GenCO: Generating Diverse Solutions to Design Problems with Combinatorial Nature

Generating diverse objects (e.g., images) using generative models (such as GAN or VAE) has achieved impressive results in the recent years, to help solve many design problems that are traditionally done by humans. Going beyond image generation, we aim to find solutions to more general design problems, in which both the diversity of the design and conformity of constraints are important. Such a setting has applications in computer graphics, animation, industrial design, material science, etc, in which we may want the output of the generator to follow discrete/combinatorial constraints and penalize any deviation, which is non-trivial with existing generative models and optimization solvers. To address this, we propose GenCO, a novel framework that conducts end-to-end training of deep generative models integrated with embedded combinatorial solvers, aiming to uncover high-quality solutions aligned with nonlinear objectives. While structurally akin to conventional generative models, GenCO diverges in its role - it focuses on generating instances of combinatorial optimization problems rather than final objects (e.g., images). This shift allows finer control over the generated outputs, enabling assessments of their feasibility and introducing an additional combinatorial loss component. We demonstrate the effectiveness of our approach on a variety of generative tasks characterized by combinatorial intricacies, including game level generation and map creation for path planning, consistently demonstrating its capability to yield diverse, high-quality solutions that reliably adhere to user-specified combinatorial properties.