Response-Specific Surrogate Selection for Particle Swarm Optimization of End-Milling Parameters in AISI 1045 Steel

Background: When a small design-of-experiments dataset is used to optimize a machining process with particle swarm optimization (PSO), the regression model chosen as the fitness function is rarely validated against more than one candidate response, checked against alternative model families, or checked for the optimization that follows from using the same cross-validation score to both tune and report a model. Methods: We revisit 24 end-milling trials on AISI 1045 steel (fifteen one-factor-at-a-time runs plus a Taguchi L9 array; every value was independently verified against the underlying thesis records) in which cutting force, cutting-zone temperature, and X-ray diffraction residual stress were measured. A multiple linear regression (MLR), a quadratic response-surface model (RSM), a support vector regression (SVR), and a Gaussian process regression (GPR) were each cross-validated by nested leave-one-out cross-validation against every response, with bootstrap 95% confidence intervals and paired bootstrap significance tests on the resulting R2 values, as well as a variance-inflation-factor check on the combined design matrix. The best-validated model per response was then used inside an identical constricted-PSO routine, which was run across 30 random seeds per fitness function to assess the convergence stability. Results: Design collinearity was not a concern (all VIF ≤ 1.28). Under the nested validation, the response-specific pattern held for temperature and residual stress but not for cutting force: the SVR was the only model to beat the MLR by a margin that survived a paired bootstrap test (residual stress, P (SVR not better) = 0.02); for force, a quadratic RSM model outperformed all three other families (R2 = 0.72 vs. 0.39 for MLR and 0.28 for GPR), and the GPR’s earlier apparent advantage for force did not survive the leakage-free hyperparameter selection. The residual-stress PSO result was stable across seeds: 27 of 30 of the SVR-fitness runs converged to the same interior optimum (579.8 rpm, 40 mm/min, 0.413 mm; mean −472.5 MPa, SD 3.4 MPa), against a boundary optimum found deterministically by every MLR-fitness run (355 rpm, 40 mm/min, 0.5 mm, −434.6 MPa). The validated interior optimum also predicted a 55% lower cutting force and a slightly lower temperature at the same operating point. Conclusions: Whether a nonlinear surrogate should replace a linear one is response-specific and must be checked with a leakage-free validation scheme rather than assumed; for this dataset, that check overturns the original force-model recommendation while confirming the residual-stress result under both cross-model and multi-seed checks. The residual-stress optimum remains a model prediction pending physical confirmation.