Inverse Multiobjective Optimization by Generative Model Prompting

The integration of multiobjective optimizers with inverse models—that map points on the Pareto front to corresponding nondominated solutions—has drawn attention. These inverse models serve a dual purpose, not only facilitating the generation of candidate solutions during the optimization process, but also offering insights for multiobjective decision-making upon completion of optimization. However, today’s inverse models mainly serve to capture one-to-one mapping relations, restricting them to learn only from nondominated solution samples. As a result, the information embedded in dominated samples is not fully utilized. In this paper, we introduce a novel approach of building conditional inverse generative models (invGMs) from optimization data, making the most of both nondominated and dominated solution samples during training. Different from standard inverse models, decision-makers can query such invGMs with prompts expressed in the form of any desired objective function values, leading them to produce a corresponding solution. Through iterative prompting, invGMs are shown to accelerate the creation of diverse sets of high-quality solutions even during the course of multiobjective optimization runs. Empirical studies on three industrial optimization problems highlight the proposed method’s faster convergence rate and improved inverse modeling accuracy.