The article "Efficient computation paths for the systematic analysis of sensitivities" by Paolo Greppi and Elisabetta Arato has been published in Computer Physics Communications Volume 184, Issue 1 (January 2013), Pages 79-85.
A systematic sensitivity analysis requires computing the model on all points of a multi-dimensional grid covering the domain of interest, defined by the ranges of variability of the inputs.
The issues to efficiently perform such analysis on algebraic models are handling solution failures within and close to the feasible region and minimizing the total iteration count. Scanning the domain in the obvious order is sub-optimal in terms of total iterations and is likely to cause many solution failures.
The problem of choosing a better order can be translated geometrically into finding Hamiltonian paths on certain grid graphs.
This work proposes two paths, one based on a mixed-radix Gray code and the other, a quasi-spiral path, produced by a novel heuristic algorithm. Some simple, easy-to-visualize examples are presented, followed by performance results for the quasi-spiral algorithm and the practical application of the different paths in a process simulation tool.