A modification of the self-tuning meta-heuristic, called Co-Operation of Biology Related Algorithms, for multiobjective optimization problems with binary variables (COBRA-bm) is introduced. Its basic idea consists of a cooperative work of five well-known bionic algorithms such as the Particle Swarm Optimization, the Wolf Pack Search, the Firefly Algorithm, the Cuckoo Search Algorithm and the Bat Algorithm, namely their versions for solving optimization problems with binary variables, with the use of Pareto optimality theory. The performance of the mentioned algorithms as well as COBRA-bm on the set of benchmark functions is reported. It was established that the proposed approach COBRA-bm performs either comparably or better than its component bionic algorithms and can be used instead any of them.