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Generating diverse objects (e.g., images) using generative models (such asGAN or VAE) has achieved impressive results in the recent years, to help solvemany design problems that are traditionally done by humans. Going beyond imagegeneration, we aim to find solutions to more general design problems, in whichboth the diversity of the design and conformity of constraints are important.Such a setting has applications in computer graphics, animation, industrialdesign, material science, etc, in which we may want the output of the generatorto follow discrete/combinatorial constraints and penalize any deviation, whichis non-trivial with existing generative models and optimization solvers. Toaddress this, we propose GenCO, a novel framework that conducts end-to-endtraining of deep generative models integrated with embedded combinatorialsolvers, aiming to uncover high-quality solutions aligned with nonlinearobjectives. While structurally akin to conventional generative models, GenCOdiverges in its role - it focuses on generating instances of combinatorialoptimization problems rather than final objects (e.g., images). This shiftallows finer control over the generated outputs, enabling assessments of theirfeasibility and introducing an additional combinatorial loss component. Wedemonstrate the effectiveness of our approach on a variety of generative taskscharacterized by combinatorial intricacies, including game level generation andmap creation for path planning, consistently demonstrating its capability toyield diverse, high-quality solutions that reliably adhere to user-specifiedcombinatorial properties.

GenCO: Generating Diverse Solutions to Design Problems with Combinatorial Nature