# MODRL/D-EL: Multiobjective Deep Reinforcement Learning with Evolutionary Learning for Multiobjective Optimization

arXiv: https://arxiv.org/abs/2107.07961 · HTML: https://mlsanity.com/paper/2107.07961/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 16 Jul 2021.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [Deep Reinforcement Learning for Multi-objective Optimization](https://mlsanity.com/paper/1906.02386/) (2019)
- [Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networking](https://mlsanity.com/paper/2005.11081/) (2020)
- [Learning to Solve Vehicle Routing Problems with Time Windows through Joint Attention](https://mlsanity.com/paper/2006.09100/) (2020)
- [Proximal Distilled Evolutionary Reinforcement Learning](https://mlsanity.com/paper/1906.09807/) (2019)
- [Safe Mutations for Deep and Recurrent Neural Networks through Output Gradients](https://mlsanity.com/paper/1712.06563/) (2017)
- [MODRL/D-AM: Multiobjective Deep Reinforcement Learning Algorithm Using Decomposition and Attention Model for Multiobjective Optimization](https://mlsanity.com/paper/2002.05484/) (2020)

## Built on by (most cited first, 8 of 8)

- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2310.15196/) (2023)
- [Pareto Set Learning for Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2501.06773/) (2025)
- [Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement](https://mlsanity.com/paper/2310.15195/) (2023)
- [A Survey on Learnable Evolutionary Algorithms for Scalable Multiobjective Optimization](https://mlsanity.com/paper/2206.11526/) (2022)
- [Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computation](https://mlsanity.com/paper/2506.08898/) (2025)
- [Context-aware Diversity Enhancement for Neural Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2405.08604/) (2024)

## Abstract (arXiv)

Learning-based heuristics for solving combinatorial optimization problems has recently attracted much academic attention. While most of the existing works only consider the single objective problem with simple constraints, many real-world problems have the multiobjective perspective and contain a rich set of constraints. This paper proposes a multiobjective deep reinforcement learning with evolutionary learning algorithm for a typical complex problem called the multiobjective vehicle routing problem with time windows (MO-VRPTW). In the proposed algorithm, the decomposition strategy is applied to generate subproblems for a set of attention models. The comprehensive context information is introduced to further enhance the attention models. The evolutionary learning is also employed to fine-tune the parameters of the models. The experimental results on MO-VRPTW instances demonstrate the superiority of the proposed algorithm over other learning-based and iterative-based approaches.