tually achieves differs from the target mutation strength as adaptation is not instantaneous. The mutation strength that is achieved is too large for low noise levels, and too small for high noise levels. The performance loss as compared to optimally adapted mutation strengths has been found to be below 20% in the idealized model from Section VII and below about 30% in the improved model from Section VIII. In the presence of (not too much) noise, the larger than optimal mutation strengths have the advantage of reducing the noise-to-signal ratio that the strategy operates under. Of particular importance to the practitioner is the problem of choosing appropriate settings for the population size parameters. The investigation presented in this paper suggests that between 25% and 30% of the candidate solutions generated should be retained to serve as the population of the next time step. As for choosing how many candidate solutions to generate per time step, higher values buy additional robustness, i.e., the ability to proceed in the presence of higher levels of noise-at the price of decreased efficiency. Cumulative step length adaptation drives the mutation strength to zero if there is too much noise present. A useful course of action is therefore to start out with a relatively small number of candidate solutions to generate per time step, and to gradually increase that number if the strategy is observed to stall. The choice of values for and has been found to be rather uncritical. Overall, the performance of the (=; )-ES with cumulative step length adaptation is robust in that it degrades gradually with increasing noise levels. An empirical evaluation of direct optimization strategies in the presence of noise in [17] has shown that this is not necessarily true for other commonly used approaches, thus making the evolution strategy a promising candidate for the optimization of noisy objective functions.  REFERENCES Zhiyun Lin, Mireille Broucke, and Bruce Francis Abstract-The problem of achieving a specified formation among a group of mobile autonomous agents by distributed control is studied. If convergence to a point is feasible, then more general formations are achievable too, so the focus is on convergence to a point (the agreement problem). Three formation strategies are studied and convergence is proved under certain conditions. Also, motivated by the question of whether collisions occur, formation evolution is studied.
To handle the above mentioned challenges, we adopted the technique from REF , which addresses the problem of predicting group convergence of mobile autonomous agents.
Local control strategies for groups of mobile autonomous agents
IEEE Transactions on Automatic Control
IEEE Transactions on Automatic Control
Computer Science Mathematics