Dynamic Partitioning for Balancing Exploitation and Exploration in Constrained Optimization: A Multi-Agent Approach
Diane C. Villanueva, Rodolphe Le Riche, Gauthier Picard, Raphael T. Haftka · 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2012
In this article, we define optimization subtasks that employ different approximations of the data in subregions through the choice of surrogate, which creates surrogate-based agents. Through design space partitioning, which assigns agents to subregions of the design space, the agents solve the optimization problem in their respective subregions, and use the feasibility and objective function value to assess the value of the solutions in order to center the subregions at local and global optima. Further, we introduce methods to create agents at run-time which allows additional exploration by creating a finer partition of the design space. The end result of this dynamic partitioning is a multi-agent system that inherently balances exploitation and exploration in the design space. We illustrate this approach on a constrained optimization problem with small, disconnected feasible regions. It was observed that the agents were effective at locating global and local optima. Nomenclature c = center f = objective function F = objective function values associated with design of experiments in database g = constraint G = constraint values associated with design of experiments in database t = time x = design variables X = design of experiments in database f ̂ = surrogate prediction of f g ̂ = surrogate prediction of g I.