Multi-Agent Global Optimization with Decision Variable Coupling

A cooperative, multi-agent global optimization problem is considered, where the global cost function is the sum of the agents' private, non-convex costs. In contrast to all previously considered setups, evaluating the private costs involves a global experiment, using a common instance of the decision vector. This is relevant when each agent can only control a part ('subvariable') of the decision vector, but its private cost is also affected by the other subvariables. A novel cooperative optimization method using Set Membership identification and consensus-based techniques is proposed, to make all agents agree on the next global decision vector to be tested. A trade-off between exploitation close to the best point found and exploration around the search set is achieved, even without explicitly sharing the private costs' information. Statistical tests show that the proposed distributed method is competitive with respect to a centralized one.