The phase field for fracture (PFF) model has gained prominence in fracture mechanics as a robust framework for simulating crack propagation in materials. It replaces sharp crack interfaces with a diffuse transition zone, making it well-suited for complex fracture problems, including crack initiation, branching, and coalescence. Accurate parameter identification in this model is essential to ensure that finite element analysis (FEA) simulation results match experimental observations and accurately predict material behavior under different loading conditions. Key parameters in the phase-field model, such as fracture toughness Gc length scale parameter lc, and material elasticity (E), control the accuracy of predictions. Incorrect parameters can lead to unrealistic crack paths or failure to replicate experimental results. Identifying these parameters is challenging due to the nonlinear and computationally expensive nature of the model. Metaheuristic optimization algorithms like particle swarm optimization (PSO) and enhanced JAYA (EJAYA) are powerful tools and effective in automatically identifying the fracture mechanics parameter by minimizing the difference between force–displacement experimental and simulated results. PSO is generally preferred for its superior handling of complex, multimodal search spaces and faster convergence. However, EJAYA provides a simpler and more robust alternative for less complex or computationally constrained problems. In the present work, a comparison between these two algorithms is investigated in detail such as computational cost, desired accuracy, and complexity of the parameter space. The results prove that proper algorithm selection is very much essential for inverse problems and that depends on the specific problem's requirements.