Space mapping-based optimization with the macroscopic limit of interacting particle systems

TL;DR

This paper introduces a space mapping-based optimization method that leverages the relationship between microscopic particle systems and their macroscopic PDE limits, enabling efficient optimization in complex bounded domains.

Contribution

The paper presents a novel algorithm that uses macroscopic PDE models to optimize microscopic particle systems, addressing challenges in direct microscopic optimization.

Findings

Validated with a toy problem allowing direct optimization

Successfully applied to evacuation dynamics

Optimized conveyor belt transportation with promising results

Abstract

We propose a space mapping-based optimization algorithm for microscopic interacting particle dynamics which are inappropriate for direct optimization. This is of relevance for example in applications with bounded domains such that the microscopic optimization is difficult. The space mapping algorithm exploits the relationship of the microscopic description of the interacting particle system and the corresponding macroscopic description as partial differential equation in the "many particle limit". We validate the approach with the help of a toy problem that allows for direct optimization. Then we study the performance of the algorithm in two applications. An evacuation dynamic is considered and the transportation of goods on a conveyor belt is optimized. The numerical results underline the feasibility of the proposed approach.