Deep Learning the Efficient Frontier of Convex Vector Optimization Problems

TL;DR

This paper introduces a neural network approach to efficiently approximate the weakly efficient frontier in convex vector optimization problems, providing accurate bounds and scalability to high-dimensional cases.

Contribution

The authors develop a novel neural network architecture that approximates the efficient frontier of CVOPs with error bounds, scalable to large problem sizes.

Findings

Effective approximation of the weakly efficient frontier in CVOPs

Maintains accuracy even in high-dimensional problems

Provides both inner and outer bounds with error estimates

Abstract

In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater's condition. The proposed machine learning methodology provides both an inner and outer approximation of the weakly efficient frontier, as well as an upper bound to the error at each approximated efficient point. In numerical case studies we demonstrate that the proposed algorithm is effectively able to approximate the true weakly efficient frontier of CVOPs. This remains true even for large problems (i.e., many objectives, variables, and constraints) and thus overcoming the curse of dimensionality.