SimpleEvol: An Agent-Loop Framework for LLM-Driven Automated Heuristic Design with Minimal Human Priors

Jianghan Zhu; Cong Zhang; Rongjie Zhu; Chi Zhang; Zhiguang Cao

cs.AISep 29, 2026

SimpleEvol: An Agent-Loop Framework for LLM-Driven Automated Heuristic Design with Minimal Human Priors

Authors: Jianghan Zhu, Cong Zhang, Rongjie Zhu, Chi Zhang, Zhiguang Cao

Organizations: School of Computing and Information Systems, Singapore Management University, Singapore · Independent Researcher · School of Teacher Education, Nanjing University of Information Science and Technology, China · Department of Mathematics, National University of Singapore, Singapore

Abstract

Large language models (LLMs) have emerged as powerful tools for automated heuristic design (AHD), enabling iterative generation and refinement of heuristics. However, the dominant paradigm embeds LLMs as narrow, fixed components, such as crossover or mutation, within heavily hand-engineered evolutionary frameworks. We argue this misapprehends LLMs. It treats them as specialized tools rather than general reasoners, constrains them to low-level operations, and underutilizes their autonomy. Moreover, the extensive human priors in these frameworks violate the bitter lesson principle that general methods scaling with computation surpass hand-crafted solutions. This raises a key question: which AHD framework designs best convert stronger LLM capabilities into better heuristics? To address this, we propose metrics for LLM-driven AHD framework handcraftedness (AHI) and intelligence conversion efficiency (ICE). Evaluating ten LLMs across three challenging combinatorial optimization problems, we obtain a notable finding that frameworks with fewer human priors consistently yield higher ICE. Based on this finding, we propose SimpleEvol, an agent-loop framework for AHD which removes nearly all human priors and allows the LLM to operate autonomously. SimpleEvol consistently achieves the highest ICE, often by a large margin. Our results challenge the trend toward complex AHD pipelines and point to a lighter and more model-centric alternative, suggesting that reducing human priors is a more effective strategy to scale up with model intelligence. The source code is available at https://github.com/HenryZhu1029/SimpleEvol-Master.

Figures & tables

Framework	$M$	$K$	$\log_{10}(1+Q)$	AHI
FunSearch	3	1	2.915	6.915
EoH	2	4	2.919	8.919
ReEvo	2	4	3.112	9.112
SimpleEvol (ours)	1	2	3.001	6.001

Table 1: AHI of different AHD frameworks.

Figure 2 : Relationship between model intelligence and AHD performance on TSP and CVRP.



Method	AHI	ICE(TSP)	ICE(CVRP)
FunSearch	6.915	1.8174	5.4381
EoH	8.919	1.5082	3.6572
ReEvo	9.112	0.8230	2.0824
SimpleEvol (ours)	6.001	2.1941	6.2128

Table 2: ICE on TSP Constructive and CVRP-ACO, together with handcraftedness index (AHI).

Panel of Figure 3 — Figure 3 : Relative framework advantage under different model intelligence. The upper-left number in each cell denotes the performance rank on each backbone model.


Task	N=50				N=100				N=200
Task	Fun.	EoH	ReEvo	Ours	Fun.	EoH	ReEvo	Ours	Fun.	EoH	ReEvo	Ours
TSP-SC.	5.50%	6.76%	7.98%	4.77%	7.33%	8.44%	10.06%	6.47%	10.35%	10.56%	12.10%	9.49%
CVRP-ACO	1.04%	0.71%	0.49%	0.34%	4.83%	6.70%	5.98%	4.31%	4.46%	4.28%	4.38%	4.26%

Table 3: Performance comparison of AHD frameworks using GPT-5-mini . Step-by-step construction is abbreviated as SC. FunSearch [ 53 ] is abbreviated as Fun. The best result of each setting is in bold.

Appendix figures & tables28 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 6 — Figure 6 : Template of the system generator prompt.

Panel of Figure 8 — Figure 8 : Template of the summary injection prompt.

Panel of Figure 9 — Figure 9 : Template of the user generator prompt.

Panel of Figure 10 — Figure 10 : Meta-information feedback of heuristic evaluation.

Panel of Figure 11 — Figure 11 : Template of the initial user prompt.

Framework	Problem	$D_{\text{train}}$	$D_{\text{test}}$
GLS	FSSP	Number of Iterations: 1000	Same as $D_{\text{train}}$
ACO	CVRP	Number of Ants: 30; Number of Iterations: 100	Same as $D_{\text{train}}$

Appendix

Table 4 : Search framework hyperparameters for different problem settings.

	Benchmark
Model	MMLU-Pro		IFBench		AIME 2025		LiveCodeBench		$I(m)$
	Score	Ratio	Score	Ratio	Score	Ratio	Score	Ratio
GPT-4o-mini	64.8	1.00	31.0	1.00	14.7	1.00	23.4	1.00	1.00
GPT-4.1-nano	65.7	1.04	32.0	1.03	24.0	1.63	32.6	1.39	1.25
Claude Sonnet 3.7	80.3	1.27	44.0	1.42	21.0	1.43	39.4	1.68	1.44
DeepSeek-v3	81.9	1.30	41.0	1.32	41.0	2.79	40.5	1.73	1.70

Appendix

Table 5 : Benchmark scores (Score) and normalized ratios (Ratio) used to compute the model intelligence score

I(m)

. Ratios are normalized with respect to the weakest model (GPT-4o-mini), and

I(m)

is computed based on aggregated normalized performance across benchmarks.



Instance	EoH	ReEvo	FunSearch	SimpleEvol (ours)
bier127.tsp	13.60%	8.33%	20.69%	7.16%
ch130.tsp	10.63%	12.24%	20.04%	10.12%
eil51.tsp	8.85%	14.20%	7.27%	11.96%
fl417.tsp	13.49%	10.59%	33.06%	10.50%

Appendix

Table 6 : Results of LLM-based AHD methods for TSP on TSPLIB instances. Following the same protocol as ReEvo [ 52 ] , we compute the reported optimality gap from the average over three runs with different starting nodes. For each instance, the best result across all methods is marked in bold .



Method	TSP Constructive				CVRP-ACO
Method	ICE	LOO-mean	LOO-std	$\mathrm{ICE}_{\mathrm{AA}}$	ICE	LOO-mean	LOO-std	$\mathrm{ICE}_{\mathrm{AA}}$
FunSearch	1.8174	1.8110	0.4258	2.2103	5.4381	5.4112	0.9423	6.8866
EoH	1.5082	1.4969	0.4040	1.8132	3.6572	3.6853	0.9137	5.5700
ReEvo	0.8230	0.8201	0.2981	1.4627	2.0824	2.0223	1.1802	5.3194

Appendix

Table 7 : Robustness of AHI–ICE relationship under leave-one-out regression and an alternative intelligence metric.

\mathrm{ICE}_{\mathrm{AA}}

is computed by replacing our benchmark-based

I(m)

with the Artificial Analysis Intelligence Index [ 49 ] . The highest value of ICE for each setting is marked in bold, while the second largest value is underlined.

Task	Comparison	$\Delta$	$\Pr(\Delta>0)$
TSP Constructive	SimpleEvol $-$ FunSearch	0.380	85.5%
	SimpleEvol $-$ EoH	0.688	95.3%
	SimpleEvol $-$ ReEvo	1.369	97.6%
	SimpleEvol $-$ MCTS-AHD	1.442	98.9%
CVRP-ACO	SimpleEvol $-$ FunSearch	0.771	79.1%
	SimpleEvol $-$ EoH	2.562	88.7%

Appendix

Table 8 : Bayesian-bootstrap uncertainty of pairwise ICE differences.

\Delta

denotes

\mathrm{ICE}_{\mathrm{SimpleEvol}}-\mathrm{ICE}_{A}

\Pr(\Delta>0)

is estimated from 10,000 Bayesian-bootstrap replicates.

Panel of Figure 12 — Figure 12 : Best-so-far search trajectories under GPT-5-mini . Lower gap is better. Solid curves show the mean across independent runs, and shaded regions indicate $\pm$ 1 standard deviation. Only the CVRP-ACO panel uses a symmetric-log scale to accommodate the wide range of early-stage gaps and negative gaps relative to the reference solution.

Task	Method	50	100	200	400	600
TSP Constructive	ReEvo	0.585	0.783	0.891	0.981	0.843
	EoH	1.393	0.568	1.046	1.290	1.582
	FunSearch	0.482	0.862	1.328	1.315	1.776
	SimpleEvol	0.936	0.823	1.403	1.835	2.436
CVRP-ACO	ReEvo	1.012	1.158	1.420	1.892	2.225
	EoH	0.213	1.318	2.868	2.560	3.215

Appendix

Table 9 : ICE at different heuristic-evaluation budgets. The highest ICE at each checkpoint within each task is shown in bold.

Figure 13 : Relationship between model intelligence and AHD performance on FSSP-GLS. Left: 64-instance held-out IDD synthetic instances. Right: Taillard benchmark instances.


Task	Method	Runtime (hrs)	Input Tokens (M)	Output Tokens (M)	# Queries
TSP Constructive	FunSearch	11.13	1.111	1.479	821
	EoH	5.23	0.687	1.100	828
	ReEvo	3.60	3.602	2.249	1293
	SimpleEvol (ours)	10.55	4.517	1.988	1001
CVRP-ACO	FunSearch	16.86	1.826	2.008	822

Appendix

Table 10 : Training time, token usage, and LLM query counts of all methods averaged across 10 models.

Panel of Figure 14 — Figure 14 : Computational cost comparison of LLM-based AHD methods.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	5.6750	–	7.7680	–	10.6590	–	–	1.0000
GPT-4o-mini	6.3438	11.79%	8.8025	13.32%	12.4151	16.48%	13.86%	7.2152
GPT-4.1-nano	6.2518	10.16%	8.7732	12.94%	12.2825	15.23%	12.78%	7.8256
Claude Sonnet 3.7	6.1693	8.71%	8.7684	12.88%	12.4542	16.84%	12.81%	7.8065

Appendix

Table 11 : Detailed performance of SimpleEvol across backbone models on the TSP test sets.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	5.6750	–	7.7680	–	10.6590	–	–	1.0000
GPT-4o-mini	6.3942	12.67%	8.8689	14.17%	12.4607	16.90%	14.58%	6.8574
GPT-4.1-nano	6.3294	11.53%	8.8852	14.38%	12.3365	15.74%	13.88%	7.2029
Claude Sonnet 3.7	6.1857	9.00%	8.7873	13.12%	12.4140	16.47%	12.86%	7.7749

Appendix

Table 12 : Detailed performance of FunSearch across backbone models on the TSP test sets.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	5.6750	–	7.7680	–	10.6590	–	–	1.0000
GPT-4o-mini	6.5120	14.75%	9.1810	18.19%	12.7930	20.02%	17.65%	5.6647
GPT-4.1-nano	6.2992	11.00%	8.7966	13.24%	12.2683	15.10%	13.11%	7.6261
Claude Sonnet 3.7	6.2576	10.27%	8.7952	13.22%	12.5031	17.30%	13.60%	7.3546

Appendix

Table 13 : Detailed performance of EoH across backbone models on the TSP test sets.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	5.6750	–	7.7680	–	10.6590	–	–	1.0000
GPT-4o-mini	6.3526	11.94%	8.8555	14.00%	12.4488	16.79%	14.24%	7.0207
GPT-4.1-nano	6.3886	12.58%	9.0631	16.67%	12.6207	18.40%	15.88%	6.2957
Claude Sonnet 3.7	6.2048	9.34%	8.6615	11.50%	12.2265	14.71%	11.85%	8.4402

Appendix

Table 14 : Detailed performance of ReEvo across backbone models on the TSP test sets.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	5.6750	–	7.7680	–	10.6590	–	–	1.0000
GPT-4o-mini	6.2326	9.83%	8.7412	12.53%	12.2513	14.94%	12.43%	8.0446
GPT-4.1-nano	6.2886	10.81%	9.0136	16.04%	12.5707	17.94%	14.93%	6.6989
Claude Sonnet 3.7	6.2341	9.85%	8.6815	11.76%	12.2565	14.99%	12.20%	8.1968

Appendix

Table 15 : Detailed performance of MCTS-AHD across backbone models on the TSP test sets.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	8.8880	–	14.9320	–	27.1590	–	–	1.0000
GPT-4o-mini	9.2702	4.30%	16.1382	8.08%	28.6203	5.38%	5.92%	16.8932
GPT-4.1-nano	9.1717	3.19%	16.1514	8.17%	28.9365	6.54%	5.97%	16.7569
Claude Sonnet 3.7	9.2351	3.90%	15.9603	6.89%	28.3293	4.31%	5.03%	19.8669

Appendix

Table 16 : Detailed performance of SimpleEvol across backbone models on the CVRP test sets.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	8.8880	–	14.9320	–	27.1590	–	–	1.0000
GPT-4o-mini	9.2106	3.63%	16.5272	10.68%	29.5915	8.96%	7.76%	12.8926
GPT-4.1-nano	9.3651	5.37%	16.5791	11.03%	29.1303	7.26%	7.89%	12.6813
Claude Sonnet 3.7	9.0786	2.14%	16.1344	8.05%	28.8580	6.26%	5.48%	18.2346

Appendix

Table 17 : Detailed performance of FunSearch across backbone models on the CVRP test sets.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	8.8880	–	14.9320	–	27.1590	–	–	1.0000
GPT-4o-mini	9.1090	2.49%	16.1046	7.85%	28.4425	4.73%	5.02%	19.9131
GPT-4.1-nano	9.2774	4.38%	16.5862	11.08%	29.2250	7.61%	7.69%	13.0055
Claude Sonnet 3.7	8.9577	0.78%	15.8456	6.12%	28.6107	5.35%	4.08%	24.4939

Appendix

Table 18 : Detailed performance of EoH across backbone models on the CVRP test sets.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	8.8880	–	14.9320	–	27.1590	–	–	1.0000
GPT-4o-mini	9.3572	5.28%	16.1092	7.88%	29.2078	7.54%	6.90%	14.4882
GPT-4.1-nano	9.1683	3.15%	16.1404	8.09%	28.9847	6.72%	5.99%	16.6958
Claude Sonnet 3.7	9.0870	2.24%	15.9228	6.64%	28.2793	4.12%	4.33%	23.0788

Appendix

Table 19 : Detailed performance of ReEvo across backbone models on the CVRP test sets.


LLM Model	$N=50$		$N=100$		$N=200$		Avg Gap $\downarrow$	$P(m)\uparrow$
LLM Model	Obj.	Gap	Obj.	Gap	Obj.	Gap	Avg Gap $\downarrow$	$P(m)\uparrow$
Opt (best known)	8.8880	–	14.9320	–	27.1590	–	–	1.0000
GPT-4o-mini	9.2480	4.05%	15.7320	5.36%	28.3610	4.43%	4.61%	21.6855
GPT-4.1-nano	9.1572	3.03%	16.0282	7.34%	29.1074	7.17%	5.85%	17.0997
Claude Sonnet 3.7	9.1691	3.16%	15.7503	5.48%	28.2169	3.90%	4.18%	23.9271

Appendix

Table 20 : Detailed performance of MCTS-AHD across backbone models on the CVRP test sets.



LLM Model	Avg Gap (IDD) $\downarrow$	$P(m)_{\text{idd}}\uparrow$	Avg Gap (Taillard) $\downarrow$	$P(m)_{\text{OOD}}\uparrow$

LLM-based AHD: FunSearch
GPT-4o-mini	3.07%	32.5862	0.33%	307.5031
GPT-4.1-nano	3.02%	33.1680	0.27%	366.1662

Appendix

Table 21 : Performance comparison across AHD frameworks on IDD and Taillard (OOD) instances.

Resources	Type	License / Availability	URL
LKH3	Code	Available for academic research use	http://webhotel4.ruc.dk/ keld/research/LKH-3/
POMO	Code	Available online	https://github.com/yd-kwon/POMO/tree/master
DeepACO	Code	MIT License	https://github.com/henry-yeh/DeepACO
FunSearch	Code	Apache License	https://github.com/google-deepmind/funsearch
EoH	Code	MIT License	https://github.com/FeiLiu36/EoH
ReEvo	Code	MIT License	https://github.com/ai4co/reevo

Appendix

Table 22 : Licenses for codebases, datasets, and public leaderboard for benchmark scores.

Explore similar work

MeEvo: Metacognitive Evolution Combined with Natural Evolution for Automatic Heuristic Design
Jun 12, 2026Zishang Qiu, Xinan Chen, Rong Qu +1Automated Heuristic Design Evolutionary Search
School of Computer Science, University of Nottingham Ningbo China, Ningbo, China · School of Computer Science, University of Nottingham, Nottingham, UK
AHD Agent: Agentic Reinforcement Learning for Automatic Heuristic Design
May 9, 2026Haoze Lv, Ning Lu, Ziang Zhou +1Automated Heuristic Design Agentic Optimization
Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology · Zhongguancun Academy · The Hong Kong University of Science and Technology
MOSAIC: Adversarial Co-evolution of Specialist Heuristics and Problem Instances for LLM-based Automated Heuristic Design
Jul 31, 2026Oguzhan Gungordu, Siheng Xiong, Faramarz FekriAutomated Heuristic Design Heuristics
Georgia Institute of Technology

Jun 12, 2026, cs.NEJ/K move · Enter open · S save

MeEvo: Metacognitive Evolution Combined with Natural Evolution for Automatic Heuristic Design

Zishang Qiu, Xinan Chen, Rong Qu, Ruibin Bai

School of Computer Science, University of Nottingham Ningbo China, Ningbo, China · School of Computer Science, University of Nottingham, Nottingham, UK

Automated Heuristic Design Evolutionary Search Metacognition Efficient Exploration Refinement

Open paper AskPDF arXiv

Large Language Models (LLMs) have advanced Automatic Heuristic Design (AHD) by enabling heuristic generation through reasoning and code synthesis. In LLM-based AHD, the LLM reasons about algorithm design and generates executable heuristic code. Existing architectures adopt two main paradigms: Natural Evolution applies crossover and mutation to this code to explore diverse strategies, but discards the reasoning traces behind the design decisions, weakening knowledge retention; Metacognitive Evolution retains these reasoning traces and refines them through reflection, but lacks population-level recombination, limiting exploration. These limitations reduce search efficiency, stability, and solution quality on complex problems. To address this gap, we propose MeEvo, an AHD framework that cyclically couples Natural Evolution and Metacognitive Evolution with operator balance that shifts from exploration to exploitation. Natural Evolution explores heuristic code while recording LLM-generated reasoning traces, fitness values, errors and best heuristic into a shared history; Metacognitive Evolution then reflects on this history to generate improved heuristics that feed into the next Natural Evolution cycle. This design enables population-driven exploration and reflection-driven refinement to reinforce each other. Experiments on five optimization problems show that MeEvo achieves stronger performance and lower variance than tested LLM-based AHD architectures, especially on complex constrained tasks.

Abstract

Explore similar work

MeEvo: Metacognitive Evolution Combined with Natural Evolution for Automatic Heuristic Design

AHD Agent: Agentic Reinforcement Learning for Automatic Heuristic Design

MOSAIC: Adversarial Co-evolution of Specialist Heuristics and Problem Instances for LLM-based Automated Heuristic Design