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GenCO: Generating Diverse Designs with Combinatorial Constraints

Aaron Ferber, Arman Zharmagambetov, Taoan Huang, Bistra Dilkina, Yuandong Tian

TL;DR

GenCO presents a unified framework that guarantees feasibility of generated designs under hard combinatorial constraints by training a deep generator to produce latent codes that map, via a differentiable solver, to feasible solutions. By optimizing a group loss over the solution set and an individual loss on solutions, GenCO achieves diverse, high-quality designs while accommodating nonlinear objectives. The approach is demonstrated across game level design, path planning maps, and inverse photonic design, where end-to-end training through differentiable solvers yields improved diversity and feasibility compared to traditional GAN/VAE baselines and postprocessing methods. This framework enables practical, constraint-satisfying design generation with broad applicability, though it hinges on differentiable solvers and explicit constraint representations and acknowledges broader deployment considerations such as fairness and privacy.

Abstract

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.

GenCO: Generating Diverse Designs with Combinatorial Constraints

TL;DR

GenCO presents a unified framework that guarantees feasibility of generated designs under hard combinatorial constraints by training a deep generator to produce latent codes that map, via a differentiable solver, to feasible solutions. By optimizing a group loss over the solution set and an individual loss on solutions, GenCO achieves diverse, high-quality designs while accommodating nonlinear objectives. The approach is demonstrated across game level design, path planning maps, and inverse photonic design, where end-to-end training through differentiable solvers yields improved diversity and feasibility compared to traditional GAN/VAE baselines and postprocessing methods. This framework enables practical, constraint-satisfying design generation with broad applicability, though it hinges on differentiable solvers and explicit constraint representations and acknowledges broader deployment considerations such as fairness and privacy.

Abstract

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.
Paper Structure (26 sections, 8 equations, 3 figures, 6 tables, 1 algorithm)

This paper contains 26 sections, 8 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Traditional constrained object generation
  4. Infeasibility penalization
  5. Optimization-based priors
  6. Enhacing combinatorial optimization with generative models
  7. GenCO: Method Description
  8. Assumptions
  9. Experiments
  10. Metrics
  11. Explicitly Constrained GAN: Game Level Design
  12. Baselines
  13. Results
  14. Uniqueness
  15. Map generation for path planning
  16. ...and 11 more sections

Figures (3)

  • Figure 1: GenCO diagram. A neural generator projects noise to a latent space which then gets used by a solver to generate provably feasible solutions. The solutions are then penalized with generative losses like Wasserstein distance (WGAN) or reconstruction (VQVAE) which can be backpropagated through the full pipeline. Additionally, GenCO can optimize individual objectives.
  • Figure 2: Generated zelda level examples. "GenCO Updated" obtains solutions that seem more realistic than the empty MILP postprocessed GAN levels and GenCO Fixed Adversary levels.
  • Figure 3: A subset of generated Warcraft map images. "Ordinary GAN" generates "very costly" maps (e.g. mountains, lakes) along the Shortest Path from top-left to bottom-right; "GAN + semantic loss" generates less costly maps but they are less diverse; GenCO: SP path is cheap and the map is diverse at the same time.