In principle, I have no problem with random searches. Many government agencies use random searches, for example the IRS randomly audits people and customs randomly inspects cargo containers. However, I would impose two conditions.

1. It needs to be truly random, with no human input. The output of the machine that selects people should be plainly visible, so that there is no room for staff to manipulate it.

2. The additional search given to selectees should be constitutionally permissible for the general public. Being randomly selected does not constitute an elevated level of suspicion that justifies a more intensive search than what the doctrine of administrative search normally permits.