the deterministic criteria of accuracy and quality of motion are preserved.
