# GRIDS: Interactive Layout Design with Integer Programming

arXiv: https://arxiv.org/abs/2001.02921 · HTML: https://mlsanity.com/paper/2001.02921/

## Key facts

- Cited by 9 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 9 Jan 2020.

## Built on by (most cited first, 9 of 9)

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- [Graph4GUI: Graph Neural Networks for Representing Graphical User Interfaces](https://mlsanity.com/paper/2404.13521/) (2024)
- [From Fragment to One Piece: A Survey on AI-Driven Graphic Design](https://mlsanity.com/paper/2503.18641/) (2025)
- [Cross-Domain Document Layout Analysis Using Document Style Guide](https://mlsanity.com/paper/2201.09407/) (2022)
- [Adaptive 3D UI Placement in Mixed Reality Using Deep Reinforcement Learning](https://mlsanity.com/paper/2504.21731/) (2025)
- [Evolving Thematic Map Design in Academic Cartography: A Thirty-Year Study Based on Multilingual Journals](https://mlsanity.com/paper/2604.22539/) (2026)
- [StructLayoutFormer:Conditional Structured Layout Generation via Structure Serialization and Disentanglement](https://mlsanity.com/paper/2510.26141/) (2025)
- [LAPPI: Interactive Optimization with LLM-Assisted Preference-Based Problem Instantiation](https://mlsanity.com/paper/2512.14138/) (2025)

## Abstract (arXiv)

Grid layouts are used by designers to spatially organise user interfaces when sketching and wireframing. However, their design is largely time consuming manual work. This is challenging due to combinatorial explosion and complex objectives, such as alignment, balance, and expectations regarding positions. This paper proposes a novel optimisation approach for the generation of diverse grid-based layouts. Our mixed integer linear programming (MILP) model offers a rigorous yet efficient method for grid generation that ensures packing, alignment, grouping, and preferential positioning of elements. Further, we present techniques for interactive diversification, enhancement, and completion of grid layouts (Figure 1). These capabilities are demonstrated using GRIDS1, a wireframing tool that provides designers with real-time layout suggestions. We report findings from a ratings study (N = 13) and a design study (N = 16), lending evidence for the benefit of computational grid generation during early stages of design.