Pareto optimization with small data by learning across common objective spaces

Abstract

In multi-objective optimization, it becomes prohibitively difficult to cover the Pareto front (PF) as the number of points scales exponentially with the dimensionality of the objective space. The challenge is exacerbated in expensive optimization domains where evaluation data is at a premium. To overcome insufficient representations of PFs, Pareto estimation (PE) invokes inverse machine learning to map preferred but unexplored regions along the front to the Pareto set in decision space. However, the accuracy of the inverse model depends on the training data, which is inherently scarce/small given high-dimensional/expensive objectives. To alleviate this small data challenge, this paper marks a first study on multi-source inverse transfer learning for PE. A method to maximally utilize experiential source tasks to augment PE in the target optimization task is proposed. Information transfers between heterogeneous source-target pairs is uniquely enabled in the inverse setting through the unification provided by common objective spaces. Our approach is tested experimentally on benchmark functions as well as on high-fidelity, multidisciplinary simulation data of composite materials manufacturing processes, revealing significant gains to the predictive accuracy and PF approximation capacity of Pareto set learning. With such accurate inverse models made feasible, a future of on-demand human-machine interaction facilitating multi-objective decisions is envisioned.