{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T02:34:40Z","timestamp":1762050880981,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,7]],"date-time":"2022-05-07T00:00:00Z","timestamp":1651881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A new hybrid metaheuristic method for optimizing the objective function on a parallelepiped set of admissible solutions is proposed. It mimics the behavior of a school of river perch when looking for food. The algorithm uses the ideas of several methods: a frog-leaping method, migration algorithms, a cuckoo algorithm and a path-relinking procedure. As an application, a wide class of problems of finding the optimal control of deterministic discrete dynamical systems with a nonseparable performance criterion is chosen. For this class of optimization problems, it is difficult to apply the discrete maximum principle and its generalizations as a necessary optimality condition and the Bellman equation as a sufficient optimality condition. The desire to extend the class of problems to be solved to control problems of trajectory bundles and stochastic problems leads to the need to use not only classical adaptive random search procedures, but also new approaches combining the ideas of migration algorithms and swarm intelligence methods. The efficiency of this method is demonstrated and an analysis is performed by solving several optimal deterministic discrete control problems: two nonseparable problems (Luus\u2013Tassone and LiHaimes) and five classic linear systems control problems with known exact solutions.<\/jats:p>","DOI":"10.3390\/a15050157","type":"journal-article","created":{"date-parts":[[2022,5,8]],"date-time":"2022-05-08T08:04:21Z","timestamp":1651997061000},"page":"157","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm"],"prefix":"10.3390","volume":"15","author":[{"given":"Andrei V.","family":"Panteleev","sequence":"first","affiliation":[{"name":"Department of Mathematics and Cybernetics, Moscow Aviation Institute (National Research University), 4, Volokolamskoe Shosse, 125993 Moscow, Russia"}]},{"given":"Anna A.","family":"Kolessa","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Cybernetics, Moscow Aviation Institute (National Research University), 4, Volokolamskoe Shosse, 125993 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,7]]},"reference":[{"unstructured":"Luus, R. (2000). Iterative Dynamic Programming, Chapman & Hall\/CRC. [1st ed.].","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Yang, X.S., Chien, S.F., and Ting, T.O. (2015). Bio-Inspired Computation and Optimization, Morgan Kaufmann. [1st ed.].","key":"ref_2","DOI":"10.1016\/B978-0-12-801538-4.00001-X"},{"unstructured":"Goldberg, D. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company. [1st ed.].","key":"ref_3"},{"doi-asserted-by":"crossref","unstructured":"Michalewicz, Z., and Fogel, D. (2004). How to Solve It: Modern Heuristics, Springer. [2nd ed.].","key":"ref_4","DOI":"10.1007\/978-3-662-07807-5"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1134\/S1064230719030079","article-title":"Method of Parametric Optimization of Nonlinear Continuous Systems of Joint Estimation and Control","volume":"58","author":"Davtyan","year":"2019","journal-title":"J. Comput. Syst. Sci. Int."},{"doi-asserted-by":"crossref","unstructured":"Panteleev, A.V., and Lobanov, A.V. (2021). Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector. Algorithms, 14.","key":"ref_6","DOI":"10.3390\/a14110332"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1134\/S1064230718010082","article-title":"Application of a Memetic Algorithm for the Optimal Control of Bunches of Trajectories of Nonlinear Deterministic Systems with Incomplete Feedback","volume":"57","author":"Panteleev","year":"2018","journal-title":"J. Comput. Syst. Sci. Int."},{"key":"ref_8","first-page":"1","article-title":"A review of population-based meta-heuristic algorithms","volume":"5","author":"Beheshti","year":"2013","journal-title":"Int. J. Adv. Soft Comput. Appl."},{"unstructured":"Brownlee, J. (2011). Clever Algorithms: Nature-Inspired Programming Recipes, LuLu.com. [1st ed.].","key":"ref_9"},{"doi-asserted-by":"crossref","unstructured":"Chambers, D.L. (2001). Practical Handbook of Genetic Algorithms, Applications, Chapman & Hall\/CRC. [2nd ed.].","key":"ref_10","DOI":"10.1201\/9781420035568"},{"doi-asserted-by":"crossref","unstructured":"Floudas, C., and Pardalos, P. (2009). Encyclopedia of Optimization, Springer. [2nd ed.].","key":"ref_11","DOI":"10.1007\/978-0-387-74759-0"},{"doi-asserted-by":"crossref","unstructured":"Floudas, C.A., Pardalos, P.M., Adjiman, C.S., Esposito, W.R., G\u00fcm\u00fc\u015f, Z.H., Harding, S.T., Klepeis, J.L., Meyer, C.A., and Schweiger, C.A. (1999). Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers. [1st ed.].","key":"ref_12","DOI":"10.1007\/978-1-4757-3040-1"},{"doi-asserted-by":"crossref","unstructured":"Gendreau, M. (2010). Handbook of Metaheuristics, Springer. [2nd ed.].","key":"ref_13","DOI":"10.1007\/978-1-4419-1665-5"},{"doi-asserted-by":"crossref","unstructured":"Glover, F.W., and Kochenberger, G.A. (2003). Handbook of Metaheuristics, Kluwer Academic Publishers.","key":"ref_14","DOI":"10.1007\/b101874"},{"doi-asserted-by":"crossref","unstructured":"Neri, F., Cotta, C., and Moscato, P. (2012). Handbook of Memetic Algorithms, Springer. [1st ed.].","key":"ref_15","DOI":"10.1007\/978-3-642-23247-3"},{"unstructured":"Yang, X.S. (2010). Nature-Inspired Metaheuristic Algorithms, Luniver Press. [2nd ed.].","key":"ref_16"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1038\/s41598-017-18940-4","article-title":"On the efficiency of nature-inspired metaheuristics in expensive global optimization with limited budget","volume":"8","author":"Sergeyev","year":"2018","journal-title":"Sci. Rep."},{"doi-asserted-by":"crossref","unstructured":"Sergeyev, Y.D., and Kvasov, D.E. (2017). Deterministic Global Optimization: An Introduction to the Diagonal Approach, Springer. [1st ed.].","key":"ref_18","DOI":"10.1007\/978-1-4939-7199-2"},{"unstructured":"Pinter, J.D. (1996). Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications), Kluwer Academic Publishers. [1st ed.].","key":"ref_19"},{"doi-asserted-by":"crossref","unstructured":"Dragoi, E.N., and Dafinescu, V. (2021). Review of Metaheuristics Inspired from the Animal Kingdom. Mathematics, 9.","key":"ref_20","DOI":"10.3390\/math9182335"},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1007\/s00170-021-07682-3","article-title":"Review on model predictive control: An engineering perspective","volume":"117","author":"Schwenzer","year":"2021","journal-title":"Int. J. Adv. Manuf. Technol."},{"doi-asserted-by":"crossref","unstructured":"Davendra, D., and Zelinka, I. (2016). Self-Organizing Migrating Algorithm. Methodology and Implementation. Studies in Computational Intelligence, Springer. [1st ed.].","key":"ref_23","DOI":"10.1007\/978-3-319-28161-2"},{"doi-asserted-by":"crossref","unstructured":"Yang, X.S., and Deb, S. (2009, January 9\u201311). Cuckoo search via Levy flights. Proceedings of the World Congress on Nature and Biologically Inspired Computing, Coimbatore, India.","key":"ref_24","DOI":"10.1109\/NABIC.2009.5393690"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1061\/(ASCE)0733-9496(2003)129:3(210)","article-title":"Optimization of water distribution network design using the shuffled frog leaping algorithm","volume":"129","author":"Eusuff","year":"2003","journal-title":"J. Water Resour. Plan. Manag."},{"key":"ref_26","first-page":"653","article-title":"Fundamentals of scatter search and path relinking","volume":"39","author":"Glover","year":"2000","journal-title":"Control. Cybern."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1007\/978-981-16-8759-4_62","article-title":"Application of the Sparrow Colony Optimization Method in the Optimal Open Loop Control Problems for Discrete Deterministic Dynamical Systems","volume":"Volume 272","author":"Solovev","year":"2022","journal-title":"SMART Automatics and Energy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1080\/03052150500384759","article-title":"Shuffled frog-leaping optimization algorithm: Memetic meta-heuristic for discrete optimization","volume":"38","author":"Eusuff","year":"2007","journal-title":"Eng. Optimiz."},{"key":"ref_29","first-page":"330","article-title":"Engineering optimization by cuckoo search","volume":"1","author":"Yang","year":"2010","journal-title":"Int. J. Math. Model. Numer. Optim."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/5\/157\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:07:34Z","timestamp":1760137654000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/5\/157"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,7]]},"references-count":29,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["a15050157"],"URL":"https:\/\/doi.org\/10.3390\/a15050157","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,5,7]]}}}