Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm
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,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/15/5/157 |
| _version_ | 1797502217450684416 |
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| author | Andrei V. Panteleev Anna A. Kolessa |
| author_facet | Andrei V. Panteleev Anna A. Kolessa |
| author_sort | Andrei V. Panteleev |
| collection | DOAJ |
| description | 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–Tassone and LiHaimes) and five classic linear systems control problems with known exact solutions. |
| first_indexed | 2024-03-10T03:29:48Z |
| format | Article |
| id | doaj.art-ed6f34f3aa8b4d5d8521ae0e287983ab |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T03:29:48Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-ed6f34f3aa8b4d5d8521ae0e287983ab2023-11-23T09:45:28ZengMDPI AGAlgorithms1999-48932022-05-0115515710.3390/a15050157Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization AlgorithmAndrei V. Panteleev0Anna A. Kolessa1Department of Mathematics and Cybernetics, Moscow Aviation Institute (National Research University), 4, Volokolamskoe Shosse, 125993 Moscow, RussiaDepartment of Mathematics and Cybernetics, Moscow Aviation Institute (National Research University), 4, Volokolamskoe Shosse, 125993 Moscow, RussiaA 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–Tassone and LiHaimes) and five classic linear systems control problems with known exact solutions.https://www.mdpi.com/1999-4893/15/5/157bio-inspired algorithmsmetaheuristicoptimal controldiscrete dynamical systemmigration algorithmperch |
| spellingShingle | Andrei V. Panteleev Anna A. Kolessa Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm Algorithms bio-inspired algorithms metaheuristic optimal control discrete dynamical system migration algorithm perch |
| title | Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm |
| title_full | Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm |
| title_fullStr | Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm |
| title_full_unstemmed | Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm |
| title_short | Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm |
| title_sort | optimal open loop control of discrete deterministic systems by application of the perch school metaheuristic optimization algorithm |
| topic | bio-inspired algorithms metaheuristic optimal control discrete dynamical system migration algorithm perch |
| url | https://www.mdpi.com/1999-4893/15/5/157 |
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