# Graph-Based Modeling and Simulation of Complex Systems

## TL;DR

This paper introduces graph-based abstractions for modeling complex cyber-physical systems, enabling scalable optimization and simulation across diverse computing architectures through a Julia package.

## Contribution

It presents novel algebraic and computing graph abstractions that improve modeling, analysis, and simulation of complex systems in a scalable and flexible manner.

## Key findings

- The algebraic graph abstraction aids in optimization problem decomposition.
- The computing graph abstraction supports implementation of algorithms in distributed environments.
- The Julia package Plasmo.jl enables practical application of these abstractions.

## Abstract

We present graph-based modeling abstractions to represent cyber-physical dependencies arising in complex systems. Specifically, we propose an algebraic graph abstraction to capture physical connectivity in complex optimization models and a computing graph abstraction to capture communication connectivity in computing architectures. The proposed abstractions are scalable and are used as the backbone of a Julia -based software package that we call Plasmo.jl . We show how the algebraic graph abstraction facilitates the implementation, analysis, and decomposition of optimization problems and we show how the computing graph abstraction facilitates the implementation of optimization and control algorithms and their simulation in virtual environments that involve distributed, centralized, and hierarchical computing architectures.