Multi-mesh multi-objective optimization with application to a model problem in urban design

TL;DR

This paper introduces a multi-mesh finite element approach for optimizing urban settlement layouts, balancing wind flow and view considerations efficiently without extensive mesh regeneration.

Contribution

It develops a multi-mesh finite element methodology for multi-objective urban layout optimization, integrating wind flow modeling and view assessment.

Findings

Efficient evaluation of multiple settlement configurations.

Effective multi-objective optimization balancing wind and view.

Mesh generation costs are significantly reduced.

Abstract

We present an application of multi-mesh finite element methods as part of a methodology for optimizing settlement layouts. By formulating a multi-objective optimization problem, we demonstrate how a given number of buildings may be optimally placed on a given piece of land with respect to both wind conditions and the view experienced from the buildings. The wind flow is modeled by a multi-mesh (cut finite element) method. This allows each building to be embedded in a boundary-fitted mesh which can be moved freely on top of a fixed background mesh. This approach enables a multitude of settlement layouts to be evaluated without the need for costly mesh generation when changing the configuration of buildings. The view is modeled by a measure that takes into account the totality of unobstructed view from the collection of buildings, and is efficiently computed by rasterization.