# Multi-objective Pointer Network for Combinatorial Optimization

arXiv: https://arxiv.org/abs/2204.11860 · HTML: https://mlsanity.com/paper/2204.11860/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 25 Apr 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Deep Reinforcement Learning for Multi-objective Optimization](https://mlsanity.com/paper/1906.02386/) (2019)
- [Learn to Design the Heuristics for Vehicle Routing Problem](https://mlsanity.com/paper/2002.08539/) (2020)
- [Learning Heuristics over Large Graphs via Deep Reinforcement Learning](https://mlsanity.com/paper/1903.03332/) (2019)
- [A Comprehensive Survey on the Multiple Travelling Salesman Problem: Applications, Approaches and Taxonomy](https://mlsanity.com/paper/2102.12772/) (2021)

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

- [Learning to Insert for Constructive Neural Vehicle Routing Solver](https://mlsanity.com/paper/2505.13904/) (2025)

## Abstract (arXiv)

Multi-objective combinatorial optimization problems (MOCOPs), one type of complex optimization problems, widely exist in various real applications. Although meta-heuristics have been successfully applied to address MOCOPs, the calculation time is often much longer. Recently, a number of deep reinforcement learning (DRL) methods have been proposed to generate approximate optimal solutions to the combinatorial optimization problems. However, the existing studies on DRL have seldom focused on MOCOPs. This study proposes a single-model deep reinforcement learning framework, called multi-objective Pointer Network (MOPN), where the input structure of PN is effectively improved so that the single PN is capable of solving MOCOPs. In addition, two training strategies, based on representative model and transfer learning, respectively, are proposed to further enhance the performance of MOPN in different application scenarios. Moreover, compared to classical meta-heuristics, MOPN only consumes much less time on forward propagation to obtain the Pareto front. Meanwhile, MOPN is insensitive to problem scale, meaning that a trained MOPN is able to address MOCOPs with different scales. To verify the performance of MOPN, extensive experiments are conducted on three multi-objective traveling salesman problems, in comparison with one state-of-the-art model DRL-MOA and three classical multi-objective meta-heuristics. Experimental results demonstrate that the proposed model outperforms all the comparative methods with only 20% to 40% training time of DRL-MOA.