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GenCO: Generating Diverse Designs with Combinatorial Constraints
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Proposes GenCO, a framework that trains deep generators (WGAN, VQVAE) end-to-end through differentiable combinatorial solvers so generated designs are guaranteed feasible and diverse, and optimizes nonlinear objectives.
Problem
Generating diverse, high-quality designs that must satisfy hard combinatorial constraints while matching a data distribution and optimizing nonlinear objectives; standard GANs/VAEs do not guarantee feasibility and post-hoc fixing hurts diversity.
Approach
Learn a generator over a latent cost/design space c that is mapped through a combinatorial solver g(c) to a provably feasible solution x; the generative (group) loss is computed on feasible solutions x rather than soft outputs, and the whole pipeline is trained end-to-end via differentiating through the solver.
Key results
- Zelda: GenCO (updated adversary) reaches 99.5% unique levels vs 52% for GAN + MILP fix, with GAN loss -10.10 vs 0.22.
- Warcraft: GenCO achieves SP loss 23.99 vs 36.45 for Ordinary GAN, with density 0.94 and coverage 0.93.
- Photonic: GenCO (reconstruction + objective) yields 100% unique solutions with average solution loss 0 and density 0.153 vs 30.6% unique for VQVAE + postprocess.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train the adversary jointly instead of keeping it fixed (ablation) | GenCO on Zelda game levels · Zelda game levels | % Unique: 0.22 -> 0.995 | Helped |
| Train the adversary jointly instead of keeping it fixed (ablation) | GenCO on Zelda game levels · Zelda game levels | Coverage: 0.98 -> 0.82 | Hurt |
| Include the shortest-path objective in training | Ordinary GAN on Warcraft maps · Warcraft maps | SP loss: 36.45 -> 23.99 | Helped |
| Include the shortest-path objective in training | Ordinary GAN on Warcraft maps · Warcraft maps | GAN loss: 0.6147 -> 0.6360 | Hurt |
| Add the semantic cost penalty | GAN on Warcraft maps · Warcraft maps | SP loss: 36.45 -> 35.61 | Helped |
| Add the semantic cost penalty | GAN on Warcraft maps · Warcraft maps | GAN loss: 0.6147 -> 0.8994 | Hurt |
| Set gamma to 1e-3 instead of 0 (ablation) | GenCO on Warcraft maps · Warcraft maps | SP loss: 36.45 -> 23.99 | Helped |
| Set gamma to 1e-3 instead of 0 (ablation) | GenCO on Warcraft maps · Warcraft maps | Density: 0.81 -> 0.94 | Helped |
| Increase gamma from 1e-3 to 5e-3 (ablation) | GenCO on Warcraft maps · Warcraft maps | SP loss: 23.99 -> 18.02 | Helped |
| Increase gamma from 1e-3 to 5e-3 (ablation) | GenCO on Warcraft maps · Warcraft maps | Density: 0.94 -> 0.49 | Hurt |
| Use reconstruction loss without objective loss (ablation) | GenCO VQVAE · Inverse photonic design | Average solution loss: 0 -> 1.155 | Hurt |
| Use reconstruction loss without objective loss (ablation) | GenCO VQVAE · Inverse photonic design | Coverage: 0.738 -> 0.693 | Hurt |
Surprising findings
- On Warcraft, a high solver-loss weight (gamma=1e-2) collapses generated maps to blank images with zero shortest-path cost, and density/coverage are counterintuitive for sparse discrete levels.
- Density and coverage metrics behave counterintuitively in sparse discrete settings, so GenCO scored lower on them in Zelda despite higher uniqueness and realism.
Limitations
- Requires differentiable solvers and an explicit mathematical representation of constraints; scalability and solver differentiability are bottlenecks.
- Cannot guarantee feasibility for constraints not explicitly encoded (e.g., fairness, desirable but unspecified properties).
- Density and coverage metrics are unreliable for sparse discrete domains; high objective weight causes degenerate outputs.
Experimental setup
Datasets: Zelda levels (50 human-crafted) Warcraft II terrain maps (10,000) photonic inverse design solutions (100)
Benchmarks: Zelda level generation Warcraft shortest-path map generation inverse photonic design
Metrics: % unique density coverage GAN loss shortest path loss Maxwell simulation solution loss
Baselines: GAN + MILP fix Ordinary GAN GAN + semantic loss VQVAE + postprocess
Builds on: Wasserstein GAN VQVAE SurCo differentiable MILP solvers
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