# Multi-Objective Graph Heuristic Search for Terrestrial Robot Design

arXiv: https://arxiv.org/abs/2107.05858 · HTML: https://mlsanity.com/paper/2107.05858/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2021.

## Built on by (most cited first, 20 of 20)

- [An End-to-End Differentiable Framework for Contact-Aware Robot Design](https://mlsanity.com/paper/2107.07501/) (2021)
- [SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments](https://mlsanity.com/paper/2303.09555/) (2023)
- [GLSO: Grammar-guided Latent Space Optimization for Sample-efficient Robot Design Automation](https://mlsanity.com/paper/2209.11748/) (2022)
- [Dynamics-Guided Diffusion Model for Sensor-less Robot Manipulator Design](https://mlsanity.com/paper/2402.15038/) (2024)
- [BodyGen: Advancing Towards Efficient Embodiment Co-Design](https://mlsanity.com/paper/2503.00533/) (2025)
- [MORPH: Design Co-optimization with Reinforcement Learning via a Differentiable Hardware Model Proxy](https://mlsanity.com/paper/2309.17227/) (2023)
- [RoboMorph: Evolving Robot Morphology using Large Language Models](https://mlsanity.com/paper/2407.08626/) (2024)
- [Enhanced Multi-Objective A* Using Balanced Binary Search Trees](https://mlsanity.com/paper/2202.08992/) (2022)
- [RoboMoRe: LLM-based Robot Co-design via Joint Optimization of Morphology and Reward](https://mlsanity.com/paper/2506.00276/) (2025)
- [House of Dextra: Cross-embodied Co-design for Dexterous Hands](https://mlsanity.com/paper/2512.03743/) (2025)
- [Embodied Co-Design for Rapidly Evolving Agents: Taxonomy, Frontiers, and Challenges](https://mlsanity.com/paper/2512.04770/) (2025)
- [C^2:Co-design of Robots via Concurrent Networks Coupling Online and Offline Reinforcement Learning](https://mlsanity.com/paper/2209.06579/) (2022)
- [Shape Your Body: Value Gradients for Multi-Embodiment Robot Design](https://mlsanity.com/paper/2606.00702/) (2026)
- [Multi-objective Conflict-based Search Using Safe-interval Path Planning](https://mlsanity.com/paper/2108.00745/) (2021)
- [UMOEA/D: A Multiobjective Evolutionary Algorithm for Uniform Pareto Objectives based on Decomposition](https://mlsanity.com/paper/2402.09486/) (2024)
- [BRIDGE: An Open-Source Humanoid Platform via Morphology-Control Co-Design for Physical AI](https://mlsanity.com/paper/2609.03497/) (2026)
- [A Grammar for the Representation of Unmanned Aerial Vehicles with 3D Topologies](https://mlsanity.com/paper/2302.13980/) (2023)
- [Solving Vision Tasks with Simple Photoreceptors Instead of Cameras](https://mlsanity.com/paper/2406.11769/) (2024)
- [MOCHA: Multi-Objective Co-Design using Hypernetwork Architectures](https://mlsanity.com/paper/2609.30570/) (2026)
- [Co-design Gym: A Unified Benchmark for Embodiment-Policy Co-optimization](https://mlsanity.com/paper/2610.02366/) (2026)

## Abstract (arXiv)

We present methods for co-designing rigid robots over control and morphology (including discrete topology) over multiple objectives. Previous work has addressed problems in single-objective robot co-design or multi-objective control. However, the joint multi-objective co-design problem is extremely important for generating capable, versatile, algorithmically designed robots. In this work, we present Multi-Objective Graph Heuristic Search, which extends a single-objective graph heuristic search from previous work to enable a highly efficient multi-objective search in a combinatorial design topology space. Core to this approach, we introduce a new universal, multi-objective heuristic function based on graph neural networks that is able to effectively leverage learned information between different task trade-offs. We demonstrate our approach on six combinations of seven terrestrial locomotion and design tasks, including one three-objective example. We compare the captured Pareto fronts across different methods and demonstrate that our multi-objective graph heuristic search quantitatively and qualitatively outperforms other techniques.