{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T13:06:45Z","timestamp":1775912805308,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T00:00:00Z","timestamp":1763683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Graduate Program in Operational Applications, Aeronautics Institute of Technology (ITA), Brazil"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Hyperparameters allow metaheuristics to be tuned to a wide range of problems. However, even though formalized tuning of metaheuristic parameters can affect the quality of the solution, it is rarely performed. The empirical selection method and the trial-and-error method are the primary conventional parameter selection techniques for optimization heuristics. Both require a priori knowledge of the problem and involve multiple experiments requiring significant time and effort, yet neither guarantees the attainment of optimum parameter values. Of the studies that perform formal parameter tuning, experimental design is the most commonly used method. Although experimental design is feasible for systematic experimentation, it is also time-consuming and requires extensive effort for large optimization problems. The computational effort in this study refers to the number of experimental runs required for hyperparameter tuning, not the computational time for each run. This study proposes a simpler, faster method based on an optimized Latin hypercube sampling (OLHS) technique augmented with response surface methodology for estimating the best hyperparameter settings for a hybrid simulated annealing algorithm. The method is applied to solve the aircraft landing problem with time windows (ALPTW), a combinatorial optimization problem that seeks to determine the optimal landing sequence within a predetermined time window while maintaining minimum separation criteria. The results showed that the proposed method improves sampling efficiency, providing better coverage and higher accuracy with 70% fewer sample points and only 30% of the total runs compared to full factorial design.<\/jats:p>","DOI":"10.3390\/a18120732","type":"journal-article","created":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T12:41:58Z","timestamp":1763728918000},"page":"732","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Metaheuristic Hyperparameter Optimization Using Optimal Latin Hypercube Sampling and Response Surface Methodology"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2800-7074","authenticated-orcid":false,"given":"Daniel A.","family":"Pamplona","sequence":"first","affiliation":[{"name":"Graduate Program in Operational Applications, Aeronautical Institute of Technology, S\u00e3o Jos\u00e9 dos Campos 12228-612, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5701-0558","authenticated-orcid":false,"given":"Mateus","family":"Habermann","sequence":"additional","affiliation":[{"name":"Graduate Program in Operational Applications, Aeronautical Institute of Technology, S\u00e3o Jos\u00e9 dos Campos 12228-612, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6876-9284","authenticated-orcid":false,"given":"Sergio","family":"Rebou\u00e7as","sequence":"additional","affiliation":[{"name":"Graduate Program in Operational Applications, Aeronautical Institute of Technology, S\u00e3o Jos\u00e9 dos Campos 12228-612, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3451-6702","authenticated-orcid":false,"given":"Claudio Jorge P.","family":"Alves","sequence":"additional","affiliation":[{"name":"Department of Air Transportation, Aeronautical Institute of Technology, S\u00e3o Jos\u00e9 dos Campos 12228-612, SP, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sipper, M., Fu, W., Ahuja, K., and Moore, J.H. (2018). Investigating the parameter space of evolutionary algorithms. BioData Min, 11.","DOI":"10.1186\/s13040-018-0164-x"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1287\/opre.1050.0243","article-title":"Fine-Tuning of Algorithms Using Fractional Experimental Designs and Local Search","volume":"54","author":"Laguna","year":"2006","journal-title":"Oper. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_4","first-page":"8042436","article-title":"Improving the Fine-Tuning of Metaheuristics: An Approach Combining Design of Experiments and Racing Algorithms","volume":"2017","author":"Barbosa","year":"2017","journal-title":"J. Optim."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.asoc.2014.01.032","article-title":"Automatic parameter tuning for Evolutionary Algorithms using a Bayesian Case-Based Reasoning system","volume":"18","author":"Yeguas","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_6","first-page":"233","article-title":"Fine-tuning a Tabu Search Algorithm with Statistical Tests","volume":"5","author":"Xu","year":"1998","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1007\/s11590-020-01545-8","article-title":"Solving a home energy management problem by Simulated Annealing","volume":"15","author":"Bastianetto","year":"2021","journal-title":"Optim. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s00158-019-02223-9","article-title":"A simulated annealing approach for optimizing composite structures blended with multiple stacking sequence tables","volume":"60","author":"Zeng","year":"2019","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Xu, L., Yu, J., Zhu, Z., Man, J., Yu, P., Li, C., Wang, X., and Zhao, Y. (2023). Research and Application for Corrosion Rate Prediction of Natural Gas Pipelines Based on a Novel Hybrid Machine Learning Approach. Coatings, 13.","DOI":"10.3390\/coatings13050856"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"304","DOI":"10.5004\/dwt.2023.30032","article-title":"Application of simulated annealing algorithm in multi-objective allocation optimization of urban water resources","volume":"314","author":"Wang","year":"2023","journal-title":"Desalination Water Treat."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9625","DOI":"10.1016\/j.eswa.2008.09.063","article-title":"An improved simulated annealing for hybrid flowshops with sequence-dependent setup and transportation times to minimize total completion time and total tardiness","volume":"36","author":"Naderi","year":"2009","journal-title":"Expert. Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.jspi.2004.02.014","article-title":"An efficient algorithm for constructing optimal design of computer experiments","volume":"134","author":"Jin","year":"2005","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.cor.2015.07.002","article-title":"Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem","volume":"65","author":"Bellio","year":"2016","journal-title":"Comput. Oper. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5895","DOI":"10.1016\/j.eswa.2010.11.034","article-title":"A hybridization of simulated annealing and electromagnetism-like mechanism for a periodic job shop scheduling problem","volume":"38","author":"Jamili","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s00170-010-2932-8","article-title":"A hybrid algorithm based on particle swarm optimization and simulated annealing for a periodic job shop scheduling problem","volume":"54","author":"Jamili","year":"2011","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Yoshitake, H., Okuyama, T., Kamada, Y., Ueta, T., and Fujita, J. (2023, January 3\u20136). Multistep Hyperparameter Tuning via Reinforcement Learning for Simulated Annealing. Proceedings of the 9th International Conference on Control, Decision and Information Technologies (CoDIT), Rome, Italy.","DOI":"10.1109\/CoDIT58514.2023.10284154"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Huri, D., and Mankovits, T. (2022). Surrogate Model-Based Parameter Tuning of Simulated Annealing Algorithm for the Shape Optimization of Automotive Rubber Bumpers. Appl. Sci., 12.","DOI":"10.3390\/app12115451"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1109\/OJSP.2023.3329756","article-title":"Local Energy Distribution Based Hyperparameter Determination for Stochastic Simulated Annealing","volume":"4","author":"Onizawa","year":"2023","journal-title":"IEEE Open J. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Neum\u00fcller, C., Wagner, S., Kronberger, G., and Affenzeller, M. (2011). Parameter Meta-Optimization of Metaheuristic Optimization Algorithms. International Conference on Computer Aided Systems Theory, Springer.","DOI":"10.1007\/978-3-642-27549-4_47"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.1057\/jors.2012.114","article-title":"A hybrid simulated annealing and column generation approach for capacitated multicommodity network design","volume":"64","author":"Yaghini","year":"2013","journal-title":"J. Oper. Res. Soc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.cie.2019.04.032","article-title":"Network configuration multi-factory scheduling with batch delivery: A learning-oriented simulated annealing approach","volume":"132","author":"Marandi","year":"2019","journal-title":"Comput. Ind. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.2000.10485979","article-title":"A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code","volume":"42","author":"Mckay","year":"2000","journal-title":"Technometrics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1109\/43.75636","article-title":"Combinatorial optimization by stochastic evolution","volume":"10","author":"Saab","year":"2002","journal-title":"IEEE Trans. Comput. Des. Integr. Circuits Syst."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Giunta, A., Wojtkiewicz, S., and Eldred, M. (2003, January 6\u20139). Overview of Modern Design of Experiments Methods for Computational Simulations (Invited). Proceedings of the 41st Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.2003-649"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Miyazaki, T., Sato, I., and Shimizu, N. (2018). Bayesian Optimization of Hpc Systems for Energy Efficiency. International Conference on High Performance Computing, Springer.","DOI":"10.1007\/978-3-319-92040-5_3"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3231","DOI":"10.1016\/j.jspi.2005.01.007","article-title":"A study on algorithms for optimization of Latin hypercubes","volume":"136","author":"Liefvendahl","year":"2006","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1016\/j.ress.2007.04.005","article-title":"Extension of Latin hypercube samples with correlated variables","volume":"93","author":"Sallaberry","year":"2008","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Fang, K.-T., Li, R., and Sudjianto, A. (2005). Design and Modeling for Computer Experiments, CRC Press.","DOI":"10.1201\/9781420034899"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1080\/02664768700000020","article-title":"Maximum entropy sampling","volume":"14","author":"Shewry","year":"1987","journal-title":"J. Appl. Stat."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1430","DOI":"10.1080\/01621459.1998.10473803","article-title":"Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments","volume":"93","author":"Ye","year":"1998","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_31","first-page":"409","article-title":"Design and Analysis of Computer Experiments","volume":"4","author":"Sacks","year":"1989","journal-title":"Stat. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0378-3758(90)90122-B","article-title":"Minimax and maximin distance designs","volume":"26","author":"Johnson","year":"1990","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3782","DOI":"10.1080\/03610926.2014.966843","article-title":"Measures of uniformity in experimental designs: A selective overview","volume":"45","author":"Androulakis","year":"2016","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Hickernell, F.J. (1998). Lattice rules: How well do they measure up?. Random and Quasi-Random Point Sets, Springer.","DOI":"10.1007\/978-1-4612-1702-2_3"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Kleijnen, J.P. (2015). Design and Analysis of Simulation Experiments, Springer.","DOI":"10.1007\/978-3-319-18087-8"},{"key":"ref_36","first-page":"328","article-title":"Process and product optimization using designed experiments","volume":"2","author":"Myers","year":"2002","journal-title":"Response Surf. Methodol."},{"key":"ref_37","unstructured":"Montgomery, D.C., Peck, E.A., and Vining, G.G. (2021). Introduction to Linear Regression Analysis, John Wiley & Sons."},{"key":"ref_38","unstructured":"Belsley, D.A., Kuh, E., and Welsch, R.E. (2005). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, John Wiley & Sons."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1023\/A:1026569813391","article-title":"Using Experimental Design to Find Effective Parameter Settings for Heuristics","volume":"7","author":"Coy","year":"2001","journal-title":"J. Heuristics"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/12\/732\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T12:45:30Z","timestamp":1763729130000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/12\/732"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,21]]},"references-count":39,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["a18120732"],"URL":"https:\/\/doi.org\/10.3390\/a18120732","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,21]]}}}