This paper devotes a new method in modeling and optimizing to handle the optimization of the XY positioning mechanism. The fitness functions and constraints of the mechanism are formulated via proposing a combination of artificial neural network (ANN) and particle swarm optimization (PSO) methods. Next, the PSO is hybridized with the grey wolf optimization, namely PSO-GWO, which is applied to three scenarios in handling the single objective function. In order to search the multiple functions for the mechanism, the multiobjective optimization genetic algorithm (MOGA) is applied to the last scenario. The achieved results showed that the fitness functions are well-formulated using the PSO-based ANN method. In the scenario 1, the stroke achieved by the PSO-GWO (1852.9842 μm) is better than that gained from the GWO (1802.8087 μm). In the scenarios 2, the stress gained from the PSO-GWO (243.3183 MPa) is lower than that achieved from the GWO (245.0401 MPa). In the scenario 3, the safety factor retrieved from the PSO-GWO (1.9767) is greater than that achieved from the GWO (1.9278). In the scenario 4, by using MOGA, the optimal results found that the stroke is about (1741.3 μm) and the safety factor is 1.8929. The prediction results are well-fitted with the numerical and experimental verifications. The results of this paper are expected to facilitate the synthesis and analysis of compliant mechanisms and related engineering designs.