Tin-Smelting Parameter Optimization via an RBFN-Assisted Dynamic Multiobjective Approach

Abstract

Tin smelting in a top-blowing furnace is a key non-ferrous metallurgical process in which tin recovery, energy consumption, and the service life of the magnesia–chrome refractory lining are affected by strongly coupled operating variables. The degradation of the magnesia–chrome lining is associated with the combined effects of thermal shock, chemical attack by molten slag and metal, and mechanical wear caused by high-temperature, turbulent, and particle-laden flow during blowing, charging, and tapping operations. First-principles modeling is difficult under extreme thermochemical conditions, whereas experience-based adjustment lacks reproducibility and scalability. Existing surrogate-assisted evolutionary methods also suffer from approximation errors, unreliable constraint handling, and limited interpretability in dynamic, data-scarce industrial settings. To address these issues, this study proposes RAMOSTA, an RBFN-assisted dynamic multiobjective state transition algorithm for tin-smelting parameter optimization. The proposed method integrates radial basis function neural-network surrogate models for tin recovery, energy consumption, and refractory-lining degradation; an uncertainty-aware adaptive offset penalty strategy for conservative constraint handling; a Pareto-based dynamic state-transition optimizer for searching time-varying trade-offs with a limited number of real evaluations; and a hybrid-weight TOPSIS decision layer. The latter combines expert preferences derived using the fuzzy analytic hierarchy process (FAHP), which accounts for the relative importance and uncertainty of decision criteria, with objective weights calculated from Shapley values, which quantify the marginal contribution of each objective to the overall decision. Experiments on an industrial tin-smelting dataset compare RAMOSTA with NSGA-II, NSGA-III, MOEA/D, and C-TAEA using Pareto-front quality, constraint satisfaction, hypervolume, and inverted generational distance.