# Manifold Interpolation for Large-Scale Multi-Objective Optimization via Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2101.02932 · HTML: https://mlsanity.com/paper/2101.02932/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2021.

## Built on by (most cited first, 7 of 7)

- [Predictive GAN-powered Multi-Objective Optimization for Hybrid Federated Split Learning](https://mlsanity.com/paper/2209.02428/) (2022)
- [A Survey on Learnable Evolutionary Algorithms for Scalable Multiobjective Optimization](https://mlsanity.com/paper/2206.11526/) (2022)
- [Multi-View Subgraph Neural Networks: Self-Supervised Learning with Scarce Labeled Data](https://mlsanity.com/paper/2404.12569/) (2024)
- [Ask, Attend, Attack: A Effective Decision-Based Black-Box Targeted Attack for Image-to-Text Models](https://mlsanity.com/paper/2408.08989/) (2024)
- [Diffusion Model-Based Multiobjective Optimization for Gasoline Blending Scheduling](https://mlsanity.com/paper/2402.14600/) (2024)
- [Efficiently Tackling Million-Dimensional Multiobjective Problems: A Direction Sampling and Fine-Tuning Approach](https://mlsanity.com/paper/2304.04067/) (2023)
- [Analytical Discovery of Manifold with Machine Learning](https://mlsanity.com/paper/2504.02511/) (2025)

## Abstract (arXiv)

Large-scale multiobjective optimization problems (LSMOPs) are characterized as involving hundreds or even thousands of decision variables and multiple conflicting objectives. An excellent algorithm for solving LSMOPs should find Pareto-optimal solutions with diversity and escape from local optima in the large-scale search space. Previous research has shown that these optimal solutions are uniformly distributed on the manifold structure in the low-dimensional space. However, traditional evolutionary algorithms for solving LSMOPs have some deficiencies in dealing with this structural manifold, resulting in poor diversity, local optima, and inefficient searches. In this work, a generative adversarial network (GAN)-based manifold interpolation framework is proposed to learn the manifold and generate high-quality solutions on this manifold, thereby improving the performance of evolutionary algorithms. We compare the proposed algorithm with several state-of-the-art algorithms on large-scale multiobjective benchmark functions. Experimental results have demonstrated the significant improvements achieved by this framework in solving LSMOPs.