The paper presents evolutionary approach, based on genetic algorithm, to solving a variation of the traveling salesman problem in mobile robotics. It is a modified version of time-constrained profit-based traveling salesman problem with additional constraint on the volume capacity of the traveling agent. The research was motivated by the problem of optimal strategy synthesis for autonomous mobile robot for competition in mobile robotics Eurobot 2024. However, the addressed problem is general enough to cover the wide spectrum of applications in different domains, including package collecting/delivery or field sample collecting for laboratory analysis. The addressed problem is global combinatorial optimization problem and due to its NP-hard complexity and multiple imposed constraints, we have solved it using genetic algorithm. We have particularly investigated the process of initial population engineering, i.e. the influence of the amount of hand-coded domain-related knowledge to the convergence of the algorithm.