Multi-objective optimization, Bayesian benchmarking, and SHAP-guided explainability for hybrid abaca fibre/red mud/epoxy composites

Abstract

The concurrent demand for lightweight structural materials and industrial waste valorisation has intensified interest in hybrid natural fibre composites. This work presents a computational framework built on a response surface methodology (RSM) surrogate base with two parallel optimisation approaches for the design and multi-objective optimisation of hybrid abaca fibre /red mud/ epoxy composites targeting simultaneous maximisation of tensile, flexural, and impact strengths. This three-stage framework comprises an RSM surrogate base (Stage 1) feeding two parallel optimisation routes as a multi-objective genetic algorithm (MOGA)-driven multi-objective search (Stage 2) and a Bayesian-optimisation (BO) benchmark for evaluation-efficiency comparison (Stage 3), with a SHapley Additive exPlanations (SHAP) explainability layer applied across the surrogate models. At Stage 1, RSM was applied to a 33 full-factorial experimental dataset (ASTM D638/D790/D256) to develop second-order quadratic surrogate models achieving R2 ⩾ 88.77% across all mechanical responses. At Stage 2, a within three iterations (186 design evaluations) to a 70% Pareto front, yielding three candidate compositions, all at the upper abaca bound (Aw = 7.9 wt.%). Candidate Point 3 (Rw = 11.79%, Rp = 82.07 μm) achieved tensile strength 47.88 MPa, flexural strength 42.22 MPa, and impact strength 42.93 J m−1, validated experimentally within 6.00% error. Stage 3 (benchmarking): BO with Gaussian process surrogates and expected improvement acquisition identified a model-predicted candidate optimum in only 50 evaluations, reducing computational cost by 73%, demonstrating the feasibility of rapid-screening campaigns for related fibre systems. The BO result (+29.0% tensile strength relative to MOGA Candidate Point 3) is a Random Forest (RF) surrogate prediction and has not been experimentally validated. Complementing the optimisation, SHAP analysis of RF surrogate models trained on the RSM-MOGA surrogate dataset (CV R2 ⩾ 0.88) provides quantitative per-variable attribution of surrogate model predictions: red mud content (Rw) is the dominant tensile driver (mean |SHAP| = 6.40 MPa), while abaca content (Aw) governs both flexural (|SHAP| = 2.92 MPa) and impact (|SHAP| = 3.22 J m−1) responses, overturning the ranking produced by conventional linear sensitivity analysis and providing surrogate-model-level validation for the MOGA-optimal composition.