# R2 Indicator and Deep Reinforcement Learning Enhanced Adaptive Multi-Objective Evolutionary Algorithm

arXiv: https://arxiv.org/abs/2404.08161 · HTML: https://mlsanity.com/paper/2404.08161/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 5 of its 76 references that are in the map.
- First posted on arXiv 11 Apr 2024.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 5 of 5)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Deep Reinforcement Learning Based Parameter Control in Differential Evolution](https://mlsanity.com/paper/1905.08006/) (2019)
- [Learning adaptive differential evolution algorithm from optimization experiences by policy gradient](https://mlsanity.com/paper/2102.03572/) (2021)

## Built on by (most cited first, 3 of 3)

- [Toward Automated Algorithm Design: A Survey and Practical Guide to Meta-Black-Box-Optimization](https://mlsanity.com/paper/2411.00625/) (2024)
- [Meta-Black-Box Optimization with Ensemble Surrogate Modeling for Robustness-Accuracy Trade-off within SAEA](https://mlsanity.com/paper/2606.00862/) (2026)
- [Reinforcement learning to choose optimizers](https://mlsanity.com/paper/2609.01811/) (2026)

## Abstract (arXiv)

Choosing an appropriate optimization algorithm is essential to achieving success in optimization challenges. Here we present a new evolutionary algorithm structure that utilizes a reinforcement learning-based agent aimed at addressing these issues. The agent employs a double deep q-network to choose a specific evolutionary operator based on feedback it receives from the environment during optimization. The algorithm's structure contains five single-objective evolutionary algorithm operators. This single-objective structure is transformed into a multi-objective one using the R2 indicator. This indicator serves two purposes within our structure: first, it renders the algorithm multi-objective, and second, provides a means to evaluate each algorithm's performance in each generation to facilitate constructing the reinforcement learning-based reward function. The proposed R2-reinforcement learning multi-objective evolutionary algorithm (R2-RLMOEA) is compared with six other multi-objective algorithms that are based on R2 indicators. These six algorithms include the operators used in R2-RLMOEA as well as an R2 indicator-based algorithm that randomly selects operators during optimization. We benchmark performance using the CEC09 functions, with performance measured by inverted generational distance and spacing. The R2-RLMOEA algorithm outperforms all other algorithms with strong statistical significance (p<0.001) when compared with the average spacing metric across all ten benchmarks.