Optimizing a Bi-Objective Mathematical Model for Minimizing Spraying Time and Drift Proportion

Abstract

The global agriculture sector faces many challenges in its mission to meet the increasing demand for food and fiber. Climate change, increasing population growth, emergence of crop diseases, damage to crops from rodents and critters, and shrinking farming land in some regions are among these challenges. Application of agrochemicals has proven to be an efficient answer to some of these challenges. However, the impacts of these products on human health and the environment combined with the increased requirement for sustainable farming requires the development of optimal spraying practices that would balance out all interests and concerns. In this paper, a mathematical model is developed to jointly minimize spraying time and drift losses. The obtained bi-objective mixed integer nonlinear programming model is solved for a case study example published in the crop protection literature. Optimal solutions are obtained using the weighted sum method and the epsilon-constraint approach. The results showed that valid and reasonable solutions can be obtained by selecting the appropriate combination of boom height, nozzle spacing, nozzle type, and tractor travel speed. Useful insights are obtained through various computational experiments.

The effects of Surfactin on sprayed droplets in flat fan, full cone, and low energy precision application bubbler nozzles: droplet formation and spray breakup

“…The droplet size in the fan and cone nozzles decreased as the operating pressure of the nozzle increased (Supplementary Table S4 and Figure 7), consistent with the literature (Solomon et al, 1985;Butler Ellis and Tuck, 1999;Negeed et al, 2011;Davanlou et al, 2015;Broniarz-Press et al, 2016;Kooij et al, 2018;Nadeem et al, 2019;Li et al, 2021;Makhnenko et al, 2021;Chen et al, 2022). The addition of Surfactin to the distilled water decreased the volumetric median droplet diameter (D V50 ) of each fan nozzle by 4%-33% (Supplementary Table S4 and Figure 7).…”

“…The full cone nozzle had more droplets forming than the fan nozzle due to the more 3-D cone shape compared to the flat fan, thereby allowing more droplet interactions and coalescence, and droplet interactions with the spray sheet creating breakup in areas not observed (Saha et al, 2012;Davanlou et al, 2015). The decrease in droplet size is expected with an increase in breakup length; as the spray sheet moves from the nozzle it becomes thinner, thereby decreasing the size of the droplets (Dombrowski and Johns, 1963;Qin et al, 2010;Kooij et al, 2018;Nadeem et al, 2019;Asgarian et al, 2020;Agbaglah, 2021;Li et al, 2021;Makhnenko et al, 2021;Sijs et al, 2021).…”

“…The droplet size is impacted by spray dynamics and is related to the breakup length. For example, increasing the operating pressure (Solomon et al, 1985;Butler Ellis and Tuck, 1999;Negeed et al, 2011;Davanlou et al, 2015;Broniarz-Press et al, 2016;Kooij et al, 2018;Nadeem et al, 2019;Li et al, 2021;Makhnenko et al, 2021;Chen et al, 2022) or increasing the breakup length (Qin et al, 2010;Kooij et al, 2018;Nadeem et al, 2019;Asgarian et al, 2020;Sijs et al, 2021) will decrease the droplet size. The droplet size also decreases in pure liquids with a decreased surface tension (Butler Ellis and Tuck, 1999;Butler Ellis et al, 2001;Dexter, 2001;Davanlou et al, 2015;Sijs and Bonn, 2020;Makhnenko et al, 2021).…”

Optimisation of the Spraying Process of Strawberries under Varying Operational Conditions

“…The optimisation process was then carried out to maximise the percentage area coverage [25]. Nadeem et al [26] proposed the bi-objective mathematical model of the spraying process to optimise spraying time and drift proportion. The authors presented the optimal values of boom height, speed, nozzle spacing, and operating pressure for a specific nozzle type.…”