Developing a Multi-Objective Game Theoretic Design of Path-Generating Planar Mechanism

This article addresses the bi-level multi-objective optimization problems raised in reliability-based robust design optimization of mechanism synthesis through establishing a state-of-the-art game theoretic scenario. A novel bi-level decentralized decision-making approach is proposed using the synergy of reliability-based robust design optimization (RBRDO), Stackelberg/cooperative game theory, Monte Carlo simulation (MCS) and genetic programming (GP). The application of the proposed approach is elaborated in a case-study of multi-objective robust synthesis of high-speed path generating four-bar. The four performance criteria, namely, accuracy (), robustness ( and ), reliability () at upper level and quality of motion () at lower level are assigned to four players so that each of whom is in charge of one objective criterion being optimized. The peak input driving torque as the dynamic constraint is associated with the upper-level problem. The genetic programming (GP) metamodel is used to capture the Stackelberg protocol between two levels i.e., constructing the follower’s rational reaction set (RRS) and the Nash arbitration scheme is hired to model the cooperative behaviors in upper level. By this way, the four-objective optimization problem of four-bar linkage is reduced into a single-objective robust design problem. The obtained results show a considerable enhancement in reliability and robust behavior of mechanism, whilst the deterministic criteria of accuracy and quality of motion is preserved.