1. Home
  2. To appear
  3. An Effective Differential Evolution Base ...

Informatica


An Effective Differential Evolution Based on Fitness Landscape Analysis for Single-Objective Bound-Constrained Optimization
Pub. online: 17 August 2026      Type: Research Article      Open accessOpen Access
Received
1 April 2026
Accepted
1 June 2026
Published
17 August 2026

Abstract

Considering the landscape information of the optimization problem represents a promising research direction, as landscape features can provide a metaheuristic algorithm with useful information for understanding the search state, allowing it to adjust the search strategy accordingly. As a successful branch of metaheuristic algorithms for solving single-objective bound-constrained problems, however, the original design of differential evolution (DE) does not sufficiently consider information about the landscape of the solution space. To address this, an effective DE based on reinforcement learning (RL) that dynamically selects a suitable mutation operator via landscape information during the convergence process is proposed in this study, which consists of two phases: offline and online. In the “offline” phase, the proposed algorithm uses an RL-based algorithm to construct a learning model to understand the relationships between landscape characteristics and search operators. Then, in the “online” phase, the learning model constructed from the offline phase and a lightweight fitness landscape analysis (FLA) method are used by the DE to dynamically determine the suitable mutation operator based on the search state encountered by DE during the convergence process, which can reduce the costs for the FLA in every iteration. To understand the performance of the proposed algorithm, the CEC2021 and CEC2022 benchmark functions are used to evaluate its search performance against different DE-based algorithms for solving single-objective optimization problems. Simulation results show that the proposed algorithm outperforms other state-of-the-art DE-based algorithms and other DE algorithms based on FLA and RL in most cases.

References

 
Abualigah, L., Elaziz, M.A., Khasawneh, A.M., Alshinwan, M., Ibrahim, R.A., Al-qaness, M.A.A., Mirjalili, S., Sumari, P., Gandomi, A.H. (2022). Meta-heuristic optimization algorithms for solving real-world mechanical engineering design problems: a comprehensive survey, applications, comparative analysis, and results. Neural Computing and Applications, 34, 4081–4110.
 
Bergstra, J., Bardenet, R., Bengio, Y., Kégl, B. (2011). Algorithms for hyper-parameter optimization. Advances in Neural Information Processing Systems, 24.
 
Blum, C., Roli, A. (2003). Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Computing Surveys, 35(3), 268–308.
 
da Costa Oliveira, A.L., Britto, A., Gusmão, R. (2023). Machine learning enhancing metaheuristics: a systematic review. Soft Computing, 27(21), 15971–15998.
 
Dokeroglu, T., Sevinc, E., Kucukyilmaz, T., Cosar, A. (2019). A survey on new generation metaheuristic algorithms. Computers & Industrial Engineering, 137, 106040.
 
Dorigo, M., Maniezzo, V., Colorni, A. (1991). Ant System: An Autocatalytic Optimizing Process. Technical report, Dipartimento di Elettronica, Politecnico di Milano, Italy. Technical Report 91-016. Available at https://citeseerx.ist.psu.edu/viewdoc/download?rep=rep1&type=pdf&doi=10.1.1.51.4214, Accessed 2022.08.01.
 
Elaziz, M.A., Dahou, A., Abualigah, L., Yu, L., Alshinwan, M., Khasawneh, A.M., Lu, S. (2021). Advanced metaheuristic optimization techniques in applications of deep neural networks: a review. Neural Computing and Applications, 33, 14079–14099.
 
Glover, F. (1989). Tabu search—Part I. ORSA Journal on Computing, 1(3), 190–206.
 
Glover, F., Kochenberger, G.A. (Eds.) (2003). Handbook of Metaheuristics. Kluwer Academic Publishers, Boston, MA.
 
Grefenstette, J.J. (1999). Evolvability in dynamic fitness landscapes: a genetic algorithm approach. In: Proceedings of the Congress on Evolutionary Computation, Vol. 3, pp. 2031–2038.
 
Holland, J.H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI.
 
Jones, T., Forrest, S. (1995). Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings of the International Conference on Genetic Algorithms, pp. 184–192.
 
Kennedy, J., Eberhart, R.C. (1995). Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1948.
 
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P. (1983). Optimization by Simulated Annealing. Science, 220(4598), 671–680.
 
Kumar, A., Price, K.V., Mohamed, A.W., Hadi, A.A., Suganthan, P.N. (2021). Problem definitions and evaluation criteria for the CEC 2022 special session and competition on single objective bound constrained numerical optimization. Technical report, Nanyang Technological University, Singapore. Available at https://github.com/P-N-Suganthan/2022-SO-BO, Accessed 2024.05.01.
 
Liang, J.J., Qu, B., Suganthan, P.N., Hernández-Díaz, A.G. (2013). Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Technical report. Available at https://github.com/P-N-Suganthan/CEC2013, Accessed 2024.05.01.
 
Lin, M., Wang, Z., Zheng, W. (2023). Hybrid particle swarm-differential evolution algorithm and its engineering applications. Soft Computing, 27(22), 16983–17010.
 
Liu, Y., Sun, Y., Xue, B., Zhang, M., Yen, G.G., Tan, K.C. (2023). A survey on evolutionary neural architecture search. IEEE Transactions on Neural Networks and Learning Systems, 34(2), 550–570.
 
Malan, K.M., Engelbrecht, A.P. (2009). Quantifying ruggedness of continuous landscapes using entropy. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1440–1447.
 
Malan, K.M., Engelbrecht, A.P. (2013). A survey of techniques for characterising fitness landscapes and some possible ways forward. Information Sciences, 241, 148–163.
 
Merz, P., Freisleben, B. (1999). Fitness Landscapes and Memetic Algorithm Design. New Ideas in Optimization. McGraw-Hill Ltd., UK, GBR, pp. 245–260.
 
Mnih, V., Kavukcuoglu, K., Silver, D., Rusu, A.A., Veness, J., Bellemare, M.G., Graves, A., Riedmiller, M.A., Fidjeland, A., Ostrovski, G., Petersen, S., Beattie, C., Sadik, A., Antonoglou, I., King, H., Kumaran, D., Wierstra, D., Legg, S., Hassabis, D. (2015). Human-level control through deep reinforcement learning. Nature, 518(7540), 529–533.
 
Mohamed, A.W., Hadi, A.A., Mohamed, A.K., Agrawal, P., Kumar, A., Suganthan, P.N. (2020). Problem definitions and evaluation criteria for the CEC 2021 special session and competition on single objective bound constrained numerical optimization. Technical report, Nanyang Technological University, Singapore. Available at https://github.com/P-N-Suganthan/2021-SO-BCO, Accessed 2024.05.01.
 
Ochoa, G., Malan, K. (2019). Recent advances in fitness landscape analysis. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 1077–1094.
 
Osaba, E., Villar-Rodriguez, E., Del Ser, J., Nebro, A.J., Molina, D., LaTorre, A., Suganthan, P.N., Coello Coello, C.A., Herrera, F. (2021). A tutorial on the design, experimentation and application of metaheuristic algorithms to real-world optimization problems. Swarm and Evolutionary Computation, 64, 100888.
 
Pitzer, E., Affenzeller, M. (2012). A comprehensive survey on fitness landscape analysis. In: Recent Advances in Intelligent Engineering Systems, pp. 161–191.
 
Rani, R., Jain, S., Garg, H. (2024). A review of nature-inspired algorithms on single-objective optimization problems from 2019 to 2023. Artificial Intelligence Review, 57(126), 1–51.
 
Reidys, C.M., Stadler, P.F. (2001). Neutrality in fitness landscapes. Applied Mathematics and Computation, 117(2), 321–350.
 
Richter, H., Engelbrecht, A.P. (Eds.) (2014). Recent Advances in the Theory and Application of Fitness Landscapes. Springer, Berlin, Heidelberg.
 
Seyyedabbasi, A. (2023). A reinforcement learning-based metaheuristic algorithm for solving global optimization problems. Advances in Engineering Software, 178, 103411.
 
Sharma, V., Tripathi, A.K. (2022). A systematic review of meta-heuristic algorithms in IoT based application. Array, 14, 100164.
 
Shen, L., He, J. (2010). A mixed strategy for Evolutionary Programming based on local fitness landscape. In: IEEE Congress on Evolutionary Computation, pp. 1–8.
 
Soler-Dominguez, A., Juan, A.A., Kizys, R. (2017). A survey on financial applications of metaheuristics. ACM Computing Surveys, 50(1), 1–23.
 
Stadler, P.F. (2002). Fitness landscapes. In: Lässig, M., Valleriani, A. (Eds.), Biological Evolution and Statistical Physics. Springer, Berlin, Heidelberg, pp. 183–204.
 
Storn, R., Price, K. (1995). Differential evolution – a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report, International Computer Science Institute (ICSI). Technical Report TR-95-012, Available at https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.67.5398&rep=rep1&type=pdf, Accessed 2024.05.01.
 
Talbi, E.-G. (2021). Machine learning into metaheuristics: a survey and taxonomy. ACM Computing Surveys, 54(6), 1–32.
 
Tan, Z., Li, K. (2021). Differential evolution with mixed mutation strategy based on deep reinforcement learning. Applied Soft Computing, 111, 107678.
 
Tan, Z., Li, K., Wang, Y. (2021). Differential evolution with adaptive mutation strategy based on fitness landscape analysis. Information Sciences, 549, 142–163.
 
Tan, Z., Tang, Y., Li, K., Huang, H., Luo, S. (2022a). Differential evolution with hybrid parameters and mutation strategies based on reinforcement learning. Swarm and Evolutionary Computation, 75, 101194.
 
Tan, Z., Tang, Y., Huang, H., Luo, S. (2022b). Dynamic fitness landscape-based adaptive mutation strategy selection mechanism for differential evolution. Information Sciences, 607, 44–61.
 
Tanabe, R., Fukunaga, A. (2013). Success-history based parameter adaptation for differential evolution. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 71–78.
 
Tanabe, R., Fukunaga, A.S. (2014). Improving the search performance of SHADE using linear population size reduction. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1658–1665.
 
Tessari, M., Iacca, G. (2022). Reinforcement learning based adaptive metaheuristics. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 1854–1861.
 
Tong, H., Huang, C., Minku, L.L., Yao, X. (2021). Surrogate models in evolutionary single-objective optimization: a new taxonomy and experimental study. Information Sciences, 562, 414–437.
 
Tsai, C.W., Chiang, M.C. (2023). Handbook of Metaheuristic Algorithms: From Fundamental Theories to Advanced Applications. Elsevier.
 
Vassilev, V.K., Fogarty, T.C., Miller, J.F. (2000). Information characteristics and the structure of landscapes. Evolutionary Computation, 8(1), 31–60.
 
Velasco, L., Guerrero, H., Hospitaler, A. (2024). A literature review and critical analysis of metaheuristics recently developed. Archives of Computational Methods in Engineering, 31, 125–146.
 
Wang, M., Li, B., Zhang, G., Yao, X. (2018). Population evolvability: dynamic fitness landscape analysis for population-based metaheuristic algorithms. IEEE Transactions on Evolutionary Computation, 22(4), 550–563.
 
Weinberger, E.D. (1990). Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics, 63, 325–336.
 
Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83.
 
Wolpert, D.H., Macready, W.G. (1997). No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1(1), 67–82.
 
Wright, S. (1932). The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: Proceedings of the International Congress of Genetics, Vol. 1, pp. 356–366.
 
Yaqoob, A., Verma, N.K., Aziz, R.M. (2024). Metaheuristic algorithms and their applications in different fields. Metaheuristics for Machine Learning: Algorithms and Applications. John Wiley & Sons, pp. 1–35.
 
Yue, C., Price, K.V., Suganthan, P.N., Liang, J., Ali, M.Z., Qu, B., Awad, N.H., Biswas, P.P. (2019). Problem definitions and evaluation criteria for the CEC 2020 special session and competition on single objective bound constrained numerical optimization. Technical report, Zhengzhou University, China. Available at https://github.com/P-N-Suganthan/2020-Bound-Constrained-Opt-Benchmark, Accessed 2024.05.01.
 
Zhang, J., Sanderson, A.C. (2009). JADE: adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation, 13(5), 945–958.
 
Zhang, L., Lu, G., Yan, X., Xia, P., Chen, Z., Wu, D. (2025). A differential evolution optimized hybrid XGBoost for accurate carbon emission prediction. Environmental Modelling & Software, 193, 106627.
 
Zhang, Z., Wu, Z., Zhang, H., Wang, J. (2023). Meta-learning-based deep reinforcement learning for multiobjective optimization problems. IEEE Transactions on Neural Networks and Learning Systems, 34(10), 7978–7991.
 
Zhou, X., Song, J., Wu, S., Wang, M. (2023). Artificial bee colony algorithm based on online fitness landscape analysis. Information Sciences, 619, 603–629.
 
Zou, F., Chen, D., Liu, H., Cao, S., Ji, X., Zhang, Y. (2022). A survey of fitness landscape analysis for optimization. Neurocomputing, 503, 129–139.

Biographies

Tsai Chun-Wei
cwtsai@mail.cse.nsysu.edu.tw

C.-W. Tsai received his PhD degree in computer science and engineering from National Sun Yat-sen University, Kaohsiung, Taiwan, in 2009. He is currently an associate professor and the associate vice president for Library and Information Services at National Sun Yat-sen University. He has also been a joint-appointment associate professor with the College of Semiconductor and Advanced Technology Research at National Sun Yat-sen University and a global joint-appointment professor at Kyungpook National University, Daegu, Korea, since 2024 and 2026, respectively. His research interests include computational intelligence, cloud computing, and the Internet of Things.

Chen Cheng-Chun

C.-C. Chen received his BS degree in computer science and information engineering from National Chi Nan University, Nantou, Taiwan, in 2022, and his MS degree in Computer Science and Engineering from National Sun Yat-sen University, Kaohsiung, Taiwan, in 2024. His research interests include metaheuristic algorithms, machine learning, and single-objective optimization.

Chen Kuan-Heng

K.-H. Chen received his BS degree in aeronautics and astronautics from National Cheng Kung University, Tainan, Taiwan, in 2024, and his MS degree in computer science and engineering from National Sun Yat-sen University, Kaohsiung, Taiwan, in 2026. His research interests include metaheuristic algorithms, reinforcement learning, fitness landscape analysis, and single-objective optimization.

Gipiškis Rokas

R. Gipiškis received his PhD in computer science from Vilnius University in 2025. He is currently a researcher at the Institute of Data Science and Digital Technologies (Vilnius University) and a research analyst at AI Standards Lab, a non-profit focused on technical AI safety standards. His research interests include model interpretability, evaluation, risk management, and technical AI governance.

Kurasova Olga

O. Kurasova received a PhD degree in computer science from the Institute of Mathematics and Informatics, Vytautas Magnus University (Lithuania), in 2005. She is currently employed as a principal researcher and a professor at the Institute of Data Science and Digital Technologies, Vilnius University (Lithuania). Her research interests include data mining methods, optimization theory and applications, artificial intelligence, neural networks, visualization of multidimensional data, multiple criteria decision support, parallel computing, and image processing. She is the author of more than 100 scientific publications.


Full article Related articles PDF XML
Full article Related articles PDF XML

Copyright
© 2026 Vilnius University
Open access article under the CC BY license.

Keywords
single-objective optimization differential evolution fitness landscape analysis reinforcement learning and metaheuristic algorithm

Funding
National Science and Technology Council of Taiwan, ROC, under Contracts NSTC112-2628-E-110-001-MY3, NSTC114-2634-F-110-001-MBK, NSTC114-2221-E-110-023-MY3, and NSTC115-2221-E-110-039-MY3.

Metrics
since January 2020
102

Article info
views

32

Full article
views

32

PDF
downloads

7

XML
downloads


Share


RSS