Traveling Salesman Problem on TSP50
0Optimality GapNeuOpt
Evaluation results
| Method | Links | |||
|---|---|---|---|---|
| NeuOptType=LS+RL2024.02 | 0 | 1.32 | — | |
| EoHType=GLS+LHH2024.02 | 0 | 1.9 | — | |
| KGLS-ReEvoType=GLS+LHH2024.02 | 0 | 0.03 | — | |
| ConcordeType=Exact, Decoding Strategy=Greedy Decoding2025.02 | 0 | 180 | 5.69 | |
| LKH3Type=Heuristics, Decoding Strategy=Greedy Decoding2025.02 | 0 | 180 | 5.69 | |
| OptimalHeuristic Framework=Constructive2026.01 | 0 | — | 5.68 | |
| DeepACO2026.01 | 0 | — | 5.785 | |
| NeuOpt*Type=LS+RL2025.12 | 0 | — | — | |
| EoHType=GLS+LHH2025.12 | 0 | — | — | |
| KGLS-ReEvoType=GLS+LHH2025.12 | 0 | — | — | |
| KGLS-MCTS-AHDType=GLS+LHH2025.12 | 0 | — | — | |
| EoH2025.10 | 0 | — | — | |
| ConcordeType=Exact2026.05 | 0 | 13 | 5.69 | |
| GurobiType=Exact2026.05 | 0 | 2 | 5.69 | |
| LKH3Type=Heuristic2026.05 | 0 | 6 | 5.69 | |
| NeuralGLS+Type=GLS+SL2024.02 | 0.003 | 10.01 | — | |
| Fast T2TType=SL+G, Sampling steps (Ts)=3, Gradient search steps (Tg)=3, Decoding Strategy=Greedy Decoding2025.02 | 0.01 | 180 | 5.69 | |
| MViewRouterType=RL+S, Augmentation=×8 aug.2026.05 | 0.01 | 12 | 5.69 | |
| KGLSType=GLS2024.02 | 0.017 | 0.03 | — | |
| KGLSType=GLS2025.12 | 0.017 | — | — | |
| KGLS-RoCoType=GLS+LHH2025.12 | 0.018 | — | — | |
| Fast T2TType=SL+G, Sampling steps (Ts)=5, Decoding Strategy=Greedy Decoding2025.02 | 0.02 | 60 | 5.69 | |
| Fast T2TType=SL+G, Sampling steps (Ts)=2, Gradient search steps (Tg)=2, Decoding Strategy=Greedy Decoding2025.02 | 0.02 | 120 | 5.69 | |
| PointerformerType=RL2026.05 | 0.02 | 12 | 5.69 | |
| POMO+POType=PO+S2026.05 | 0.02 | 9 | 5.69 | |
| T2TType=SL+G, Sampling steps (Ts)=50, Gradient search steps (Tg)=30, Decoding Strategy=Greedy Decoding2025.02 | 0.03 | 1,560 | 5.69 | |
| Fast T2TType=SL+G, Sampling steps (Ts)=1, Gradient search steps (Tg)=1, Decoding Strategy=Greedy Decoding2025.02 | 0.03 | 3,240 | 5.69 | |
| POMOType=RL+S, Augmentation=×8 aug.2026.05 | 0.03 | 9 | 5.69 | |
| Fast T2TType=SL+G, Sampling steps (Ts)=3, Decoding Strategy=Greedy Decoding2025.02 | 0.05 | 1,500 | 5.69 | |
| GNNGLSType=GLS+SL2024.02 | 0.052 | 3.83 | — | |
| GNNGLSType=GLS+SL2025.12 | 0.052 | — | — | |
| T2TType=SL+G, Sampling steps (Ts)=50, Gradient search steps (Tg)=15, Decoding Strategy=Greedy Decoding2025.02 | 0.07 | 1,080 | 5.69 | |
| MViewRouterType=RL+S, Augmentation=ori.2026.05 | 0.08 | 2 | 5.7 | |
| DIFUSCOType=SL+S2026.05 | 0.09 | — | 5.7 | |
| CODEEVOLVEAggregation strategy=Best2025.10 | 0.1 | — | — | |
| POMOType=RL+S, Augmentation=no aug.2026.05 | 0.12 | 1 | 5.7 | |
| Sym-NCOType=RL+S2026.05 | 0.16 | 9 | 5.7 | |
| TransformerType=RL+G, Decoding Strategy=Greedy Decoding2025.02 | 0.31 | 840 | 5.71 | |
| Fast T2TType=SL+G, Sampling steps (Ts)=1, Decoding Strategy=Greedy Decoding2025.02 | 0.31 | 660 | 5.71 | |
| POMOHeuristic Framework=Constructive2026.01 | 0.38 | — | 5.7 | |
| DIFUSCOType=SL+G, Sampling steps (Ts)=100, Decoding Strategy=Greedy Decoding2025.02 | 0.41 | 1,080 | 5.71 | |
| DIFUSCOType=SL+G, Sampling steps (Ts)=50, Decoding Strategy=Greedy Decoding2025.02 | 0.45 | 540 | 5.71 | |
| DIFUSCOType=SL+G2026.05 | 0.45 | 9 | 5.71 | |
| PathWiseLLM Backbone=GPT-5-nano, Reasoning Level=medium2026.01 | 0.47 | — | 5.812 | |
| POMOType=RL+G, Decoding Strategy=Greedy Decoding2025.02 | 0.64 | 60 | 5.73 | |
| CODEEVOLVEAggregation strategy=Mean2025.10 | 1.1 | — | — | |
| Image DiffusionType=SL+G, Decoding Strategy=Greedy Decoding2025.02 | 1.23 | — | 5.76 | |
| PathWiseLLM Backbone=GPT-5-nano, Reasoning Level=low2026.01 | 1.28 | — | 5.859 | |
| PathWiseLLM Backbone=GPT-4o-mini, Reasoning Level=N/A2026.01 | 1.54 | — | 5.874 | |
| AMType=RL+G, Decoding Strategy=Greedy Decoding2025.02 | 1.76 | 120 | 5.8 | |
| EoHLLM Backbone=GPT-4o-mini, Reasoning Level=N/A2026.01 | 1.85 | — | 5.892 | |
| ReEvoLLM Backbone=GPT-4o-mini, Reasoning Level=N/A2026.01 | 1.92 | — | 5.896 | |
| MCTS-AHDLLM Backbone=GPT-4o-mini, Reasoning Level=N/A2026.01 | 2.13 | — | 5.908 | |
| HSEvoLLM Backbone=GPT-4o-mini, Reasoning Level=N/A2026.01 | 2.45 | — | 5.927 | |
| MCTS-AHDLLM Backbone=GPT-5-nano, Reasoning Level=low2026.01 | 2.51 | — | 5.93 | |
| EoHLLM Backbone=GPT-5-nano, Reasoning Level=medium2026.01 | 2.76 | — | 5.945 | |
| OR ToolsType=Heuristic2026.05 | 2.87 | 5 | 5.85 | |
| 20ptType=Heuristics, Decoding Strategy=Greedy Decoding2025.02 | 2.95 | — | 5.86 | |
| GCNType=SL+G, Decoding Strategy=Greedy Decoding2025.02 | 3.1 | 3,300 | 5.87 | |
| EoHLLM Backbone=GPT-5-nano, Reasoning Level=low2026.01 | 3.14 | — | 5.967 | |
| HSEvoLLM Backbone=GPT-5-nano, Reasoning Level=low2026.01 | 3.35 | — | 5.979 | |
| MCTS-AHDLLM Backbone=GPT-5-nano, Reasoning Level=medium2026.01 | 4.17 | — | 6.026 | |
| ReEvoLLM Backbone=GPT-5-nano, Reasoning Level=medium2026.01 | 4.53 | — | 6.047 | |
| HSEvoLLM Backbone=GPT-5-nano, Reasoning Level=medium2026.01 | 4.58 | — | 6.05 | |
| TIDEHeuristic Framework=Constructive2026.01 | 4.76 | — | 5.95 | |
| ACO2026.01 | 6.19 | — | 6.143 | |
| ReEvoLLM Backbone=GPT-5-nano, Reasoning Level=low2026.01 | 6.27 | — | 6.148 | |
| HSEvoHeuristic Framework=Constructive2026.01 | 8.04 | — | 6.13 | |
| T2TType=SL+G, Sampling steps (Ts)=1, Gradient search steps (Tg)=1, Decoding Strategy=Greedy Decoding2025.02 | 8.15 | 3,300 | 6.15 | |
| MCTS-AHDHeuristic Framework=Constructive2026.01 | 8.19 | — | 6.14 | |
| ReEvoHeuristic Framework=Constructive2026.01 | 8.27 | — | 6.15 | |
| ReVEL2026.03 | 9.2 | — | — | |
| EoH2026.03 | 10.24 | — | — | |
| ReEvo2026.03 | 11.63 | — | — | |
| EoHHeuristic Framework=Constructive2026.01 | 12.11 | — | 6.36 | |
| DIFUSCOType=SL+G, Sampling steps (Ts)=1, Decoding Strategy=Greedy Decoding2025.02 | 12.84 | 960 | 6.42 | |
| GreedyHeuristic Framework=Constructive2026.01 | 22.62 | — | 6.96 | |
| ACOFramework=ACO2026.01 | — | — | 5.99 | |
| DeepACOFramework=ACO2026.01 | — | — | 5.84 | |
| EoHFramework=ACO2026.01 | — | — | 5.85 | |
| EoH2026.05 | — | 0.13 | 6.912 | |
| HSEvoFramework=ACO2026.01 | — | — | 5.84 | |
| LEHD2026.05 | — | 0.1 | 5.739 | |
| LKH2026.05 | — | 1.05 | 5.709 | |
| MCTS-AHDFramework=ACO2026.01 | — | — | 5.82 | |
| ReEvoFramework=ACO2026.01 | — | — | 5.84 | |
| ReEvo2026.05 | — | 0.05 | 7.014 | |
| Teacher-Aware Heuristic Evolution2026.05 | — | 0.28 | 6.387 | |
| TIDEFramework=ACO2026.01 | — | — | 5.8 |