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.