CONSTRAINT HANDLING AND SIMPLEX INITIALIZATION STRATEGY FOR THE NELDER-MEAD SIMPLEX METHOD APPLIED TO THE MELTDOWN CALIBRATION PROBLEM

This paper proposes a strategy for constraint handling in the Nelder-Mead simplex method based on a lexicographic dominance operator. Once this operator is defined, constraint handling is naturally absorbed by the original method. Furthermore, a new initialization strategy is also presented based on the variables' bounds and the initial point. The proposed method is applied to the meltdown calibration problem, which is a parameter estimation of a physicochemical simulator of Electric Arc Furnaces. Numerical experiments on real-world scenarios are conducted, and the results show that the proposed modifications outperform the original version in 93% of runs in terms of feasibility and objective function value, evidencing the robustness of the proposed modifications.