# Meta-Learning-Based Deep Reinforcement Learning for Multiobjective Optimization Problems

arXiv: https://arxiv.org/abs/2105.02741 · HTML: https://mlsanity.com/paper/2105.02741/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 62 references that are in the map.
- First posted on arXiv 6 May 2021.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (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)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learning](https://mlsanity.com/paper/2010.12367/) (2020)
- [Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/1911.09539/) (2019)
- [Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning](https://mlsanity.com/paper/2004.01608/) (2020)
- [Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2012.10638/) (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)
- [PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization](https://mlsanity.com/paper/1701.00879/) (2017)
- [Online 3D Bin Packing with Constrained Deep Reinforcement Learning](https://mlsanity.com/paper/2006.14978/) (2020)
- [Meta-Learning for Multi-objective Reinforcement Learning](https://mlsanity.com/paper/1811.03376/) (2018)
- [Combining Reinforcement Learning with Lin-Kernighan-Helsgaun Algorithm for the Traveling Salesman Problem](https://mlsanity.com/paper/2012.04461/) (2020)
- [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, 20 of 20)

- [Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillation](https://mlsanity.com/paper/2210.07686/) (2022)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [Algorithm Evolution Using Large Language Model](https://mlsanity.com/paper/2311.15249/) (2023)
- [Large Language Model for Multi-objective Evolutionary Optimization](https://mlsanity.com/paper/2310.12541/) (2023)
- [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)
- [Reinforcement Learning-based Non-Autoregressive Solver for Traveling Salesman Problems](https://mlsanity.com/paper/2308.00560/) (2023)
- [Constrained Multi-objective Optimization with Deep Reinforcement Learning Assisted Operator Selection](https://mlsanity.com/paper/2402.12381/) (2024)
- [Non-orthogonal Age-Optimal Information Dissemination in Vehicular Networks: A Meta Multi-Objective Reinforcement Learning Approach](https://mlsanity.com/paper/2402.12260/) (2024)
- [Context-aware Diversity Enhancement for Neural Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2405.08604/) (2024)
- [Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphs](https://mlsanity.com/paper/2506.22095/) (2025)
- [Be Bayesian by Attachments to Catch More Uncertainty](https://mlsanity.com/paper/2310.13027/) (2023)
- [Preference-Agile Multi-Objective Optimization for Real-time Vehicle Dispatching](https://mlsanity.com/paper/2604.10664/) (2026)
- [A general optimization solver based on OP-to-MaxSAT reduction](https://mlsanity.com/paper/2604.21961/) (2026)
- [WeCon: An Efficient Weight-Conditioned Neural Solver for Multi-Objective Combinatorial Optimization Problems](https://mlsanity.com/paper/2605.22876/) (2026)
- [NeurGO: Learning to Generate Elite Candidates for Meta-Black-Box Expensive Optimization](https://mlsanity.com/paper/2607.23408/) (2026)

## Abstract (arXiv)

Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to flexibly and efficiently deal with multiple subproblems determined by weight decomposition of objectives. This paper proposes a concise meta-learning-based DRL approach. It first trains a meta-model by meta-learning. The meta-model is fine-tuned with a few update steps to derive submodels for the corresponding subproblems. The Pareto front is then built accordingly. Compared with other learning-based methods, our method can greatly shorten the training time of multiple submodels. Due to the rapid and excellent adaptability of the meta-model, more submodels can be derived so as to increase the quality and diversity of the found solutions. The computational experiments on multiobjective traveling salesman problems and multiobjective vehicle routing problem with time windows demonstrate the superiority of our method over most of learning-based and iteration-based approaches.