## 1 Introduction
In turn, among bio-inspired methods, bird-inspired algorithms that imitate the characteristic features of the behavior of flocks of various birds during foraging, migration, and hunting are widely used: Bird Mating Optimizer (BMO), Chicken Swarm Optimization (CSO), Crow Search Algorithm (CSA), Cuckoo Search (CS), Cuckoo Optimization Algorithm (COA), Emperor Penguin Optimizer (EPO), Emperor Penguins Colony (EPC), Harris Hawks Optimization (HHO), Migrating Bird Optimization (MBO), Owl Search Algorithm (OSA), Pigeon Inspired Optimization (PIO), Raven Roosting Optimization (RRO), Satin Bowerbird Optimizer (SBO), Seagull Optimization Algorithm (SOA), and the Sooty Tern Optimization Algorithm (STOA) [15; 24; 25; 26]. One of the applications of bio-inspired optimization algorithms is the problem of finding control laws for discrete dynamical systems [1; 10]. As a rule, to solve this class of optimal control problems, the necessary optimality conditions are applied, which are reduced to solve a boundary value problem for a system of difference equations. For systems with convex varying, the discrete maximum principle is applied. An alternative way is to apply sufficient optimality conditions in the form of the Bellman's equation. In this case, the optimal control found in the form of feedback depends on the state vector of the system, which is more preferable. However, it is well known that with an increase in the state vector dimension, the computational costs of using the dynamic programming procedure increase significantly. Special problems are caused by the solution of nonseparable problems, as well as problems in which the vector variation is not convex and, therefore, the discrete maximum principle is not valid. Since the problem of optimal control of discrete systems is finite dimensional, the use of efficient bio-inspired optimization methods for its resolution is natural. The article is devoted to the development of the swarm intelligence and bird-inspired groups of methods based on observing the process of searching for food by a flock of tomtits, organizing their sequential movement under the influence of the leader of the flock. To simulate the trajectories of movement of each tomtit, the solution of a stochastic differential equation with jumps is used. The parameters of the random process--the drift vector and the diffusion matrix--depend on the position of all members of the flock and their individual achievements. The method is hybrid because it also uses the ideas of particle swarm optimization methods [15; 16; 17], methods that imitate the behavior of cuckoos with Levy flights [29], and the Luus-Jaakola method with successive reduction and further incomplete restoration of the search area [1]. Based on the assertion of the Free Lunch Theorem [30], it can be argued that the problem of developing new efficient global optimization algorithms used to solve complex optimal control problems remains relevant. In particular, the method should allow us to solve both separable and nonclassical nonseparable optimization problems for discrete deterministic dynamical control systems [1,10]. As a benchmark of problems for assessing the accuracy of the method and computational costs, a set of nonlinear nonseparable and classical linear separable problems with known best or exact solutions was used. The paper is organized as follows. Section 2.1 contains the statement of the discrete deterministic open-loop control problem. Section 2.2 provides a description of the solution search strategy and a step-by-step novel bio-inspired metaheuristic optimization method. In Section 3, the application of the new optimization method described in Section 2.2 for the representative set of optimal control problems described in Section 2.1 is given. Recommendations on the choice of method hyperparameters are given, time costs are estimated to obtain numerical results of acceptable quality, and comparison with the results obtained by other known metaheuristic algorithms is presented.