Escaping Local Optima in a Class of Multi-Agent Distributed Optimization Problems: A Boosting Function Approach

We address the problem of multiple local optima commonly arising in optimization problems for multi-agent systems, where objective functions are nonlinear and nonconvex. For the class of coverage control problems, we propose a systematic approach for escaping a local optimum, rather than randomly perturbing controllable variables away from it. We show that the objective function for these problems can be decomposed to facilitate the evaluation of the local partial derivative of each node in the system and to provide insights into its structure. This structure is exploited by defining "boosting functions" applied to the aforementioned local partial derivative at an equilibrium point where its value is zero so as to transform it in a way that induces nodes to explore poorly covered areas of the mission space until a new equilibrium point is reached. The proposed boosting process ensures that, at its conclusion, the objective function is no worse than its pre-boosting value. However, the global optima cannot be guaranteed. We define three families of boosting functions with different properties and provide simulation results illustrating how this approach improves the solutions obtained for this class of distributed optimization problems

Active Learning of Gaussian Processes for Spatial Functions in Mobile Sensor Networks

This paper proposes a spatial function modeling approach using mobile sensor networks, which potentially can be used for environmental surveillance applications. The mobile sensor nodes are able to sample the point observations of an 2D spatial function. On the one hand, they will use the observations to generate a predictive model of the spatial function. On the other hand, they will make collective motion decisions to move into the regions where high uncertainties of the predictive model exist. In the end, an accurate predictive model is obtained in the sensor network and all the mobile sensor nodes are distributed in the environment with an optimized pattern. Gaussian process regression is selected as the modeling technique in the proposed approach. The hyperparameters of Gaussian process model are learned online to improve the accuracy of the predictive model. The collective motion control of mobile sensor nodes is based on a locational optimization algorithm, which utilizes an information entropy of the predicted Gaussian process to explore the environment and reduce the uncertainty of predictive model. Simulation results are provided to show the performance of the proposed approach. © 2011 IFAC