A sensitivity analysis indicator to adapt the shift length in a metaheuristic

Population based metaheuristics (e.g. Genetic Algorithm, Particle Swarm Optimization, ...) deal with a dichotomy between exploration (discover unexplored areas) and exploitation (dig around a good solution). The consequence is a wide exploration of the search space. A lot of information about the link between the objective function and the input variables is collected during the algorithm. Sensitivity analysis methods allow to transform this information in order to characterize the effect of an input variable on the objective function: linear impact, nonlinear impact, negligible impact. We propose to integrate a sensitivity analysis method in the optimization process in order to increase or decrease the shift length when offsetting a variable according to its behavior. The offset of a variable with a nonlinear impact has to be small in order to catch possible local optima of the objective function. On the contrary, the offset of a variable with a linear impact has to be high in order to move faster the variable toward its best position. A toy example is used to illustrate the interest of the method.