Group testing involves screening a large scale population with low prevalence to have a binary characteristic (e.g. presence of disease, product defect, system error...) in groups. If a test on a group is negative, the entire group is classified as negative. Otherwise, at least one individual is positive, and the positive group is tested again either individually or in smaller groups. We study a non-adaptive two-dimensional design with equal size groups where each individual belongs to two different groups under imperfect tests and heterogeneous risk profiles. We consider a convex combination of misclassification error and expected number of tests based objective. We have proposes a quadratic set covering model with an exponential number of variables. To solve to studied problem, we have proposed a Branch-and-Price-and-Cut algorithm where the linear relaxation is solved with column-dependent-row generation and strengthened with clique and odd-hole separation procedures. The proposed approaches are under validation on randomly generated instances with up to 36 individuals.