Rethinking Neural Multi-Objective Combinatorial Optimization via Neat Weight Embedding
Authors: Jinbiao Chen, Zhiguang Cao, Jiahai Wang, Yaoxin Wu, Hanzhang Qin, Zizhen Zhang, Yue-Jiao Gong
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results on classic MOCO problems verified the superiority of our method. Remarkably, our method also exhibits favorable generalization performance across problem sizes, even outperforming the neural method specialized for boosting size generalization. |
| Researcher Affiliation | Academia | 1School of Computer Science and Engineering, Sun Yat-sen University, P.R. China 2School of Computing and Information Systems, Singapore Management University, Singapore 3Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, Sun Yat-sen University, P.R. China 4Guangdong Key Laboratory of Big Data Analysis and Processing, Guangzhou, P.R. China 5Department of Industrial Engineering & Innovation Sciences, Eindhoven University of Technology 6Department of Industrial Systems Engineering & Management, National University of Singapore 7School of Computer Science and Engineering, South China University of Technology, P.R. China EMAIL, EMAIL EMAIL, EMAIL, EMAIL EMAIL, EMAIL |
| Pseudocode | Yes | C TRAINING ALGORITHM The training algorithm is provided in Algorithm 1. To train a unified model with cross-size generalization capability, we sample instances from various problem sizes (as in Line 7). |
| Open Source Code | Yes | All methods are executed on a machine with an RTX 3090 GPU and an Intel Xeon 4216 CPU. Our code is publicly available1. 1https://github.com/bill-cjb/WE |
| Open Datasets | Yes | We evaluate the proposed method on three classic MOCO problems that are studied in most neural MOCO literature, including the multi-objective traveling salesman problem (MOTSP) (Lust & Teghem, 2010), multi-objective capacitated vehicle routing problem (MOCVRP) (Zajac & Huber, 2021), and multi-objective knapsack problem (MOKP) (Ishibuchi et al., 2015) (see Appendix B for more details). Three common sizes are considered, i.e., n = 20/50/100 for MOTSP and MOCVRP, and n = 50/100/200 for MOKP. Instance generation For the M-objective TSP, the coordinates of each instance are sampled from uniform distribution on [0, 1]2M. Instance generation For Bi-CVRP, the coordinates of the depot and customers are sampled from uniform distribution on [0, 1]2. Instance generation The values and weight of each item are all sampled from uniform distribution on [0, 1]. |
| Dataset Splits | Yes | The model is trained over 200 epochs, with each epoch containing 100,000 randomly sampled instances. The batch size B is set to 64. ...We train a unified model across problem sizes n {20, 21, ..., 100} (except n {50, 51, ..., 200} for Bi-KP) for WE-CA, CNH, and PMOCO. For MORAM, we use the provided pretrained model. |
| Hardware Specification | Yes | All methods are executed on a machine with an RTX 3090 GPU and an Intel Xeon 4216 CPU. |
| Software Dependencies | No | The Adam (Kingma & Ba, 2015) optimizer with learning rate 10^-4 and weight decay 10^-6 is adopted. ...Our method directly inputs the weight vector into the deep model and learns weight-specific representations, which can easily tackle a batch of N weight vectors in mainstream deep learning frameworks such as Pytorch. |
| Experiment Setup | Yes | The model is trained over 200 epochs, with each epoch containing 100,000 randomly sampled instances. The batch size B is set to 64. The Adam (Kingma & Ba, 2015) optimizer with learning rate 10^-4 and weight decay 10^-6 is adopted. The N weight vectors are generated using the Das & Dennis (1998) method, with N set to 101 for M = 2 and 105 for M = 3. |