Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm

• Published in: Algorithms Vol. 15; no. 5; p. 157
• Main Authors: Panteleev, Andrei V., Kolessa, Anna A.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.05.2022
• Subjects: Algorithms; bio-inspired algorithms; Control systems; Control theory; discrete dynamical system; Dynamical systems; Exact solutions; Food; Heuristic methods; Hunting; Intelligence; Linear systems; Mathematical programming; Mathematicians; Maximum principle; metaheuristic; Methods; migration algorithm; Optimal control; Optimization; Optimization algorithms; Parallelepipeds; perch; Population; Schools; Swarm intelligence; Trajectory control
• ISSN: 1999-4893; 1999-4893
• DOI: 10.3390/a15050157

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.