TY - JOUR
T1 - Koopman-based surrogate models for multi-objective optimization of agent-based systems
AU - Niemann, Jan-Hendrik
AU - Klus, Stefan
AU - Djurdjevac Conrad, Nataša
AU - Schütte, Christof
N1 - Funding Information:
This research has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy MATH+: The Berlin Mathematics Research Center (EXC-2046/1, project ID: 390685689).
Publisher Copyright:
© 2024 The Authors
PY - 2024/4
Y1 - 2024/4
N2 - Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend potentially nonlinearly on control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.
AB - Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend potentially nonlinearly on control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.
KW - Agent-based models
KW - Data-driven model reduction
KW - Koopman operator theory
KW - Multi-objective optimization
KW - Optimal control
KW - Social dynamics
UR - http://www.scopus.com/inward/record.url?scp=85183473740&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2024.134052
DO - 10.1016/j.physd.2024.134052
M3 - Article
SN - 0167-2789
VL - 460
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
M1 - 134052
ER -