Optimization and Optimal Control of Agent-Based Models

Agent-based models are computer models made up of agents that can exist in a finite number of states. The state of the system at any given time is determined by rules governing agents' interaction. The rules may be deterministic or stochastic. Optimization is the process of finding a solution that optimizes some value that is determined by simulating the model. Optimal control of an agent-based model is the process of determining a sequence of control inputs to the model that steer the system to a desired state in the most efficient way. In large and complex models, the number of possible control inputs is too large to be enumerated by computers; hence methods must be developed for use with these models in order to find solutions without searching the entire solution space. Heuristic algorithms have been applied to such models with some success. Such algorithms are discussed; case studies of examples from biology are presented. The lack of a standard format for agent-based models is a major issue facing the study of agent-based models; presentation as polynomial dynamical systems is presented as a viable option. Algorithms are adapted and presented for use in this framework.