Robust multi-objective metaheuristic optimization of Cr(III) electrodeposition on 42CrMo4 steel for energy-efficient wear resistance

Abstract Selecting a Cr(III) electrodeposition condition for 42CrMo4 steel is a conflicting engineering problem: the current–temperature region that improves surface finish does not necessarily minimize wear or electrical demand, while the preparation route that maximizes hardness can shift the preferred operating window. Here, this conflict is resolved through an AI-inspired robust multi-objective metaheuristic framework that converts the original experimental dataset into a five-objective decision problem coupling surface roughness, wear, specific energy consumption (SEC), Faradaic efficiency and preparation-level hardness. The measured current sweep at 40 $$^{\\circ }$$ C, temperature sweep at 50 A, Vickers microhardness data, Faradaic-efficiency trend and SEC trend are represented by shape-preserving cubic interpolation; roughness and wear are combined through an explicitly identified geometric reconstruction of the two orthogonal experimental sweeps because a full current–temperature factorial matrix was unavailable. Multi-objective particle swarm optimization (MOPSO), NSGA-II and multi-objective Harris hawks optimization (MOHHO) independently search the same decision space while every candidate is stress-tested under $$\\pm 2$$ A and $$\\pm 2~^{\\circ }$$ C perturbations. Despite their different exploration mechanisms, all three algorithms converge toward a consistent favorable domain, yielding a consensus compromise near 53.6 A and 39.7 $$^{\\circ }$$ C with diamond polishing, equivalent to a mean cathodic current density of about 53.6 A dm $$^{-2}$$ for the 1.0 dm $$^{2}$$ plated specimen area. The corresponding robust reconstructed responses are approximately 0.112 $$\\mu $$ m worst-case roughness, 4.29 mg worst-case wear and 91.3% minimum Faradaic efficiency, with a preparation-level mean hardness of about 1131 HV. Because the post-Pareto selector contains engineering preferences, this point is treated in the current manuscript as an equal-weight reference compromise rather than as a universal service optimum; explicit weight-priority and non-separable current–temperature interaction stress tests are reported below. The result solves the practical selection problem of choosing one defensible operating region when experimentally favorable conditions conflict across tribology, coating quality and process energy, while preserving a clear distinction between measured observations and post-experimental reconstructed responses.