  Group testing is a screening strategy that involves dividing a population
into several disjointed groups of subjects. In its simplest implementation,
each group is tested with a single test in the first phase, while in the second
phase only subjects in positive groups, if any, need to be tested again
individually. In this paper, we address the problem of group testing design,
which aims to determine a partition into groups of a finite population in such
a way that cardinality constraints on the size of each group and a constraint
on the expected total number of tests are satisfied while minimizing a linear
combination of the expected number of false negative and false positive
classifications. First, we show that the properties and model introduced by
Aprahmian et al. can be extended to the group test design problem, which is
then modeled as a constrained shortest path problem on a specific graph. We
design and implement an ad hoc algorithm to solve this problem. On instances
based on Sant\'e Publique France data on Covid-19 screening tests, the results
of the computational experiments are very promising.
