Binary Multiagent Coordination Optimization with application to formation control design

In this paper, a novel binary swarm optimization algorithm, called Binary Multiagent Coordination Optimization (BMCO) algorithm, is proposed by introducing a communication topology for the particles in the algorithm and using recently developed multiagent consensus protocols from control theory. Due to the consensus term embedded into the update formula for the velocity, the BMCO algorithm shows a faster convergence rate than the standard Binary Particle Swarm Optimization (BPSO). We use eight benchmark functions to test the performance of the standard BPSO, BMCO, and a variation of BPSO called Novel BPSO (NBPSO). The optimal values and convergence rates of these three algorithms are provided and compared. From the numerical results, we can conclude that the performance of the BMCO algorithm is superior to that of BPSO and NBPSO. Next, as an application, we use the proposed algorithm to solve a topology optimization problem for an observer-based multiagent formation control design. In the existing literature, the topologies for positions and velocities of multiple agents are always assumed to be the same. However, in our proposed formation control protocol, these two topologies are not necessarily the same, not even all connected. To this extent, designing optimal heterogeneous topologies for the formation control protocol under the tradeoff between communication cost and operation time can be formulated as a binary optimization problem. Finally, A numerical illustration is provided by comparing the three binary algorithms to solve the topology optimization problem for multiagent formation control, and the BMCO algorithm shows the best result compared with BPSO and NBPSO.