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Group testing is a screening strategy that involves dividing a populationinto several disjointed groups of subjects. In its simplest implementation,each group is tested with a single test in the first phase, while in the secondphase only subjects in positive groups, if any, need to be tested againindividually. In this paper, we address the problem of group testing design,which aims to determine a partition into groups of a finite population in sucha way that cardinality constraints on the size of each group and a constrainton the expected total number of tests are satisfied while minimizing a linearcombination of the expected number of false negative and false positiveclassifications. First, we show that the properties and model introduced byAprahmian et al. can be extended to the group test design problem, which isthen modeled as a constrained shortest path problem on a specific graph. Wedesign and implement an ad hoc algorithm to solve this problem. On instancesbased on Sant\'e Publique France data on Covid-19 screening tests, the resultsof the computational experiments are very promising.

Group design in group testing for COVID-19 : A French case-study