# Multi-condition multi-objective optimization using deep reinforcement learning

arXiv: https://arxiv.org/abs/2110.05945 · HTML: https://mlsanity.com/paper/2110.05945/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 77 references that are in the map.
- First posted on arXiv 10 Oct 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [A review on Deep Reinforcement Learning for Fluid Mechanics](https://mlsanity.com/paper/1908.04127/) (2019)
- [Direct shape optimization through deep reinforcement learning](https://mlsanity.com/paper/1908.09885/) (2019)
- [Learning the aerodynamic design of supercritical airfoils through deep reinforcement learning](https://mlsanity.com/paper/2010.03651/) (2020)

## Built on by (most cited first, 6 of 6)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Generalization in Neural Networks: A Broad Survey](https://mlsanity.com/paper/2209.01610/) (2022)
- [Combining Multi-Objective Bayesian Optimization with Reinforcement Learning for TinyML](https://mlsanity.com/paper/2305.14109/) (2023)
- [Non-iterative generation of an optimal mesh for a blade passage using deep reinforcement learning](https://mlsanity.com/paper/2209.05280/) (2022)
- [Issues with Value-Based Multi-objective Reinforcement Learning: Value Function Interference and Overestimation Sensitivity](https://mlsanity.com/paper/2402.06266/) (2024)
- [Rethinking industrial artificial intelligence: a unified foundation framework](https://mlsanity.com/paper/2504.01797/) (2025)

## Abstract (arXiv)

A multi-condition multi-objective optimization method that can find Pareto front over a defined condition space is developed for the first time using deep reinforcement learning. Unlike the conventional methods which perform optimization at a single condition, the present method learns the correlations between conditions and optimal solutions. The exclusive capability of the developed method is examined in the solutions of a novel modified Kursawe benchmark problem and an airfoil shape optimization problem which include nonlinear characteristics which are difficult to resolve using conventional optimization methods. Pareto front with high resolution over a defined condition space is successfully determined in each problem. Compared with multiple operations of a single-condition optimization method for multiple conditions, the present multi-condition optimization method based on deep reinforcement learning shows a greatly accelerated search of Pareto front by reducing the number of required function evaluations. An analysis of aerodynamics performance of airfoils with optimally designed shapes confirms that multi-condition optimization is indispensable to avoid significant degradation of target performance for varying flow conditions.