Bi-level game theoretic approach for robust design: A case study of path-generating four-bar

This study addresses the bi-level multi-objective optimization problems (MOP) that raise in robust design and optimization of engineering systems through establishing a state-of-the-art game theoretic scenario. A novel leader-follower decentralized decision-making scenario is proposed, leveraging the synergy of game theory, Robust Design Optimization (RDO), Monte Carlo Simulation (MCS), and Artificial Intelligence (AI). The proposed algorithm can be employed for optimum robust Pareto design of a wide range of dynamical systems. In order to achieve a robust design, both the mean and variance of each objective function are considered as players in a multi-agent game setting. In this approach, both Stackelberg and cooperative games are utilized to model the behaviors of the players. Genetic Programming (GP) meta-models are employed to capture the Stackelberg protocol between two levels specifically for constructing the follower's rational reaction set (RRS). Additionally, the Nash bargaining function is -utilize to model the cooperative behaviors among players in each level. The proposed approach is applied and demonstrated through a case study involving multi-objective robust design of planar four-bar linkages. In this manner, four objective functions are assigned to four players within the system. Each player is responsible for optimizing a specific objective criterion, namely the mean of tracking error (TE), variance of tracking error, mean of transmission angle and variance of transmission angle (TA) of the linkage. As a result, the four-objective optimization problem of mechanism is transformed into a single-objective robust synthesis problem. The comparisons of the results show a significant enhancement in the robust behavior of the linkage, while ensuring that deterministic criteria such as quality of motion and precision are preserved.