- Att-GCN+MCTS [6]#: an efficient L2P solver that generalizes heatmap-based L2P solvers to larger-scale TSP instances through divide-and-conquer. However, we encountered issues running their GPU-version code, and the CPU-version code appeared to be time-consuming, taking around 28h (10s/instance) for 10k TSP100. We thus opt to use their reported results directly.
- GNN+GLS [40]: an insightful L2P solver that uses GNN to predict regrets, thereby directing the traditional local search (relocate and 2-opt) heuristics for TSP. Regrettably, the code is not optimized for batch inference and we encountered some issues loading our datasets when following their instructions. As such, we opt to use their reported results directly.
- CVAE-Opt-DE [43]: a generic L2P solver that learns to predict a latent search space for TSP and CVRP. We use their reported DE version results due to the long runtime to reproduce results.
- DPDP [42]: a state-of-the-art L2P solver that combines heatmaps with dynamic programming to efficiently solve TSP and CVRP. We run it for 100k iterations (TSP) and 1,000k iterations (CVRP).
- DIMES [7]\#: a novel L2P solver that learns to predict a latent search space and exploits differentiable optimizers to find TSP solutions. Due to incompatible issues when installing the required Pytorch extension library packages, we opt to directly use their reported results obtained by the settings of using REINFORCE, active search, Monte Carlo tree search, and meta-learning.
- DIFUSCO [15]#: a state-of-the-art L2P solver, that learns a diffusion model to predict heatmaps for TSP. We run their used settings:  $\mathrm{T} = 50$  diffusion steps,  $\mathrm{S} = 16$  samplings, and 2-opt post-processing.
-  $\mathbf{AM} + \mathbf{LCP}^{\star}$  [33]: a two-stage L2C solver that iteratively constructs (seeder) and re-constructs (reviser) parts of the solutions based on the AM [3]. For TSP, we run their optimized version with 1,280 samplings and two revisers - one revises a length of 10 nodes for 25 iterations, and the other revises a length of 20 nodes for 20 iterations. However, their code for CVRP is not publicly available. Hence for CVRP, we opt to directly use their reported results.
- Pointformer [32]: a latest L2C solver that enhances POMO with a multi-pointer Transformer and feature augmentation for TSP instances. We run it with 200 samplings and  $\times 8$  augmentations.
- Sym-NCO [13]: an effective L2C solver that enhances POMO with auxiliary losses for TSP and CVRP, aiming at better symmetry handling. We run it with 200 samplings and  $\times 8$  augmentations.
- POMO [4]: a renowned L2C solver that enhances the AM [3] with diverse rollouts and data augmentations for TSP and CVRP. We run it with 200 samplings and  $\times 8$  augmentations.
- POMO+EAS [5]: a leading L2C solver that adjusts a small subset of the pre-trained POMO model parameters on test instances for efficient active search. We run the EAS-lay version with  $\times 8$  augmentations for  $T = 200$  iterations (both TSP and CVRP) which is the best setting for CVRP.
- POMO+EAS+SGBS [34]: a state-of-the-art L2C solver that bolsters EAS by incorporating simulation-guided beam search, executing beam search and efficient active search phases alternately. We run 5 rounds (TSP) and 50 rounds (CVRP) for the short version, and 20 rounds (TSP) and 200 rounds (CVRP) for the long version. The beam search width is set as per their suggested values.
- Costa et al. [16]: a compelling L2S solver that employs RNN-based policy to control the 2-opt for solving TSP. We run it for  $\mathrm{T} = 2\mathrm{k}$  iterations.
- Sui et al. [17]: a recent L2S solver improves upon [16] by performing 3-opt, where the policy first removes three edges and then chooses a re-connection type from all candidate options. Given that their code is not available, we opt to directly use their reported results.
- Wu et al. [39]: a classic L2S solver that employs Transformer-based policy to control the 2-opt for solving TSP. We run it for  $\mathrm{T} = 5\mathrm{k}$  iterations (both TSP and CVRP).
- DACT [9]: a state-of-the-art L2S solver that enhances Wu et al. [39] via the cyclic positional encoding and dual-aspect representations. Consistent with their original best settings, we run it for 10k iterations with  $\times 4$  augmentations for TSP and  $\times 6$  augmentations for CVRP.
- NLNS [8]: a strong L2S solver that learns to control ruin-and-repair operators. Following their default settings, we run their code on 10 CPUs in parallel, executing  $\mathrm{T} = 5\mathrm{k}$  iterations.
- NCE [37]: a distinctive L2S solver that is designed to execute CROSSOVER exchanges between two CVRP solutions. As their code is not available, we opt to use their reported results directly.