# GenCO: Generating Diverse Designs with Combinatorial Constraints

arXiv: https://arxiv.org/abs/2310.02442 · HTML: https://mlsanity.com/paper/2310.02442/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 59 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 30 of 34)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers](https://mlsanity.com/paper/2003.11657/) (2020)
- [Robust Scheduling with GFlowNets](https://mlsanity.com/paper/2302.05446/) (2023)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Vector Quantized Models for Planning](https://mlsanity.com/paper/2106.04615/) (2021)
- [Generative Layout Modeling using Constraint Graphs](https://mlsanity.com/paper/2011.13417/) (2020)
- [End to end learning and optimization on graphs](https://mlsanity.com/paper/1905.13732/) (2019)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Risk Bounds and Calibration for a Smart Predict-then-Optimize Method](https://mlsanity.com/paper/2108.08887/) (2021)
- [Backpropagation through Combinatorial Algorithms: Identity with Projection Works](https://mlsanity.com/paper/2205.15213/) (2022)
- [Efficient Generation of Structured Objects with Constrained Adversarial Networks](https://mlsanity.com/paper/2007.13197/) (2020)
- [What game are we playing? End-to-end learning in normal and extensive form games](https://mlsanity.com/paper/1805.02777/) (2018)
- [Graph Transformer GANs for Graph-Constrained House Generation](https://mlsanity.com/paper/2303.08225/) (2023)
- [Video Game Level Repair via Mixed Integer Linear Programming](https://mlsanity.com/paper/2010.06627/) (2020)

## Built on by (most cited first, 3 of 3)

- [Logic Tensor Network-Enhanced Generative Adversarial Network](https://mlsanity.com/paper/2601.03839/) (2026)
- [Latent Spherical Flow Policy for Reinforcement Learning with Combinatorial Actions](https://mlsanity.com/paper/2601.22211/) (2026)
- [Generate in the Chart, Not on the Boundary: Function-Symbol Grounding for Hard Constraints in LTN-GANs](https://mlsanity.com/paper/2608.21605/) (2026)

## Abstract (arXiv)

Deep generative models like GAN and VAE have shown impressive results in generating unconstrained objects like images. However, many design settings arising in industrial design, material science, computer graphics and more require that the generated objects satisfy hard combinatorial constraints or meet objectives in addition to modeling a data distribution. To address this, we propose GenCO, a generative framework that guarantees constraint satisfaction throughout training by leveraging differentiable combinatorial solvers to enforce feasibility. GenCO imposes the generative loss on provably feasible solutions rather than intermediate soft solutions, meaning that the deep generative network can focus on ensuring the generated objects match the data distribution without having to also capture feasibility. This shift enables practitioners to enforce hard constraints on the generated outputs during end-to-end training, enabling assessments of their feasibility and introducing additional combinatorial loss components to deep generative training. We demonstrate the effectiveness of our approach on a variety of generative combinatorial tasks, including game level generation, map creation for path planning, and photonic device design, consistently demonstrating its capability to yield diverse, high-quality solutions that verifiably adhere to user-specified combinatorial properties.