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📦️This is a collection of MetaBBO papers and their corresponding code resources (👈️Click here for the paper list).

🤔What is BBO?

image description Black Box Optimization (BBO) refers to a class of optimization problems where the objective function is defined as $f: X \rightarrow \mathbb{R}$. The term "Black-Box" means that, although we can evaluate $f(X)$ for any $X$ within the search domain, we have no access to additional information such as the mathematical expression, gradients, or any structural details. The only available data comes from the input $X$ and the corresponding output $f(X)$. BBO problems can be categorized into SOP(singe-objective), MOOP(multi-objective), COP(constrained), CMOP(constrained multi-objective), MMOP(multi-modal), MMOOP(multi-modal multi-objective), LSOP(large-scale), LS-MOOP(large-scale multi-objective), CO(combinatorial) optimization problem and MILP(mixed integer linear programming) based on their specific characteristics.

🤨What is MetaBBO?

🔥Meta-Black-Box-Optimization (MetaBBO) is an emerging research topic, leveraging the generalization power of Meta Learning to enhance the performance of existing BBO optimizers, or create new ones. 🚀By utilizing Meta Learning, the reliance on expert-level knowledge is reduced, highlighting the trend toward automated algorithm design in BBO.

🚩We warmly invite you to read our survey on MetaBBO, "Toward Automated Algorithm Design: A Survey and Practical Guide to Meta-Black-Box-Optimization," for more detailed insights into MetaBBO! Besides, if you find this repository useful, please cite it in your publications or projects as follows.

@article{ma2024metabbo,
  title={Toward Automated Algorithm Design: A Survey and Practical Guide to Meta-Black-Box-Optimization},
  author={Ma, Zeyuan and Guo, Hongshu and Gong, Yue-Jiao and Zhang, Jun and Kay Chen Tan},
  journal={arXiv preprint arXiv:2411.00625},
  year={2024}
}

😁Contact Us

👨‍💻👩‍💻We are a research team mainly focus on Meta-Black-Box-Optimization (MetaBBO), which assists automated algorithm design for Evolutionary Computation.

Here is our homepage and github. 🥰🥰🥰Please feel free to contact us—any suggestions are welcome!

✨️MetaBBO is rapidly evolving, and this is by no means a comprehensive list of papers, which would be continuously matained and updated.

If you want to update the list or have any question：

😘Join us in perfecting the MetaBBO papers and their code resources together!

🌍️Useful Github Repository

👍️👍️👍️Many outstanding teams have developed excellent GitHub repositories for the Evolutionary Computation community, and we are pleased to share them here.

Repository About
MetaBox MetaBox: A Benchmark Platform for Meta-Black-Box Optimization with Reinforcement Learning
LLM4Opt A Collection on Large Language Models for Optimization
pypop7 A Pure-Python Library for POPulation-based Black-Box Optimization
EvoX Distributed GPU-Accelerated Framework for Evolutionary Computation. Comprehensive Library of Evolutionary Algorithms & Benchmark Problems
evosax Evolution Strategies in JAX

Content

We first classify them by learning paradigm, followed by different automated algorithm design tasks.

All papers are sorted by year of publication.

1. 📝Survey Papers & Benchmarks

1.1. 📚Survey Papers

Paper
He Yu and Jing Liu. "Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms". arXiv preprint arXiv:2410.20848 (2024).
Wu X, Wu S, Wu J, et al. "Evolutionary computation in the era of large language model: Survey and roadmap". arXiv preprint arXiv:2401.10034 (2024).
Song, Xingyou, et al. "Position: Leverage Foundational Models for Black-Box Optimization" Forty-first International Conference on Machine Learning (2024)
Huang, Sen, et al. "When Large Language Model Meets Optimization" arXiv preprint arXiv:2405.10098 (2024).
Sun Q, Chen Z, Xu F, et al. "A Survey of Neural Code Intelligence: Paradigms, Advances and Beyond". CoRR, (2024).
Huang S, Yang K, Qi S, et al. "When Large Language Model Meets Optimization". arXiv preprint arXiv:2405.10098 (2024).
Li P, Hao J, Tang H, et al. "Bridging Evolutionary Algorithms and Reinforcement Learning: A Comprehensive Survey on Hybrid Algorithms. IEEE Transactions on Evolutionary Computation. (2024).
Song Y, Wu Y, Guo Y, et al. "Reinforcement learning-assisted evolutionary algorithm: A survey and research opportunities. Swarm and Evolutionary Computation. (2024).
Nikolikj, Ana, et al. "Quantifying Individual and Joint Module Impact in Modular Optimization Frameworks." 2024 IEEE Congress on Evolutionary Computation. (2024).
Qian, Chao, Ke Xue, and Ren-Jian Wang. "Quality-Diversity Algorithms Can Provably Be Helpful for Optimization." arXiv preprint arXiv:2401.10539. (2024).
Huang, Beichen, et al. "Exploring the True Potential: Evaluating the Black-box Optimization Capability of Large Language Models." arXiv preprint arXiv:2404.06290. (2024).
Zhao Q, Duan Q, Yan B, et al. "Automated Design of Metaheuristic Algorithms: A Survey". Transactions on Machine Learning Research (2023).
Chernigovskaya, Maria, Andrey Kharitonov, and Klaus Turowski. "A Recent Publications Survey on Reinforcement Learning for Selecting Parameters of Meta-Heuristic and Machine Learning Algorithms." CLOSER. (2023).
Banzhaf W, Machado P. "Fundamentals of Evolutionary Machine Learning" Handbook of Evolutionary Machine Learning. (2023).
Drugan, Madalina M. "Reinforcement learning versus evolutionary computation: A survey on hybrid algorithms." Swarm and Evolutionary Computation. (2019).
Stützle T, López-Ibáñez M. "Automated design of metaheuristic algorithms". Handbook of metaheuristics (2019).

1.2. 🔍Benchmarks

Benchmark Paper Code Resource Optimization Type
GP-based He Y, Aranha C. "Evolving Benchmark Functions to Compare Evolutionary Algorithms via Genetic Programming". arXiv preprint arXiv:2403.14146 (2024). GP-based SOP,MOOP
SELECTOR Benjamins C, Cenikj G, Nikolikj A, et al. "Instance selection for dynamic algorithm configuration with reinforcement learning: Improving generalization" Proceedings of the Genetic and Evolutionary Computation Conference Companion. (2024). automl/instance-dac Comprehensive platform
MetaBox Ma, Zeyuan, et al. "MetaBox: A Benchmark Platform for Meta-Black-Box Optimization with Reinforcement Learning." Advances in Neural Information Processing Systems 36 (2023). GMC-DRL/MetaBox Comprehensive platform
NN-based Prager R P, Dietrich K, Schneider L, et al. "Neural Networks as Black-Box Benchmark Functions Optimized for Exploratory Landscape Features" Proceedings of the 17th ACM/SIGEVO Conference on Foundations of Genetic Algorithms (2023). - SOP,MOOP
NeuroEvoBench Lange, Robert, Yujin Tang, and Yingtao Tian. "Neuroevobench: Benchmarking evolutionary optimizers for deep learning applications." Advances in Neural Information Processing Systems 36 (2023) neuroevobench/neuroevobench Comprehensive platform
MA-BBOB Vermetten D, Ye F, Bäck T, et al. "MA-BBOB: A problem generator for black-box optimization using affine combinations and shifts". ACM Transactions on Evolutionary Learning, (2024). Dvermetten/Many-affine-BBOB SOP,MOOP
IEEE CEC 2022 Abhishek Kumar, Kenneth V. Price, Ali Wagdy Mohamed, Anas A. Hadi, P. N. Suganthan, "Problem definitions and evaluation criteria for the cec 2022 Special Session and Competition on Single Objective Bound Constrained Numerical Optimization." Technical Report 2022 P-N-Suganthan/2022-SO-BO SOP
Affine Recombination Dietrich K, Mersmann O. "Increasing the diversity of benchmark function sets through affine recombination" International Conference on Parallel Problem Solving from Nature. (2022). - SOP,MOOP
IEEE CEC 2021 Ali Wagdy, Anas A Hadi, Ali K. Mohamed, Prachi Agrawal, Abhishek Kumar and P. N. Suganthan, "Problem definitions and evaluation criteria for the cec 2021 Special Session and Competition on Single Objective Bound Constrained Numerical Optimization." Technical Report 2021 P-N-Suganthan/2021-SO-BCO SOP
Zigzag BBO Kudela, Jakub. "Novel zigzag-based benchmark functions for bound constrained single objective optimization." 2021 IEEE Congress on Evolutionary Computation . IEEE, (2021).
Kudela, Jakub, and Radomil Matousek. "New benchmark functions for single-objective optimization based on a zigzag pattern." IEEE Access 10 (2022).		 JakubKudela89/Zigzag SOP
HPOBench Eggensperger, Katharina, et al. "HPOBench: A collection of reproducible multi-fidelity benchmark problems for HPO." arXiv preprint arXiv:2109.06716 (2021). automl/HPOBench SOP,MOOP
DACBench Eimer, Theresa, et al. "DACBench: A benchmark library for dynamic algorithm configuration." arXiv preprint arXiv:2105.08541 (2021). automl/DACBench DAC
Olympus Häse, Florian, et al. "Olympus: a benchmarking framework for noisy optimization and experiment planning." Machine Learning: Science and Technology (2021). aspuru-guzik-group/olympus SOP,MOOP
NeurIPS BBO challenge Turner R, Eriksson D, McCourt M, et al. "Bayesian optimization is superior to random search for machine learning hyperparameter tuning: Analysis of the black-box optimization challenge 2020" NeurIPS 2020 Competition and Demonstration Track. (2021) NeurIPS BBO challenge SOP
Random function generator Tian Y, Peng S, Zhang X, et al. "A recommender system for metaheuristic algorithms for continuous optimization based on deep recurrent neural networks". IEEE transactions on artificial intelligence (2020). Random function generator SOP
CEC 2020 competition on real-world optimization problem Kumar A, Wu G, Ali M Z, et al. "A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm and Evolutionary Computation (2020). CEC 2020 real-world -
COCO Hansen, Nikolaus, et al. "COCO: A platform for comparing continuous optimizers in a black-box setting." Optimization Methods and Software (2021). numbbo/coco SOP,MOOP
EVOBBO Muñoz, Mario A., and Kate Smith-Miles. "Generating new space-filling test instances for continuous black-box optimization." Evolutionary computation (2020). andremun/EVOBBO_Instances SOP、MOOP
Bayesmark Turner R, Eriksson D. "Bayesmark: Benchmark framework to easily compare bayesian optimization methods on real machine learning tasks." (2019). Bayesmark SOP
PBO Doerr C, Ye F, Horesh N, et al. "Benchmarking discrete optimization heuristics with IOHprofiler" Proceedings of the Genetic and Evolutionary Computation Conference Companion. (2019). PBO CO
IOHprofiler (IOHexperimenter) Doerr, Carola, et al. "IOHprofiler: A benchmarking and profiling tool for iterative optimization heuristics." arXiv preprint arXiv:1810.05281 (2018).
de Nobel, Jacob, et al. "Iohexperimenter: Benchmarking platform for iterative optimization heuristics." Evolutionary Computation (2023): 1-6.		 IOHprofiler/
IOHexperimenter		 Comprehensive platform
MTMOOP Yuan Y, Ong Y S, Feng L, et al. "Evolutionary multitasking for multiobjective continuous optimization: Benchmark problems, performance metrics and baseline results." arXiv preprint arXiv:1706.02766 (2017). - MTMO
MTSOP Da B, Ong Y S, Feng L, et al. "Evolutionary multitasking for single-objective continuous optimization: Benchmark problems, performance metric, and baseline results". arXiv preprint arXiv:1706.03470 (2017). - MTSO
IEEE CEC 2017 N. H. Awad, M. Z. Ali, J. J. Liang, B. Y. Qu and P. N. Suganthan, "Problem definitions and evaluation criteria for the CEC 2017 competition on constrained real-parameter optimization." Technical Report (2017) P-N-Suganthan/CEC2017-BoundContrained SOP,MOOP
IEEE CEC 2015 J. J. Liang, B. Y. Qu, P. N. Suganthan, Q. Chen, "Problem Definitions and Evaluation Criteria for the CEC 2015 Competition on Learning-based Real-Parameter Single Objective Optimization", Technical Report, Computational Intelligence Laboratory (2015). P-N-Suganthan/CEC2015-Learning-Based SOP,MOOP
AClib Hutter, Frank, et al. "AClib: A benchmark library for algorithm configuration." Learning and Intelligent Optimization: 8th International Conference (2014). aclib.net -
IEEE CEC 2013 J. J. Liang, B-Y. Qu, P. N. Suganthan, Alfredo G. Hernández-Díaz, "Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session and Competition on Real-Parameter Optimization", Technical Report, Computational Intelligence Laboratory (2013). P-N-Suganthan/CEC2013 SOP,MOOP
Protein–Docking Hwang, Howook, et al. "Protein–protein docking benchmark version 4.0." Proteins: Structure, Function, and Bioinformatics (2010). Protein–Docking -
BBOB 2009 Hansen N, Finck S, Ros R, et al. "Real-parameter black-box optimization benchmarking 2009: Noiseless functions definitions". INRIA. (2009). BBOB 2009 SOP,MOOP
WFG Huband S, Hingston P, Barone L, et al. "A review of multiobjective test problems and a scalable test problem toolkit." IEEE Transactions on Evolutionary Computation. (2006). WFG MOOP
DTLZ Deb K, Thiele L, Laumanns M, et al. "Scalable multi-objective optimization test problems." Proceedings of the 2002 Congress on Evolutionary Computation (2002). DTLZ MOOP
ZDT Zitzler, E., Deb, K., and Thiele, L. "Comparison of Multiobjective Evolutionary Algorithms: Empirical Results." Evolutionary Computation (2000). ZDT MOOP

*The complete list of IEEE CEC series can be access at ntu.edu.sg.

*The complete list of BBOB series can be access at numbbo.

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2. 🎯MetaBBO

2.1 🤖MetaBBO-RL

2.1.1 Algorithm Selection

Algorithm Paper Optimization Type Low-Level Optimizer RL Code Resource
HHRL-MAR Zhu N, Zhao F, Cao J. "A Hyperheuristic and Reinforcement Learning Guided Meta-heuristic Algorithm Recommendation" 2024 27th International Conference on Computer Supported Cooperative Work in Design (2024) SOP SI Tabular Q-learning -
R2-RLMOEA Tahernezhad-Javazm F, Rankin D, Bois N D, et al. "R2 Indicator and Deep Reinforcement Learning Enhanced Adaptive Multi-Objective Evolutionary Algorithm". arXiv preprint arXiv:2404.08161 (2024). MOOP EAs DDQN -
RL-DAS Guo, Hongshu, et al. "Deep Reinforcement Learning for Dynamic Algorithm Selection: A Proof-of-Principle Study on Differential Evolution." IEEE Transactions on Systems, Man, and Cybernetics: Systems (2024). SOP DE PPO RL-DAS

2.1.2 Algorithm Configuration

Algorithm Paper Optimization Type Low-Level Optimizer RL Code Resource
HF Pei J, Liu J, Mei Y. "Learning from Offline and Online Experiences: A Hybrid Adaptive Operator Selection Framework" Proceedings of the Genetic and Evolutionary Computation Conference. (2024). SOP,CO DE DDQN -
UES-CMAES-RL Bolufé-Röhler A, Xu B. "Deep Reinforcement Learning for Smart Restarts in Exploration-Only Exploitation-Only Hybrid Metaheuristics Metaheuristics International Conference" (2024). SOP UES-CMAES DQN -
MTDE-L2T Wu S H, Huang Y, Wu X, et al. "Learning to Transfer for Evolutionary Multitasking". arXiv preprint arXiv:2406.14359, (2024). MTOP EC PPO -
MSoRL Wang X, Wang F, He Q, et al. "A multi-swarm optimizer with a reinforcement learning mechanism for large-scale optimization". Swarm and Evolutionary Computation (2024). LSOP PSO Tabular Q-learning -
MRL-MOEA Wang, Jing, et al. "A Novel Multi-State Reinforcement Learning-Based Multi-Objective Evolutionary Algorithm." Information Sciences (2024). MOOP MOEA Tabular Q-learning -
RLEMMO Lian, Hongqiao, et al. "RLEMMO: Evolutionary Multimodal Optimization Assisted By Deep Reinforcement Learning." Proceedings of the Genetic and Evolutionary Computation Conference (2024). MMOP DE PPO -
SA-DQN-DE Liao, Zuowen, Qishuo Pang, and Qiong Gu. "Differential evolution based on strategy adaptation and deep reinforcement learning for multimodal optimization problems." Swarm and Evolutionary Computation 87 (2024): 101568. MMOP DE DQN -
PG-DE & PG-MPEDE Zhang, Haotian, et al. "Learning to select the recombination operator for derivative-free optimization." Science China Mathematics (2024). SOP DE REINFORCE -
RLNS Hong, Jiale, Bo Shen, and Anqi Pan. "A reinforcement learning-based neighborhood search operator for multi-modal optimization and its applications." Expert Systems with Applications (2024). MMOP SSA,PSO,EO Tabular Q-learning -
RLMODE Yu, Xiaobing, et al. "Reinforcement learning-based differential evolution algorithm for constrained multi-objective optimization problems." Engineering Applications of Artificial Intelligence (2024). MOOP DE Tabular Q-learning -
GLEET Ma, Zeyuan, et al. "Auto-configuring Exploration-Exploitation Tradeoff in Evolutionary Computation via Deep Reinforcement Learning." Proceedings of the Genetic and Evolutionary Computation Conference (2024). SOP DE,PSO PPO GLEET
RLHDE Peng L, Yuan Z, Dai G, et al. "Reinforcement learning-based hybrid differential evolution for global optimization of interplanetary trajectory design". Swarm and Evolutionary Computation, (2023). SOP HLSHADE Tabular Q-learning -
AMODE-DRL Li T, Meng Y, Tang L. "Scheduling of continuous annealing with a multi-objective differential evolution algorithm based on deep reinforcement learning". IEEE Transactions on Automation Science and Engineering (2023). MOOP MODE DDQN+DDPG -
MARLABC Zhao F, Wang Z, Wang L, et al. "A multi-agent reinforcement learning driven artificial bee colony algorithm with the central controller". Expert Systems with Applications (2023). SOP ABC Tabular Q-learning -
CEDE-DRL Hu Z, Gong W, Pedrycz W, et al. "Deep reinforcement learning assisted co-evolutionary differential evolution for constrained optimization". Swarm and Evolutionary Computation (2023). SOP CO-DE DQN -
RLDMDE Yang, Qingyong, et al. "Dynamic multi-strategy integrated differential evolution algorithm based on reinforcement learning for optimization problems." Complex & Intelligent Systems (2023). SOP DE Tabular Q-learning -
RLMMDE Han Y, Peng H, Mei C, et al. "Multi-strategy multi-objective differential evolutionary algorithm with reinforcement learning". Knowledge-Based Systems (2023). MOOP MOEA Tabular Q-learning -
MPSORL Meng, Xiaoding, Hecheng Li, and Anshan Chen. "Multi-strategy self-learning particle swarm optimization algorithm based on reinforcement learning." Mathematical Biosciences and Engineering (2023). SOP PSO Tabular Q-learning -
IRLMFO Zhao F, Wang Q, Wang L. "An inverse reinforcement learning framework with the Q-learning mechanism for the metaheuristic algorithm". Knowledge-Based Systems (2023). SOP MFO IRL+Tabual Q-learning -
RLAM Yin, Shiyuan, et al. "Reinforcement-learning-based parameter adaptation method for particle swarm optimization." Complex & Intelligent Systems (2023). SOP PSO DDPG -
LADE Liu X, Sun J, Zhang Q, et al. "Learning to learn evolutionary algorithm: A learnable differential evolution". IEEE Transactions on Emerging Topics in Computational Intelligence (2023). SOP DE REINFORCE -
MOEADRL Gao, Mengqi, et al. "An efficient evolutionary algorithm based on deep reinforcement learning for large-scale sparse multiobjective optimization." Applied Intelligence (2023). LS-MOOP SpareEAs A2C -
Q-LSHADE Zhang H, Sun J, Bäck T, et al. "Controlling Sequential Hybrid Evolutionary Algorithm by Q-Learning". IEEE Computational Intelligence Magazine (2023). SOP LSHADE Tabular Q-learning -
NRLPSO Li, Wei, et al. "Reinforcement learning-based particle swarm optimization with neighborhood differential mutation strategy." Swarm and Evolutionary Computation (2023). SOP PSO Tabular Q-learning -
RL-SHADE Fister I, Fister D, Fister Jr I. "Reinforcement learning-based differential evolution for global optimization Differential Evolution: From Theory to Practice" (2022). SOP SHADE Tabular Q-learning -
RL-HPSDE Tan, Zhiping, et al. "Differential evolution with hybrid parameters and mutation strategies based on reinforcement learning." Swarm and Evolutionary Computation (2022): 101194. SOP DE Tabular Q-learning -
MOEA/D-DQN Tian, Ye, et al. "Deep reinforcement learning based adaptive operator selection for evolutionary multi-objective optimization." IEEE Transactions on Emerging Topics in Computational Intelligence (2022). MOOP MOEA DDQN -
RL-CORCO Hu Z, Gong W. "Constrained evolutionary optimization based on reinforcement learning using the objective function and constraints". Knowledge-Based Systems (2022). COP DE Tabular Q-learning -
MADAC Xue, Ke, et al. "Multi-agent dynamic algorithm configuration." Advances in Neural Information Processing Systems (2022). MOOP MOEA/D VDN -
RLLPSO Wang F, Wang X, Sun S. "A reinforcement learning level-based particle swarm optimization algorithm for large-scale optimization." Information Sciences (2022). LSOP PSO Tabular Q-learning -
RL-PSO Wu, Di, and G. Gary Wang. "Employing reinforcement learning to enhance particle swarm optimization methods." Engineering Optimization (2022). SOP PSO REINFORCE -
RLEA-SSC Xia H, Li C, Zeng S, et al. "A reinforcement-learning-based evolutionary algorithm using solution space clustering for multimodal optimization problems 2021 IEEE Congress on Evolutionary Computation (CEC). (2021). MMOP DE Tabular Q-learning -
DE-DQN Tan, Zhiping, and Kangshun Li. "Differential evolution with mixed mutation strategy based on deep reinforcement learning." Applied Soft Computing (2021). SOP DE Tabular Q-learning -
LDE Sun, Jianyong, et al. "Learning Adaptive Differential Evolution Algorithm from Optimization Experiences by Policy Gradient." IEEE Transactions on Evolutionary Computation (2021). SOP DE REINFORCE yierh/LDE
RLEPSO Yin, Shiyuan, et al. "RLEPSO: Reinforcement learning based Ensemble particle swarm optimizer." Proceedings of the 2021 4th International Conference on Algorithms, Computing and Artificial Intelligence. (2021). SOP PSO DDPG -
RLDE Hu Z, Gong W, Li S. "Reinforcement learning-based differential evolution for parameters extraction of photovoltaic models." Energy Reports (2021). SOP DE Tabular Q-learning -
LRMODE Huang Y, Li W, Tian F, et al. "A fitness landscape ruggedness multiobjective differential evolution algorithm with a reinforcement learning strategy". Applied Soft Computing (2020). MOOP DE Tabular Q-learning -
MARLwCMA Sallam, Karam M., et al. "Evolutionary framework with reinforcement learning-based mutation adaptation." IEEE Access (2020). SOP DE Tabular Q-learning -
QLPSO Xu Y, Pi D. "A reinforcement learning-based communication topology in particle swarm optimization." Neural Computing and Applications (2020). SOP PSO Tabular Q-learning -
LTO Shala G, Biedenkapp A, Awad N, et al. "Learning step-size adaptation in CMA-ES." Parallel Problem Solving from Nature–PPSN XVI: 16th International Conference (2020). SOP CMA-ES GPS -
DE-DDQN Sharma, Mudita, et al. "Deep reinforcement learning based parameter control in differential evolution." Proceedings of the Genetic and Evolutionary Computation Conference (2019). SOP DE Tabular Q-learning mudita11/DE-DDQN
QL-M/S-OPSO Liu Y, Lu H, Cheng S, et al. "An adaptive online parameter control algorithm for particle swarm optimization based on reinforcement learning" 2019 IEEE congress on evolutionary computation (2019). SOP,MOOP PSO Tabular Q-learning -
DE-RLFR Li, Zhihui, et al. "Differential evolution based on reinforcement learning with fitness ranking for solving multimodal multiobjective problems" Swarm and Evolutionary Computation (2019). MMOOP DE Tabular Q-learning -
RL-MOEA/D Ning W, Guo B, Guo X, et al. "Reinforcement learning aided parameter control in multi-objective evolutionary algorithm based on decomposition". Progress in Artificial Intelligence (2018). MOOP MOEA/D SARSA -
QFA Sadhu A K, Konar A, Bhattacharjee T, et al. "Synergism of firefly algorithm and Q-learning for robot arm path planning". Swarm and Evolutionary Computation (2018). SOP FA Tabular Q-learning -
RLMPSO Samma H, Lim C P, Saleh J M. "A new reinforcement learning-based memetic particle swarm optimizer". Applied Soft Computing (2016). SOP PSO Tabular Q-learning -

2.1.3 Algorithm Generation

Algorithm Paper Optimization Type Low-Level Optimizer RL Code Resource
ALDes Zhao, Qi, et al. "Automated Metaheuristic Algorithm Design with Autoregressive Learning." arXiv preprint arXiv:2405.03419 (2024). SOP - - -
SYMBOL Chen, Jiacheng, et al. "Symbol: Generating Flexible Black-Box Optimizers through Symbolic Equation Learning." The Twelfth International Conference on Learning Representations. (2024). SOP - PPO SYMBOL
GSF Yi, Wenjie, et al. "Automated design of metaheuristics using reinforcement learning within a novel general search framework." IEEE Transactions on Evolutionary Computation (2022) CO - PPO\DQN -

2.1.4 Solution Manipulation

Algorithm Paper Optimization Type Low-Level Optimizer RL Code Resource
MELBA Chaybouti, Sofian, et al. "Meta-learning of Black-box Solvers Using Deep Reinforcement Learning." NeurIPS 2022, MetaLearn Workshop. (2022). SOP - PPO -

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2.2 💻MetaBBO-SL

2.2.1 Algorithm Selection

Algorithm Paper Optimization Type Low-Level Optimizer Code Resource
TransOptAS Cenikj G, Petelin G, Eftimov T. "TransOptAS: Transformer-Based Algorithm Selection for Single-Objective Optimization" Proceedings of the Genetic and Evolutionary Computation Conference Companion (2024). SOP EAs,SI -
ASF-ALLFV Li Y, Liang J, Yu K, et al. "Adaptive local landscape feature vector for problem classification and algorithm selection". Applied Soft Computing, (2022). SOP EAs,SI -
AR-BB Tian Y, Peng S, Zhang X, et al. "A recommender system for metaheuristic algorithms for continuous optimization based on deep recurrent neural networks". IEEE transactions on artificial intelligence (2020). SOP EAs,SI -
Meta-VRP Gutierrez-Rodríguez A E, Conant-Pablos S E, Ortiz-Bayliss J C, et al. "Selecting meta-heuristics for solving vehicle routing problems with time windows via meta-learning". Expert Systems with Applications (2019). CO MOEA -
Meta-MOP Tian Y, Peng S, Rodemann T, et al. "Automated selection of evolutionary multi-objective optimization algorithms" 2019 IEEE Symposium Series on Computational Intelligence. (2019). MOOP MOEA -
Meta-TSP Kanda J Y, de Carvalho A C, Hruschka E R, et al. "Using meta-learning to recommend meta-heuristics for the traveling salesman problem" 2011 10th international conference on machine learning and applications and workshops. (2011). CO GA -
Meta-QAP Smith-Miles K A. "Towards insightful algorithm selection for optimisation using meta-learning concepts" 2008 IEEE international joint conference on neural networks. (2008). CO MMAS -

2.2.2 Algorithm Configuration

Algorithm Paper Optimization Type Low-Level Optimizer Code Resource
ada-smoDE Zhang H, Shi J, Sun J, et al. "A Gradient-based Method for Differential Evolution Parameter Control by Smoothing" Proceedings of the Genetic and Evolutionary Computation Conference Companion. (2024). SOP DE -

2.2.3 Solution Manipulation

Algorithm Paper Optimization Type Low-Level Optimizer Code Resource
Diffusion Evolution Zhang, Yanbo, et al. "Diffusion Models are Evolutionary Algorithms" arXiv preprint arXiv:2410.02543 (2024). SOP EAs Diffusion Evolution
RGD Beckham, Christopher, et al. "Robust Guided Diffusion for Offline Black-Box Optimization" arXiv preprint arXiv:2410.00983 (2024). SOP - RGD
GLHF Li, Xiaobin, et al. "GLHF: General Learned Evolutionary Algorithm Via Hyper Functions." arXiv preprint arXiv:2405.03728 (2024). SOP DE -
EvoTF Lange, Robert Tjarko, Yingtao Tian, and Yujin Tang. "Evolution Transformer: In-Context Evolutionary Optimization." arXiv preprint arXiv:2403.02985 (2024). SOP - RobertTLange/evosax
LEO Yu, Peiyu, et al. "Latent Energy-Based Odyssey: Black-Box Optimization via Expanded Exploration in the Energy-Based Latent Space." arXiv preprint arXiv:2405.16730 (2024). SOP - -
RIBBO Song, Lei, et al. "Reinforced In-Context Black-Box Optimization." arXiv preprint arXiv:2402.17423 (2024). SOP - RIBBO
NAP Maraval, Alexandre, et al. "End-to-end meta-Bayesian optimisation with transformer neural processes." Advances in Neural Information Processing Systems 36 (2024). SOP - -
DDOM Krishnamoorthy, Siddarth, Satvik Mehul Mashkaria, and Aditya Grover. "Diffusion models for black-box optimization" International Conference on Machine Learning. PMLR, (2023). SOP - DDOM
B2Opt Li X, Wu K, Zhang X, et al. "B2Opt: Learning to Optimize Black-box Optimization with Little Budget". arXiv preprint arXiv:2304.11787, (2023). SOP GA -
RNN-Opt TV, Vishnu, et al. "Meta-learning for black-box optimization." Joint European Conference on Machine Learning and Knowledge Discovery in Databases. (2019). SOP - -
RNN-OI Chen, Yutian, et al. "Learning to learn without gradient descent by gradient descent." International Conference on Machine Learning. PMLR (2017). SOP - -

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2.3 🧬MetaBBO-NE

2.3.1 Algorithm Configuration

Algorithm Paper Optimization Type Low-Level Optimizer Code Resource
LES Lange, Robert, et al. "Discovering evolution strategies via meta-black-box optimization." The Eleventh International Conference on Learning Representations. (2023). SOP CMA-ES LES

2.3.2 Solution Manipulation

Algorithm Paper Optimization Type Low-Level Optimizer Code Resource
LGA Lange, Robert, et al. "Discovering attention-based genetic algorithms via meta-black-box optimization." Proceedings of the Genetic and Evolutionary Computation Conference. (2023). SOP GA LGA
LTO-POMDP Gomes H S, Léger B, Gagné C. "Meta learning black-box population-based optimizers". arXiv preprint arXiv:2103.03526 (2021). SOP - LTO-POMDP

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2.4 🧠MetaBBO-ICL

2.4.1 Algorithm Selection

Algorithm Paper Optimization Type Low-Level Optimizer Code Resource
AS-LLM Wu, Xingyu, et al. "Large language model-enhanced algorithm selection: towards comprehensive algorithm representation." International Joint Conference on Artificial Intelligence (2024). SOP - -

2.4.2 Algorithm Generation

Algorithm Paper Optimization Type Low-Level Optimizer Code Resource
LLMOPT Jiang, Caigao, et al. "LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch" arXiv preprint arXiv:2410.13213 (2024). SOP - caigaojiang/LLMOPT
FunSearch Romera-Paredes B, Barekatain M, Novikov A, et al. "Mathematical discoveries from program search with large language models". Nature, (2024). CO - -
LLM-EPS Zhang R, Liu F, Lin X, et al. "Understanding the Importance of Evolutionary Search in Automated Heuristic Design with Large Language Models"International Conference on Parallel Problem Solving from Nature. (2024). - - -
LLaMoCo Ma, Zeyuan, et al. "LLaMoCo: Instruction Tuning of Large Language Models for Optimization Code Generation." arXiv preprint arXiv:2403.01131 (2024). SOP - LLaMoCo-722A
LLaMEA van Stein, Niki, and Thomas Bäck. "LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics." arXiv preprint arXiv:2405.20132 (2024). SOP - -
Evoprompting Chen, Angelica, David Dohan, and David So. "Evoprompting: Language models for code-level neural architecture search." Advances in Neural Information Processing Systems 36 (2024). SOP - -
OptiMUS AhmadiTeshnizi A, Gao W, Udell M. "OptiMUS: Scalable Optimization Modeling with (MI) LP Solvers and Large Language Models" Forty-first International Conference on Machine Learning (2024). MILP - teshnizi/OptiMUS
EoH Liu, Fei, et al. "Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model." 41st International Conference on Machine Learning (2024). CO - nobodynobodypaper/EoH
LLMOPT Huang Y, Wu S, Zhang W, et al. "Autonomous Multi-Objective Optimization Using Large Language Model". arXiv preprint arXiv:2406.08987, (2024). MOOP - -
AEL Liu, Fei, et al. "Algorithm evolution using large language model." arXiv preprint arXiv:2311.15249 (2023). CO - AEL

2.4.3 Solution Manipulation

Algorithm Paper Optimization Type Low-Level Optimizer Code Resource
Model Swarms Feng, Shangbin, et al. "Model Swarms: Collaborative Search to Adapt LLM Experts via Swarm Intelligence" arXiv preprint arXiv:2410.11163 (2024). SOP PSO -
EvoPrompt Guo, Qingyan, et al. "Connecting large language models with evolutionary algorithms yields powerful prompt optimizers." The Twelfth International Conference on Learning Representations (2024). SOP GA, DE beeevita/EvoPrompt
CCMO-LLM Wang, Zeyi, et al. "Large Language Model-Aided Evolutionary Search for Constrained Multiobjective Optimization." International Conference on Intelligent Computing (2024). CMOP - -
LEO Brahmachary, Shuvayan, et al. "Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism." arXiv preprint arXiv:2403.02054 (2024). SOP - -
EvoLLM Lange, Robert Tjarko, Yingtao Tian, and Yujin Tang. "Large Language Models As Evolution Strategies." Proceedings of the Genetic and Evolutionary Computation Conference Companion (2024). SOP - -
LMEA Liu, Shengcai, et al. "Large language models as evolutionary optimizers." IEEE Congress on Evolutionary Computation (2024). SOP - -
MOEA/D-LLM Liu, Fei, et al. "Large language model for multi-objective evolutionary optimization." arXiv preprint arXiv:2310.12541 (2023). MOOP MOEA/D MOEA/D-LLM
OPRO Yang, Chengrun, et al. "Large language models as optimizers." arXiv preprint arXiv:2309.03409 (2023). SOP - OPRO
ELM Lehman J, Gordon J, Jain S, et al. "Evolution through large models" Handbook of Evolutionary Machine Learning. (2023). CO - -
ToLLM Guo P F, Chen Y H, Tsai Y D, et al. "Towards optimizing with large language models". arXiv preprint arXiv:2310.05204, (2023). SOP - -

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3.🔧 Others

3.1📈 Evaluation Indicator

Indicator Paper
ECDF López-Ibáñez M, Vermetten D, Dreo J, et al. "Using the empirical attainment function for analyzing single-objective black-box optimization algorithms". arXiv preprint arXiv:2404.02031 (2024).
EAF da Fonseca V G, Fonseca C M. "A link between the multivariate cumulative distribution function and the hitting function for random closed sets". Statistics & probability letters (2002).

3.2📊 Landscape Feature

Feature Paper
NeurELA Ma Z, Chen J, Guo H, et al. "Neural Exploratory Landscape Analysis". arXiv preprint arXiv:2408.10672 (2024).
DoE2Vec van Stein B, Long F X, Frenzel M, et al. "Doe2vec: Deep-learning based features for exploratory landscape analysis" Proceedings of the Companion Conference on Genetic and Evolutionary Computation. (2023).
TransOpt Cenikj G, Petelin G, Eftimov T. "TransOptAS: Transformer-Based Algorithm Selection for Single-Objective Optimization" Proceedings of the Genetic and Evolutionary Computation Conference Companion. (2024).
Deep ELA Seiler M V, Kerschke P, Trautmann H. "Deep-ELA: Deep Exploratory Landscape Analysis with Self-Supervised Pretrained Transformers for Single-and Multi-Objective Continuous Optimization Problems". arXiv preprint arXiv:2401.01192 (2024).
LvsC ELA Seiler M, Škvorc U, Cenikj G, et al. "Learned Features vs. Classical ELA on Affine BBOB Functions" International Conference on Parallel Problem Solving from Nature. (2024).
Comparable Feature Long F X, Vermetten D, van Stein B, et al. "BBOB instance analysis: Landscape properties and algorithm performance across problem instances" International Conference on the Applications of Evolutionary Computation. (2023).
ISA Smith-Miles K, Muñoz M A. "Instance space analysis for algorithm testing: Methodology and software tools". ACM Computing Surveys (2023).
ELA Mersmann O, Bischl B, Trautmann H, et al. "Exploratory landscape analysis" Proceedings of the 13th annual conference on Genetic and evolutionary computation. (2011).

3.3🛠 Application

Algorithm Paper Learning paradigm Automated algorithm design task Code Application
DQLGA Q. Chen and W. Ding, "A Genetic Algorithm Based on Deep Q-learning in Optimization of Remote Sensing Data Discretization" IEEE Transactions on Evolutionary Computation (2024) Meta-RL Algorithm Configuration - Remote Sensing

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A collection of MetaBBO papers and code sources

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