Penetration is one of the most vital parameters because of its influences on weld strength and weld quality. Choosing the input parameters in submerged arc welding (SAW) has significant effects on input heat into the weld pool, which affects the quality of weldment. The amazing advancement of nanotechnology in various industrial areas persuaded researchers to use nanoparticles in new research. Zirconium dioxide (ZrO2) nanoparticles were selected in order to identify their effects in the weld pool in combination with other welding input parameters. The five-level, five-parameter central composite rotatable design, response surface methodology, the slime mold algorithm, and Harris hawks optimization were utilized to design and develop the research and finally to predict and optimize the weld penetration affected by the arc voltage, welding current, nozzle-to-plate distance, welding speed, and the thickness of ZrO2 nanoparticles coated on ST-37 steel. The main and interaction effects of input parameters on weld penetration were drawn. The results demonstrated that weld penetration decreased initially by increasing the thickness of ZrO2 nanoparticles up to 0.25 mm, which was due to reversing Marangoni convection mode. Furthermore, weld penetration increased with increase in ZrO2 nanoparticles above thicknesses of 0.75 mm. The reason for increase in weld penetration was because of the fact the ZrO2 nanoparticles have low thermal conductivity, which leads to less heat transfer. The results confirmed that the accuracy of model obtained by slime mold algorithm was 5.2 % more than response surface methodology.