Due to the growing trend towards miniaturization, small-scale manufacturing processes have become widely used in various engineering fields to manufacture miniaturized products. These processes generally exhibit complex size effects, making the behavior of materials highly dependent on their geometric dimensions. As a result, accurate understanding and modeling of such effects are crucial for optimizing manufacturing outcomes and achieving high-performance final products. To this end, advanced gradient-enhanced plasticity theories have emerged as powerful tools for capturing these complex phenomena, offering a level of accuracy significantly greater than that provided by classical plasticity approaches. However, these advanced theories often require the identification of a large number of material parameters, which poses a significant challenge due to limited experimental data at small scales and high computation costs. The present paper aims at evaluating and comparing the effectiveness of various optimization techniques, including evolutionary algorithm, response surface methodology and Bayesian optimization, in identifying the material parameter of a recent flexible gradient-enhanced plasticity model developed by the authors. The paper findings represent an attempt to bridge the gap between advanced material behavior theories and their practical industrial applications, by offering insights into efficient and reliable material parameter identification procedures.