In this research work, the problem of task allocation in a multi-agent system is considered, where each agent is a robot, and each task is represented by a position, which should be visited by one agent. This problem is very similar to the multi-agent traveling salesman problem (mTSP), which, unlike the famous traveling salesman problem, involves several traveling salesmen who visit a given number of cities exactly once and return to the starting position with minimal travel costs. Therefore, the multi-agent traveling salesman problem is analyzed as a representative of the task allocation problem. The mTSP is important for the field of route optimization and task allocation between several agents. It includes two different, but interrelated subproblems: distribute cities among agents and determine the order in which each agent visits cities. In the literature, there are 3 concepts for solving mTSP with respect to solving its two constituent subproblems: the optimization concept, where both subproblems are solved simultaneously. The Cluster-First, Route-Second concept, where the question of which tasks to assign to which salesman is first decided, and then the question of the order in which each salesman solves his tasks is decided. The Route-First, Cluster-Second concept, where the question of the order in which tasks should be visited is first decided, and then this cycle is divided between agents without changing the order of visits. This paper proposes a hybrid approach to solving the mTSP, which combines the ideas of two well-known concepts: "Cluster-First, Route-Second" and "Route-First, Cluster-Second" in order to obtain their positive aspects and get rid of their weaknesses. To evaluate the effectiveness of the developed method, a comparative study was conducted. The results were evaluated based on three key criteria: the computational time, the total length of the routes travelled by the salesmen and the maximum route length among them. The analysis of the experimental data showed that when using the proposed method, the maximum path length among the routes travelled by the agents (load imbalance) is reduced by an average of 26%.

This work solves the multi-traveling salesman problem, where predefined tasks will be distributed among several traveling salesmen. A new method for solving this problem has been developed based on reducing the size of the solution space. The developed method was tested in several scenarios, including different numbers of tasks and traveling salesmen. A comparative study of the developed method with a classical method of solving this problem was carried out. The results were evaluated in terms of the calculation time; the sum of the paths’ lengths traveled by salesmen and the maximum travel distance among salesmen. As a result, the developed method was superior to the classical one in terms of calculation time in all experiments and in terms of the sum of the lengths of the paths traveled by traveling salesmen, maximum travel distance among traveling salesmen in most experiments.

A modification on the search strategy of the bee algorithm that improves its overall performance is presented in this work. We propose efficiency-based recruitment process of the bees that perform the local search. Both the original and the modified algorithms were tested on a benchmark optimization problems and an additional statistical analysis was performed. Although the advantage varies between different comparison modules, the modified algorithm always provides an advantage in terms of the calculation time. Further, both the original and the modified algorithms were implemented to solve the problem of optimal control of an unmanned aerial vehicle; the algorithms were used for synthesizing a linear-quadratic regulator LQR. The obtained simulation results showed that the proposed modification improved the overall performance of the bee algorithm and made it more time-efficient.