Mathematics & Physics 2016, 9(1), 3–10 УДК 517.9 Collective Bionic Algorithm with Biogeography Based Migration Operator for Binary Optimization Shakhnaz A.Akhmedova∗ Eugene S. Semenkin† Department of System Analysis and Operation Research Reshetnev Siberian State Aerospace University Krasnoyarskiy Rabochiy, 31, Krasnoyarsk, 660037 Russia Received 26.11.2015, received in revised form 30.12.2015, accepted 25.01.2016 The meta-heuristic called Co-Operation of Biology Related Algorithms (COBRA) developed earlier for solving real-valued optimization problems has also been modified for solving optimization problems with binary variables (COBRA-b). <...> The algorithm COBRA-b is based on a collective work of five nature-inspired algorithms’ binary modifications such as Particle Swarm Optimization (PSO), the Wolf Pack Search Algorithm (WPS), the Firefly Algorithm (FFA), the Cuckoo Search Algorithm (CSA) and Bat Algorithm (BA). <...> Its usefulness and workability were demonstrated on various benchmarks, and COBRA-b also outperformed its components. <...> But solving problems sometimes required too many function evaluations, so the COBRA-b migration operator was modified by integrating biogeography principles for the speedup of the algorithm. <...> Numerical experiments showed that the new modification exhibits high performance and outperforms COBRA-b and therefore its components. <...> Introduction The Particle Swarm Optimization Algorithm (PSO) [1], the Wolf Pack Search Algorithm (WPS) [2], the Firefly Algorithm (FFA) [3], the Cuckoo Search Algorithm (CSA) [4] and the Bat Algorithm (BA) [5] are biology-related optimization techniques originally developed for continuous variable space. <...> These algorithms mimic the collective behaviour of corresponding animal groups that allows the global optima of real-valued functions of real variables to be found. <...> The mentioned heuristics were used for the developing of a new collective nature-inspired metaheuristic called Co-Operation of Biology Related Algorithms (COBRA) [6]. <...> For this purpose the binary modification of COBRA namely COBRA-b was developed [7]. <...> Experiments showed that the COBRA-b method works successfully and reliably but much slowlier than the original COBRA for the same problems with a smaller success rate obtained [8]. <...> Biogeography-based optimization (BBO) [9] is an evolutionary algorithm that optimizes a function <...>