Self-Guided LLM Reasoning for Error Diagnosis in Vehicle Routing Problems

Ni Zhang; Jianan Zhou; Yue-Jiao Gong; Zhiguang Cao

cs.AIOct 15, 2026

Self-Guided LLM Reasoning for Error Diagnosis in Vehicle Routing Problems

Authors: Ni Zhang, Jianan Zhou, Yue-Jiao Gong, Zhiguang Cao

Organizations: Singapore Management University · Nanyang Technological University · South China University of Technology

Abstract

Vehicle Routing Problems (VRPs) are fundamental to many real-world applications. Recent advances in large language models (LLMs) have spurred progress in solving these NP-hard problems. However, most existing approaches assume that input instances are error-free, neglecting the presence of faults commonly encountered in real-world data. In this work, we systematically investigate the capability of LLMs to detect (and correct) errors in VRP instances, and identify key limitations, particularly in handling complex instances or errors that substantially increase the LLM's reasoning burden. To overcome these challenges, we propose a self-guided reasoning framework in which LLMs autonomously generate code that provides structured insights to aid in error diagnosis. Experiments across diverse problem settings and LLMs demonstrate that our framework significantly improves error detection performance, achieving near-perfect accuracy.

Figures & tables

Figure 1: Overall error detection performance across different VRP variants, with a breakdown by error type shown below (higher is better).

Figure 2: Effect of fault number and instance scale.

Figure 3: Effect of reasoning depth on error detection performance across different VRP variants.

Figure 4: Overall framework of Self-Guided Reasoning.

Constraint Type	1	2	3	4	5	6
LLM (%)	87.27	79.42	72.42	57.42	53.97	22.30

Table 1: Average error detection rates of LLMs under different numbers of constraint types. (higher is better).

	EDR(%)	Time(m)	EDR(%)	Time(m)	EDR(%)	Time(m)	EDR(%)	Time(m)	EDR(%)	Time(m)	EDR(%)	Time(m)
	CVRP		OCVRP		CVRPTW		CVRPL		MDCVRP		CVRPB
LLM	87.25	6.35	91.88	6.20	66.50	7.00	59.50	7.38	94.42	8.15	78.50	8.25
Self-Guided	99.49	6.39	97.98	7.20	95.00	7.22	100.00	8.56	97.47	9.54	94.00	9.03
	CVRPMB		OCVRPTW		MDOCVRP		OCVRPB		CVRPLTW		MDCVRPL
LLM	77.95	9.45	79.50	10.96	94.50	8.17	84.00	8.55	59.61	9.21	59.11	8.50
Self-Guided	96.92	9.97	98.00	10.87	98.50	8.32	94.00	8.52	99.51	8.93	94.09	9.45

Table 2: Error Detection Rate (EDR) comparison across 48 VRP variants (higher is better).

Scale	50						100
Fault Number	5		10		15		5		10		15
EDR(%)	LLM	Self-Guided	LLM	Self-Guided	LLM	Self-Guided	LLM	Self-Guided	LLM	Self-Guided	LLM	Self-Guided
CVRP	97.00	100.00	87.25	99.49	86.82	98.99	94.00	98.00	89.80	97.96	82.33	97.90
CVRPTW	79.00	97.00	66.50	95.00	63.67	90.33	68.00	98.00	64.00	93.00	62.33	87.67
CVRPB	82.00	94.00	78.50	94.00	56.02	91.73	76.00	95.00	77.00	92.00	53.33	92.33
OCVRPB	93.00	95.00	84.00	94.00	71.62	88.85	85.00	99.00	79.00	89.00	64.33	87.00

Table 3: Impact of instance scale and fault number on EDR for LLM and the Self-Guided framework.

Reasoning Depth	1		2		3		4		5
EDR(%)	LLM	Self-Guided	LLM	Self-Guided	LLM	Self-Guided	LLM	Self-Guided	LLM	Self-Guided
CVRP	87.25	99.49	94.89	100.00	96.42	100.00	97.45	100.00	97.96	100.00
CVRPTW	66.50	95.00	68.00	98.00	69.00	98.00	70.00	99.00	72.50	100.00
CVRPB	78.50	94.00	85.00	96.00	90.00	96.00	94.00	99.00	99.00	100.00
OCVRPB	84.00	94.00	88.50	99.50	90.50	100.00	93.00	100.00	94.50	100.00
CVRPMBL	65.00	91.50	67.50	95.50	69.00	100.00	70.00	100.00	70.50	100.00

Table 4: Impact of Reasoning Depth on EDR for LLM and the Self-Guided Framework

	LLM		Self-Refine		Critic-Guided Refinement		CoT		Self-Guided
	EDR(%)	Time(m)	EDR(%)	Time(m)	EDR(%)	Time(m)	EDR(%)	Time(m)	EDR(%)	Time(m)
CVRP	87.25	6.35	92.86	9.60	92.35	9.12	91.33	7.13	99.49	6.39
CVRPTW	66.50	7.00	69.00	11.66	68.50	13.92	69.00	8.10	95.00	7.22
CVRPB	78.50	8.25	82.00	11.43	83.50	10.52	83.00	7.60	94.00	9.03
OCVRPB	84.00	8.55	84.50	11.33	86.00	11.08	85.00	6.78	94.00	8.52
CVRPMBL	65.00	7.63	69.00	10.12	70.50	10.50	67.00	5.88	91.50	7.93

Table 5: Comparison with Different Prompt Strategies.

	LLM		Code
	EDR(%)	Time(m)	EDR(%)	Time(m)
1D BPP	94.50	5.88	97.50	6.00
2D BPP	90.00	6.97	94.50	7.35

Table 6: EDR and Runtime on Bin Packing Problems.

	GPT-4.1		GPT-4o		Claude-4
	LLM	Self-Guided	LLM	Self-Guided	LLM	Self-Guided
CVRP	87.25	99.49	85.71	98.99	91.84	100.00
CVRPTW	66.50	95.00	60.00	93.50	68.50	96.00
CVRPB	78.50	94.00	75.00	93.00	80.00	95.50
OCVRPB	84.00	94.00	85.50	95.00	86.50	95.50
CVRPMBL	65.00	91.50	63.00	90.00	66.50	92.00

Table 7: Comparison across different LLMs with and without the Self-Guided framework on EDR (%).

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Constraint	Description
C	Capacity constraint, which limits the total demand served by each vehicle so that it does not exceed its carrying capacity.
O	Open route constraint, where vehicles are not required to return to the depot after completing their routes.
B	Backhaul constraint, where customers are partitioned into linehaul and backhaul sets, and vehicles are required to serve all linehaul customers before visiting any backhaul customers on each route.
MB	Mixed backhaul constraint, which relaxes strict service ordering and allows limited interleaving of linehaul and backhaul customers.
L	Distance limit constraint, which restricts the maximum travel distance of each route.
TW	Time window constraint, requiring each customer to be served within a specified time interval.

Appendix

Table 8: Summary of VRP constraints considered in this work.

VRP Variant	C Capacity	O Open	B Backhaul	MB Mixed Backhaul	L Distance Limit	TW Time Windows	MD Multi-Depot
CVRP	✓
OCVRP	✓	✓
CVRPB	✓		✓
CVRPL	✓				✓
CVRPTW	✓					✓
OCVRPTW	✓	✓				✓

Appendix

Table 9: VRP variants and their associated constraints.

	CVRP	OCVRP	MDCVRP	CVRPB	CVRPMB	CVRPTW	CVRPL
LLM	2	1	0	11	13	4	0
Self-Guided	0	0	0	0	0	0	0

Appendix

Table 10: Number of faults detected by LLM on correct VRP instances.

(%)	CVRP	OCVRP	MDCVRP	CVRPB	CVRPMB	CVRPTW	CVRPL
LLM	65	85	85	55	75	10	5
Self-Guided	95	95	95	85	90	90	100

Appendix

Table 11: Percentage of instances where all faults are correctly detected.

AFL	CVRP	CVRPTW	CVRPB	OCVRPB	CVRPMBL	MDCVRPMBTW	MDOCVRPBTW	MDOCVRPMBLTW
Obj.	14.19	14.59	14.87	9.30	10.14	12.83	8.71	7.91
Time (s)	10.51	11.01	10.94	11.42	12.63	11.91	12.14	12.72

Appendix

Table 12: Downstream solver performance on repaired VRP instances.

EDR(%)	1	2	3	4	5	6
LLM	87.27	79.42	72.42	57.42	53.97	22.30
Code	99.49	96.90	96.33	95.12	97.96	98.78

Appendix

Table 13: EDR under different counts of constraint types.

Method	CVRP	OCVRP	MDCVRP	CVRPB	CVRPMB	CVRPTW	CVRPL
LLM	80.50	83.00	90.00	71.50	69.00	60.50	58.00
Self-guided	97.50	95.50	96.00	89.50	91.00	89.00	87.00

Appendix

Table 14: Error Detection Rate (EDR, %) on the more challenging hard-mode dataset, where multiple errors may occur within the same node.

Error Type / Method	CVRP	OCVRP	MDCVRP	CVRPB	CVRPMB	CVRPTW	CVRPL
Format (LLM)	0	0	–	–	1	0	0
Format (Self-guided)	0	0	–	–	0	0	0
Capacity (LLM)	2	1	–	–	0	1	0
Capacity (Self-guided)	0	0	–	–	0	0	0
Backhaul (LLM)	–	–	11	12	–	–	–
Backhaul (Self-guided)	–	–	0	0	–	–	–

Appendix

Table 15: False-positive analysis on valid instances. Each entry denotes the number of valid instances incorrectly identified as containing the corresponding error type. “–” indicates that the error type is not applicable to the corresponding VRP variant.

Language Model Error Detection

Language model error detection identifies unreliable answers, reasoning steps, and actions so systems can flag, verify, or repair them.

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Vehicle Routing Problems (VRPs) are fundamental combinatorial optimization problems with widespread applications in various scenarios. The advanced optimization solvers can effectively solve such problems. However, modeling complex VRP variants for solvers often requires substantial domain expertise, which limits the accessibility of advanced optimization technologies. In this paper, we propose Reinforcement Learning Enhanced LLMAgents(RLEA), a multi-agent framework designed to automate the modeling of complex VRPs. RLEA introduces a lightweight neural Planner trained with Soft Q-learning to efficiently orchestrate the actions of LLM-based agents. In addition, we equip the system with an evolutionary memory module and retrieval-augmented generation, enabling the agent to leverage both accumulated experience and external solver knowledge during program generation and refinement for solving VRPs. We evaluated 48 distinct VRP variants across various solvers. The experimental results demonstrate that RLEA outperforms the previous state-of-the-ar method, achieving a 16.67% higher success rate while significantly reducing runtime errors. These results validate that integrating reinforcement learning with LLM-based reasoning is highly effective for automated optimization modeling. The appendix is available at: https://doi.org/10.5281/zenodo.19134435.

Abstract

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