Scale‐invariant approach to multi‐criterion optimisation under uncertainty, with applications to optimal sensor placement, in particular, to sensor placement in environmental research

How, within a given budget, can we design a sensor network that would provide us with the largest amount of useful information? There are two important aspects to this question: (a) how to best distribute the sensors over the large area, i.e. how to best divide the area of interest into zones corresponding to different sensors, and (b) what is the best location of each sensor in the corresponding zone. There is some research on the first aspect to the problem. In this paper, we show that the second aspect can be naturally formalised as a particular case of a general problem of scale‐invariant multi‐criterion optimisation under uncertainty, and we provide a solution to this general problem. As an illustrative case study, we consider the selection of locations for the Eddy towers, an important micrometeorological instrument.