# Efficiently Tackling Million-Dimensional Multiobjective Problems: A Direction Sampling and Fine-Tuning Approach

arXiv: https://arxiv.org/abs/2304.04067 · HTML: https://mlsanity.com/paper/2304.04067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 61 references that are in the map.
- First posted on arXiv 8 Apr 2023.

## Builds on (most cited first, 8 of 8)

- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization](https://mlsanity.com/paper/1701.00879/) (2017)
- [Seamlessly Unifying Attributes and Items: Conversational Recommendation for Cold-Start Users](https://mlsanity.com/paper/2005.12979/) (2020)
- [Thompson Sampling for High-Dimensional Sparse Linear Contextual Bandits](https://mlsanity.com/paper/2211.05964/) (2022)
- [Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)](https://mlsanity.com/paper/1910.04966/) (2019)
- [Manifold Interpolation for Large-Scale Multi-Objective Optimization via Generative Adversarial Networks](https://mlsanity.com/paper/2101.02932/) (2021)
- [Adaptive Operator Selection Based on Dynamic Thompson Sampling for MOEA/D](https://mlsanity.com/paper/2004.10874/) (2020)
- [Balancing Exploration and Exploitation for Solving Large-scale Multiobjective Optimization via Attention Mechanism](https://mlsanity.com/paper/2205.10052/) (2022)

## Abstract (arXiv)

We define very large-scale multiobjective optimization problems as optimizing multiple objectives (VLSMOPs) with more than 100,000 decision variables. These problems hold substantial significance, given the ubiquity of real-world scenarios necessitating the optimization of hundreds of thousands, if not millions, of variables. However, the larger dimension in VLSMOPs intensifies the curse of dimensionality and poses significant challenges for existing large-scale evolutionary multiobjective algorithms, rendering them more difficult to solve within the constraints of practical computing resources. To overcome this issue, we propose a novel approach called the very large-scale multiobjective optimization framework (VMOF). The method efficiently samples general yet suitable evolutionary directions in the very large-scale space and subsequently fine-tunes these directions to locate the Pareto-optimal solutions. To sample the most suitable evolutionary directions for different solutions, Thompson sampling is adopted for its effectiveness in recommending from a very large number of items within limited historical evaluations. Furthermore, a technique is designed for fine-tuning directions specific to tracking Pareto-optimal solutions. To understand the designed framework, we present our analysis of the framework and then evaluate VMOF using widely recognized benchmarks and real-world problems spanning dimensions from 100 to 1,000,000. Experimental results demonstrate that our method exhibits superior performance not only on LSMOPs but also on VLSMOPs when compared to existing algorithms.