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#### Keywords

- System Dynamics; Mixed-Integer Nonlinear Optimization (2) (remove)

The System Dynamics (SD) methodology is a framework for modeling and simulating
the dynamic behavior of socioeconomic systems. Characteristic for the
description of such systems is the occurrence of feedback loops together with
stocks and flows. The mathematical equations that describe the system are
usually nonlinear. Therefore seemingly simple systems can show a nonintuitive,
nonpredictable behavior over time. Controlling a dynamical system means to
define a desired final state in which the system should be, and to specify
potential interventions from outside that should keep the system on the right
track. The central question is how to compute such globally optimal control for
a given SD model. We propose a branch-and-bound approach that is based on a
bound propagation method, primal heuristics, and spatial branching. We apply our
new SD-control method to a small System Dynamics model, that describes the
evolution of a social-economic system over time. We examine the problem of
steering this system on a sustainable consumption path.

We consider a system dynamics model that describes the effect of human activity on natural resources. The central stocks are the accumulated profit, the industry structures, and the water resources. The model can be controlled through two time-dependent parameters. The goal in this paper is to find a parameter setting that leads to a maximization of a performance index, which reflects both environmental and economic aspects. Thus, the goal is to identify the most sustainable stock of industry structures within the model's constraints and assumptions. In order to find a proven global optimal parameter set, we formulate the System Dynamics Optimization model as a mixed-integer nonlinear problem that is accessible for numerical solvers. Due to the dynamic structure of the model, certain steps of the solution process must be handled with greater care, compared to standard non-dynamic problems. We describe our approach of solving the industry structure model and present computational results. In addition, we discuss the limitations of the approach and next steps.