Robustness of Multidimensional Optimization Outcomes: A General Approach and a Case Study

In multidimensional parameter optimization of complex systems, the preferred solution must also be robust to virtually inevitable perturbations and uncertainties. Having a conceptually simple and computationally facile metric that can help distinguish between candidate optimum solutions in a post processing step is useful. Motivated by free energy function in statistical physics, which evaluates a trade-off between entropy and enthalpy, here we introduce a novel statistical robustness metric that assesses robustness with respect to possible to inevitable uncertainties in the objective function values or optimal parameters. The metric is the expected value 〈E〉 of the objective function, evaluated using weighted samples in a box around each optimum. The width of the sample distribution is problem-specific. As a case study, the proposed robustness metric is employed to find the most robust optimal solution in 5-dimensional parameter space in the context of dielectric boundary optimization in atomistic modeling, relevant to computational drug discovery.