## 1 Introduction  
In global optimization problems, the objective function often has a high computational complexity, high dimensionality, and non-trivial landscape. Such tasks are of high practical significance, and a lot of methods have been proposed as a basis to find their solutions. Localization capability with a high probability of sub-optimal (close to optimal) solutions is one of the main advantages of this class of algorithms, in addition to their versatility and simplicity of implementation. In practically important optimization problems, it is often sufficient to make such decisions. Some methods are specially developed or are best suited for solving optimal problems with mathematical models of a certain type. Thus, the mathematical apparatus of linear programming is specially designed to solve problems with linear optimality criteria and linear constraints on variables and leads to the solution of most of the problems formulated in this formulation. Dynamic programming is well suited for solving optimization problems of multi-stage processes, especially those in which the state of each stage is defined by a relatively small number of state variables. However, in the presence of a significant number of these variables, that is, with a high dimension in each stage, the use of the dynamic programming method is difficult due to the limited speed and memory capacity of computers. Perhaps the best way to choose the optimization method that is most suitable for solving the corresponding problem is to study the possibilities and experiences of using various optimization methods. Bio-inspired algorithms are an actively developing area of heuristic optimization and decision-making methods [1]. Meta-heuristic optimization methods motivated by examples in nature are becoming more common in real-life applications. At the moment, the most promising direction can be considered the creation of new versions of bio-inspired algorithms, which take into account problem-oriented information about the search area for optimal solutions, as well as the history of the search. Bio-inspired algorithms exploit the principles of the collective behavior of living organisms, such as insect swarms or bird flocks. Bio-inspired algorithms, in a broader sense, define the behavior of communicative agents in a multi-agent system. Whereas every agent has a limited processing capability, the system of agents (such as a swarm) as a whole can accomplish complicated tasks, such as searching for resources. Many current meta-heuristic algorithms have been presented that are influenced by natural or social events, such as grey wolf optimizer (GWO) [2], artificial bee colony (ABC) [3], particle swarm optimization (PSO) [4], firefly algorithm (FA) [5], krill herd (KH) [6], polar bear optimization [7], and red fox optimization [8]. Such algorithms are commonly used in various domains, including scientific computing [9], image recognition [10], software bug detection [11], industrial production optimization [12], and disease recognition from biomedical images [13; 14]. The No Free Lunch theorem [15], which proved that, for an optimization algorithm, any improvement in performance for a single category of problems leads to a decrease in performance for another category, has motivated the comparison of bio-inspired algorithms for solving various optimization problems. As a rule, it is impossible to recommend the adoption of any one method without exception to solve all problems that arise in practice. To create new, highly efficient bio-inspired algorithms, a method such as hybridization is used. Hybridization is an evolutionary meta-heuristic approach [16]. Meta-heuristics are flexible and easy to use since they replicate physical or biological events and only address inputs and outcomes. Meta-heuristics are also a type of probabilistic optimization approach. This trait enables them to efficiently avoid local optima, which are common in real-world issues.