ParetoTransport improves design optimization by shaping solution distributions
ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Front
Machine Learning
Summary
Designing things with multiple goals often requires finding the best balance among those goals, which is called the Pareto front. The researchers focus on offline methods that must improve candidate solutions without trying them out again, pushing them closer to that ideal balance while spreading them evenly. They introduce ParetoTransport, a technique that guides a pre-trained model to shift entire groups of solutions toward the best trade-offs using a mathematical way of matching distributions. This approach helps control where and how solutions move toward the Pareto front, resulting in more balanced and higher-quality sets of designs.
multi-objective optimizationPareto frontoffline optimizationgenerative modelsflow-matchingWasserstein distancedistribution matchingmass transportpopulation-level guidance
Authors
Stephanie Holly, Sepp Hochreiter, Werner Zellinger
Abstract
Offline multi-objective optimization requires not only moving the objective vectors of candidate designs toward the Pareto front, but also distributing them effectively along it. Generative methods have recently emerged as a natural approach because they learn a distribution over feasible designs while allowing generation to be steered toward promising designs. Existing methods, however, largely retain classical sample-wise guidance strategies, leaving the distribution-level modeling capability of generative methods underused. We propose ParetoTransport, a training-free guidance method for pre-trained flow-matching models that explicitly specifies and refines a population-level distribution in objective space. ParetoTransport guides a flow-matching sampler to iteratively transport the empirical offline distribution toward the Pareto front, with Wasserstein matching to intermediate proxy distributions. This directly controls distributional displacement and mass allocation along the front. We establish a convergence result and demonstrate state-of-the-art performance on standard offline MOO benchmarks, extending recent evaluations beyond hypervolume to generational distance, inverted generational distance, and Wasserstein distance.