## 8 Conclusions  
A flat fan spray nozzle serves the purpose of spraying onto a surface or an object moving in a transverse direction with respect to the direction of the jet, a typical example being the nozzles in a car washing tunnel. The reduction of the unevenness of the transverse sprayed liquid dosage is of interest to agricultural and horticultural bodies, to railway maintenance services, in production lines of foamed foam, in the paper, food, or pharmaceutical industries, in the spraying of rubber surfaces and asphalt, in road defrosting, in air humidification, in sprinkling and continuous painting lines, in fire protection systems, in the creation of a uniform flame by jet engines, etc. Moreover, the use of atomised scrubbing liquids to capture particulate matter and/or gaseous pollutants in liquid droplets, e.g., in wet scrubbers [1]. This means that the solution to the problem presented here may be easily adapted to the situation in which nozzles are placed in a configuration different from the one on the spraying beam of a field sprayer. It may apply, for example, to nozzles placed in a circle or inside a workspace, such as in a jet engine or in a device used for producing food or pharmaceuticals, for example, in the process of spray drying or in the processes of agglomeration, coating, or encapsulation [51,52].  
The value of the coefficient of variation for the sprayed liquid falling from the entire boom sprayer does not have to result only from the random sequence of mounting individual nozzles on the boom but may also be the result of planning the sequence of mounting nozzles on the boom.  
The retrofitting of a data collection and processing system with the above-described permutation algorithm in automatic devices for the assessment of the technical condition of agricultural sprayers will allow for modelling the quality of the field boom operation in laboratory conditions. This applies both to the correction of the uniformity parameter in the equipment already operated and the improvement of the coefficient of variation in the newly manufactured equipment, allowing a certain predetermined tolerance for deviations from the standard for each nozzle.  
Further work is required to collect a large database of spray distribution patterns to compare the possible metaheuristic implementations and to select the best parameters for controlling them.  
The comprehensive use of the permutation algorithm may significantly improve the condition of plant protection equipment and, by increasing the uniformity of spraying, reduce the number of preparations used in agricultural treatments.  
The algorithm also allows for selecting out of a given number of \(N\geq 24\) nozzles, even ones with decalibration, \(n\leq N\) nozzles that best meet the standards of coverage uniformity (\(n\leq 24\)). The application of, among others, the above-mentioned permutation algorithm, not only for field sprayers, allows one to select nozzles for replacement and thus reduce the operating costs of sprayers. This means using a relatively cheap automated expert service instead of the costly purchase of a set of new nozzles.  
Conceptualization, J.W.; methodology, J.W. and S.P.; software, J.W.; validation, J.W. and S.P.; formal analysis, J.W. and S.P.; investigation, S.P.; resources, J.W.; data curation, S.P.; writing--original draft preparation, J.W.; writing--review and editing, S.P.; visualization, J.W. and S.P.; supervision, S.P.; project administration, J.W. and S.P.; funding acquisition, J.W. and S.P. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.