# UMOEA/D: A Multiobjective Evolutionary Algorithm for Uniform Pareto Objectives based on Decomposition

arXiv: https://arxiv.org/abs/2402.09486 · HTML: https://mlsanity.com/paper/2402.09486/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 70 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Revisiting Scalarization in Multi-Task Learning: A Theoretical Perspective](https://mlsanity.com/paper/2308.13985/) (2023)
- [Scalable Pareto Front Approximation for Deep Multi-Objective Learning](https://mlsanity.com/paper/2103.13392/) (2021)
- [Multi-Objective Graph Heuristic Search for Terrestrial Robot Design](https://mlsanity.com/paper/2107.05858/) (2021)
- [Pareto Domain Adaptation](https://mlsanity.com/paper/2112.04137/) (2021)
- [Pareto Navigation Gradient Descent: a First-Order Algorithm for Optimization in Pareto Set](https://mlsanity.com/paper/2110.08713/) (2021)
- [Optimization on Pareto sets: On a theory of multi-objective optimization](https://mlsanity.com/paper/2308.02145/) (2023)
- [MOEA/D with Uniformly Randomly Adaptive Weights](https://mlsanity.com/paper/1908.05383/) (2019)
- [Complexity iteration analysis for strongly convex multi-objective optimization using a Newton path-following procedure](https://mlsanity.com/paper/2004.02979/) (2020)
- [Multiobjective Optimization of Non-Smooth PDE-Constrained Problems](https://mlsanity.com/paper/2308.01113/) (2023)

## Built on by (most cited first, 1 of 1)

- [LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch](https://mlsanity.com/paper/2409.02969/) (2024)

## Abstract (arXiv)

Multiobjective optimization (MOO) is prevalent in numerous applications, in which a Pareto front (PF) is constructed to display optima under various preferences. Previous methods commonly utilize the set of Pareto objectives (particles on the PF) to represent the entire PF. However, the empirical distribution of the Pareto objectives on the PF is rarely studied, which implicitly impedes the generation of diverse and representative Pareto objectives in previous methods. To bridge the gap, we suggest in this paper constructing uniformly distributed Pareto objectives on the PF, so as to alleviate the limited diversity found in previous MOO approaches. We are the first to formally define the concept of ``uniformity" for an MOO problem. We optimize the maximal minimal distances on the Pareto front using a neural network, resulting in both asymptotically and non-asymptotically uniform Pareto objectives. Our proposed method is validated through experiments on real-world and synthetic problems, which demonstrates the efficacy in generating high-quality uniform Pareto objectives and the encouraging performance exceeding existing state-of-the-art methods. The detailed model implementation and the code are scheduled to be open-sourced upon publication.