The Use of the Permutation Algorithm for Suboptimising the Position of Used Nozzles on the Field Sprayer Boom

Abstract

The worn-out nozzles of field sprayers cause agricultural treatment to be uneven and therefore ineffective. Spray nozzles are consumable elements of the field sprayer that are subject to inspection and in the event of their excessive wear should be replaced with new ones to ensure the proper execution of agricultural treatment. The aim of the study is to propose, using operational research methods, an expert methodology allowing further operation of worn-out and often expensive sprayer nozzles, including standard, universal, anti-drift, or ejector nozzles. The previous attempts, performed with the use of the random computer optimisation method, did not guarantee a global solution in the entire population of all possible permutations without repetitions of 24 worn-out nozzles (for a field boom with a width of 12 m) or even estimating approximation to this solution. The process of measuring the wear of nozzles, the simulation of the entire virtual field boom, and the permutation algorithm proposed here allow you to specify a suboptimal solution of an NP-hard problem separately for each sprayer, i.e., to indicate in a very short time such a permutation out of 24! ≈ 6.20448 × 10+23 permutations of nozzles with variable degrees of wear, which is close to the optimal permutation of used nozzles on the field sprayer boom, in terms of the coefficient of variation. The use of expert methodology allows for reducing the operating costs of sprayers by using a relatively cheap automated expert service instead of the costly purchase of a set of new nozzles for field sprayers. Many areas of application of this methodology have been indicated.